Methods and Applications of Signal Processing in Seismic Network Operations

Lecture Notes in Earth Sciences Editors: S. Bhattacharji, Brooklyn G. M. Friedman, Brooklyn and Troy H. J. Neu,,ebauer, Bonn A. Seilacher, Tuebingen and Yale

98

Springer Berlin Heidelberg New York Hong Kong London Milan Paris Tokyo

Tetsuo Takanami Genshiro Kitagawa

Methods and Applications of Signal Processing in Seismic Network Operations With 155 Figures and 11 Tables

Springer

Editors Dr. T e t s u o T a k a n a m i Hokkaido University The Institute of Seismology and Volcanology Graduate School of Science N - 1 0 , W-8, K i t a - k u 060-0810 Sapporo Japan Dr. G e n s h i r o K i t a g a w a The Institute of Statistical Mathematics 4-6-7 Minami-Azabu, Minato-ku 106-8569 Tokyo Japan

" F o r all L e c t u r e N o t e s in E a r t h S c i e n c e s p u b l i s h e d till n o w p l e a s e s e e final p a g e s of the book" ISSN 0930-0317ISBN 3-540-43718-5

S p r i n g e r - V e r l a g B e r l i n H e i d e l b e r g N e w York

Library of Congress Cataloging-in-Publication Data Takanami, Tetsuo, 1945Methods and applications of signal processing in seismic network operations ! Tetsuo Takanami, Genshiro Kitagawa. p. cm. -- (Lecture notes in earth sciences) Includes bibliographical references and index. ISBN 3540437185 (soflcover: alk. paper) 1. Signal processing - Digital techniques. 2. Seismology -- Methodology. I. Kitagawa, G. (Genshiro), 1948- II. Title. III. Series. QE541. T35 2002 551.22'0285--dc21

2002026903

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, an d storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Sp~inger-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science+Business Media GmbH http://www.springer.de 9 Springer-Verlag Berlin Heidelberg 2003 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publicatiotl does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Production: PRO EDIT GmbH, Heidelberg, Germany Typesetting: Camera ready by author Printed on acid-free paper SPIN: 10754596 32/3130/Di - 5 4 3 2 I 0

Preface

This book should prove useful for seismologists and engineers involved in seismic network operations. Recent pro~ess in the measurement and digital signal processing devices has made it possible to obtain a vast. amount of earthquake data on seismic networks. Since 1979 several areas in Japan have been specified as priority observation areas and well-equipped nation-wide seismological network systems have been installec[ The advances in earthquake monitoring and seismic network operation are expected to have a significant effect on the realization of earthquake prediction. In practice, however, the earth's surface is under the continuous influences of natural forces such as the effect of the past earthquakes, wave, wind, tide, air pressure, precipitation and a variety of human induced sources. Therefore it is almost impossible to describe the response to these noise inputs precisely. The development of a proper methodology, in particular a statistical method, is indispensable for a vast amount of seismic data in fast and reliable automatic processing. In this book, we selected fourteen contributions by the specialists in the fields of signal processing problems in seismology.

Tetsuo Takanami The Institute of Seismology and Volcanology Graduate School of Science Hokkaido University Sapporo, Japan Genshiro Kitagawa The Institute of Statistical Mathematics Tokyo, Japan June 2002

V

Contents

Extraction of Small Seismic Signal by State Space Modeling

1

Genshiro Kitagawa and Tetsuo Takanami 1 2

3

4

5 A

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Tile Model and the State Space Representation . . . . . . . . . . . . . 2 2.1 Tile Models for tile Extraction of Seismic Signal . . . . . . . . 2 2.2 The State Space Representation . . . : . . . . . . . . . . . . . 2 Estimation of the Model and Decomposition . . . . . . . . . . . . . . . 3 3.1 Extraction of the Signal by the Kalman Filter and Smoother . . 3 3.2 Estimation of the Model Parameters . . . . . . . . . . . . . . . 4 3.3 Estimation of the Time Varying Variance by Piecewise Modeling 5 3.4 Estimation of the Time Varying Variance by Self-organizing State Space Model . . . . . . . . . . . . . . . . . . . . . . . . . 6 Analysis of Urakawa-Oki Earthquake Data . . . . . . . . . . . . . . . . 7 4.1 Estimation of the Models for Decomposition . . . . . . . . . . . 7 4.2 Decomposition by Piecewise Modeling . . . . . . . . . . . . . . 8 4.3 Decomposition by Self-organizing State Space Model . . . . . . . 8 Possible Extensions of the Method . . . . . . . . . . . . . . . . . . . . 11 Monte Carlo Filter and Smoother . . . . . . . . . . . . . . . . . . . . . 11

M u l t i v a r i a t e T i m e Series M o d e l t o E s t i m a t e A r r i v a l T i m e s o f W a v e s

13

Tetsuo Takanami and Genshiro Kitagawa 1 2 3

4 5

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Estimation of Arrival Time and 3-D Locally Stationa D' A R Model to Estimate S~Arrival Times . . . . . . . . . . . . . . . . . . . . . . . . . . Computationally Efficient Procedure for Multivariate Locally Stationary AR, Model Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Householder Method for Multivariate AR Model Fitting . . . . 3.2 Augmentation of Data . . . . . . . . . . . . . . . . . . . . . . 3.3 Fitting Locally Stationary AR Model . . . . . . . . . . . . . . 3.4 The Number of Necessary Operations . . . . . . . . . . . . . . . Posterior Probabilities of the Arrival Time . . . . . . . . . . . . . . . Application of the Multivariate Locally Stationary A R Model Estimating of Arrival Times . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Vii

13 14 16 16 20 21 22 22 23

5.1 D a t a Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 D e t e r m i n a t i o n of P - a r r i v a l T i m e . . . . . . . . . . . . . . . . . 5.3 D e t e r m i n a t i o n of S - a r r i v a l T i m e . . . . . . . . . . . . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A u t o m o t i c Interpretation of Regional S h o r t Using C U S U M - S A A l g o r i t h m s

Period

9_3 25 28 30 37

Seismic Signals 41

Z o i t a n A. Der a n d R o b e r t H. S h u m w a y Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,1 Genera] Statistical Background . . . . . . . . . . . . . . . . . . 1,2 P r e - F i l t e r i n g Issues . . . . . . . . . . . . . . . . . . . . . . . . . 1,3 Onsest Estimation Toolkit . . . . . . . . . . . . . . . . . . . . P r a c t i c a l E x a m p l e s of the A p p l i c a t i o n of M e t h o d o l o g y D e s c r i b e d . . . 2.1 P e r f o r m a n c e of t h e C U S U M P r o c e d u r e for E s t i m a t i o n g P n Onset T i m e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 D e v e l o p m e n t of M e t h o d s to S e g m e n t C o m p l e t e R e g i o n a l Seismograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Application

o f Autoregressive Processing to the A n a l y s i s

41 42 45 46 47 47 53 56

of Seismo-

grams

61

Mark Leonard l 2 3 4 5 6 7

Introduction ................................ The Autoregressive Model ........................ The Data ................................. Characterisation of a Seismogram Using an AR Model ......... Power Spectrum Estimation ....................... E r r o r P r e d i c t i v e F i l t e r i n g for Signal to Noise I m p r o v e m e n t . . . . . . Onset Time Estimation ........................... 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Akaike Information Criterion . . . . . . . . . . . . . . . . . . . 7.3 Summary of Methods ........................ 7.4 P i c k i n g P Phases . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Hi-net : High Sensitivity Seismograph Network, Japan

61 62 64 64 65 68 69 69 70 70 72 76

79

Kazushige Obara 1

Background

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII

79

2 3 4 5

Overview of Hi-net . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hi-net Station and Sensor . . . . . . . . . . . . . . . . . . . . . . . . . D a t a Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D a t a Flow of Hi-net . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Sub-Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Monitor Center . . . . . . . . . . . . . . . . . . . . . . . . . . . D a t a Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary ..................................

79 80 82 84 84 85 86 87 87

A PC-Based Computer Package for Automatic Detection and Location of Earthquakes: Application to a Seismic Network in Eastern Sicily (Italy) 89 Domenico Patan~, Ferruccio Ferrari, Elisabetta Giampiccolo and Stefano Gresta 1 2 3

4 5 6

7

8 A B

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 PC-Based Seismic Monitoring and New Visual Object-Based Oriented Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 PC-Seism Architecture 93 3.1 Database Management . . . . . . . . . . . . . . . . . . . . . . . 93 3.2 Automatic and Interactive Signal Processing . . . . . . . . . . . 95 3.3 Automatic Signal and Event Location .............. 96 T h e Eastern Sicily Seismic Network by I N G V - C T . . . . . . . . . . . . 104 Seismic Signals in Tectonic and Volcanic Areas . . . . . . . . . . . . . 106 Application of ASDP Software: A Case Study at Mount E t n a . . . . . 108 6.1 Automatic Detection Statistics . . . . . . . . . . . . . . . . . . 109 6.2 Automatic Location Statistics . . . . . . . . . . . . . . . . . . 110 On-Line Processing of I N G V - C T Seismic D a t a [ P r e l i m i n a r y Results by ASDP Apprication . . . . . . . . . . . . . . . . . . . . . . . 115 7.1 First Application of A u t o m a t i c Polarization and Spectral AnalysisI19 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Short-Term Average (STA), Long-Term Average (LTA) and Characteristic Function (CF) . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Covariance Matrix Decomposition Method (CMD) . . . . ' ....... 128 .

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The SIL Seismological Data Acquisition System - As Operated I c e l a n d a n d in S w e d e n -

in 131

Reynir B55varsson and BjSrn Lund 1 2

Introduction A u t o m a t i c Operation of the SIL System . . . . . . . . . . . . . . . . . 2.1 Remote Site Single-Station Analysis . . . . . . . . . . . . . . . 2.2 Continuous Ground Motion Monitoring . . . . . . . . . . . . . 2.3 SIL Centre iViulti-Station Analysis ................ .

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131 133 133 135 136

2.4 The Alert System . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Teleseismic Waveform D a t a Acquisition . . . . . . . . . . . . . . SIL Multi-Event Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Absolute and Relative Location . . . . . . . . . . . . . . . . . . 3.2 Spectral A m p l i t u d e Correlation and G r o u p i n g . . . . . . . . . 3.3 Stress Tensor Inversion of E a r t h q u a k e Focal Mechanisms . . . . 3.4 A u t o m a t i c Reading of Onset and F i r s t Motion Direction . . . . Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . .

137 138 139 139 140 143 144 145

Microearthquake Analysis at Local Seismic Networks in Iceland and Sweden and Earthquake Precursors 149 R a g n a r Slunga 1 2

3 4

5

6 7

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Routine Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 E a r t h q u a k e Detection and Location . . . . . . . . . . . . . . . 2.2 Interactive Analysis . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Spectral Analysis of Waveforms . . . . . . . . . . . . . . . . . . 2.4 Fault Plane Solutions . . . . . . . . . . . . . . . . . . . . . . . 2.5 E s t i m a t e of Fault Radius and Related P a r a m e t e r s . . . . . . . Multievent Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Multievent High Accuracy Locations . . . . . . . . . . . . . . . The Icelandic Experience 1990 - 2001 . . . . . . . . . . . . . . . . . . 4.1 Foreshock Activity . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Fault R a d i u s Variations . . . . . . . . . . . . . . . . . . . . . . 4.3 A s p e r i t y Breaking and Domino P a t t e r n . . . . . . . . . . . . . 4.4 Swarms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Low Stress Drop Events . . . . . . . . . . . . . . . . . . . . . . A Simple E a r t h q u a k e Warning Algorithm, EQ~\'4 . . . . . . . . . . . . 5.1 Input Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Adaptivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 E a r t h q u a k e Warning P a r a m e t e r , E Q W P . . . . . . . . . . . . . 5.4 False A l a r m Rate . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

150 150 150 151 152 152 153 154 154 155 155 156 159 160 160 162 162 163 163 165 168 170

Single S t a t i o n R e a l - T i m e P a n d S P h a s e P i c k e r s for S e i s m i c O b s e r vatories 173 Reinoud Sleeman and Torild van Eck 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P Wave Picker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Dual Autoregressive Model A p p r o a c h . . . . . . . . . . . . . . 2.2 P Phase Picker I m p l e m e n t a t i o n . . . . . . . . . . . . . . . . . . X

173 175 175 176

S Wave Picker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Wavelet Transform . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Polarization Analysis and Characteristic Function . . . . . . . . 3.3 Denoising and Scale Selection . . . . . . . . . . . . . . . . . . . 3.4 S Phase Picker I m p l e m e n t a t i o n . . . . . . . . . . . . . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

176 178 182 185 187 189

Recognizing Explosion Sites Using Self-organizing Properties of Their Temporal and Spatial Shooting Practice 195 M a t t i Tarvainen 1 2 3 4 A1 A2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . Testing SOM with Real D a t a . . . . . . . . . . . . . . . . . . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . Self-organizing Maps . . . . . . . . . . . . . . . . . . . . C o m p u t a t i o n and Selection of the Maps . . . . . . . . . . . . . . . . .

Automatic Activity

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

195 197 201 202 204 206

Hypocenter Location at Times of Extremely High Seismic 209

Shigeki Horiuchi 1 2

3 4 5 6

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Event Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 A u t o m a t i c Picking of P and S Waves . . . . . .......... 2.3 Elimination of Wrong Readings . . . . . . . . . . . . . . . . . . Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . An E x a m p l e of A u t o m a t i c Hypocenter Location . . . . . . . . . . . . Swarm Mode Processing . . . . . . . . . . . . . . . . . . . . . . . . . F u t u r e Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

209 210 210 211 212 213 215 215 218

Application of Pattern Recognition to Seismic Event I)iscrimination221 Shin~ya T s u k a d a and Kazuo Ohtake I n t r o d u c t i o n ................................ Pattern Recognition ............................ Making Pattern and Calculation ..................... Example of Earthquake Discrimination .................. Conclusion and Future Subjects .....................

XI

221 223 224 228 233

Extraction

of Hydrological Anomalies Related to Earthquakes

235

Norio M a t s u m o t o and Genshiro K i t a g a w a 1 2

3 4 5 6 A

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis M e t h o d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Modeling of G r o u n d w a t e r Level . . . . . . . . . . . . . . . . . . 2.2 S t a t e Space Modeling and K a l m a n F i l t e r . . . . . . . . . . . . 2.3 E s t i m a t i o n of P a r a m e t e r s and Orders . . . . . . . . . . . . . . . . P r e s e n t a t i o n of D a t a . . . . . . . . . . . . . . . . . . . . . . . . . . . Change of Residual W a t e r Level . . . . . . . . . . . . . . . . . . . . . S t a t i s t i c a l and Conceptual Modeling for the Response to P r e c i p i t a t i o n Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Response to P r o c i p i t a t i o n by Using the Linear T A N K Model . . . . .

235 236 236 236 238 238 240 245 248 250

O n t h e R e a l t i m e M o n i t o r i n g o f t h e L o n g - P e r i o d S e i s m i c W a v e f i e l d 251 Hitoshi K a w a k a t s u Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . Long-Period Seismic Wavefield vs. E a r t h q u a k e Activity Field Realtime Monitoring . . . . . . . . . . . . . . . . . . . . . . . Seismometer as a Cross-Correlator . . . . . . . . . . . . . . . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

XII

. . . . ..... . . . . . . . . .

251 251 254 256 256

List of Contributors Reynir Bj5~)varsson Uppsala University, Dept. of Earth Sciences, S-75236 Uppsala, Sweden, e-mail: [email protected] Zoltan A. Der

ENSCO Inc., Springfield, VA, U.S.A.

Torild van Eck Royal Netherlands Meteorological Institute (KNMI), P.O. Box 201, 3730 AE De Bilt, Netherlands Ferruccio Ferrari Istituto Nazionale di Geofisica e Vulcanogia, Piazza Roma 2; 95123 Cat.ania, Italy Elisabetta Giampiccolo Dipartimento di Scienze Geologiche, University of Catania; Corso Italia 55; 95129 Catania, Italy Stefano Gresta Dipartimento di Scienze Geologiche, University of Catania; Corso Italia 55; 95129 Catania, Italy Shigeki ttoriuchi National Research Institute for Earth Science and Disaster Prevention, Independent Administrative Institute, Tennodai .3-1, Tsukuba, Ibaraki 305-0006, Japan, e-mail: [email protected] Hitoshi Kawakatsu Earthquake Research Institute, University of Tokyo, 1-1-1, Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan, e-mail: [email protected] Genshiro Kitagawa The Institute of Statistical Mathematics, 4-6-7, Minaaz~i-Azabu, Miuato-ku, Tokyo 106-8569, Japan, e-mail: kitagawa~ism.ac.jp Mark Leonard ASGO, PO Box 378, Canberra City, ACT 2601, Australia: e-mail: mark.leonard~ga.gov.au BjSrn Lurid

Uppsala University, Dept. of Earth Sciences, S-75236 Uppsala, Sweden

Norio M a t s u m o t o Geological Survey of Japan, National Institute of Advanced Industrial Science and Technology, Tsukuba 305-8567, Japan, e:mail: n.matsumotoC~aist.go.jp Kazushige Obara National Research Institute for Earth Science and Disaster Prevention, 3-1, Tennno-dai, Tsukuba, Ibaraki 305-0006, Japan, , e-mail: obarx~bosai.go.jp Kazuo Ohtake Seismolo~cal and Volcanological Department, Japan Meteorological Agency, Ote-machi 1-3-4, Chiyoda, Tokyo 100-8122, Japan, e-mail: ohtake~met.kishou.go.jp Domenico Patan~ Istituto Nazionale di Geofisica e Vulcanogia, Piazza Roma 2; 95123 Catania, Italy, e-mail: patane~ct.ingv.it R o b e r t H. Shumway

University of Caliibrnia at Davis, Davis, CA, U.S.A.

Reinoud Sleeman Royal Netherlands Meteorological Institute (KNMI), P.O. Box 201, 3730 AE De Bilt, Netherlands, e-mail: sleeman~knmi.nl XIII

Ragnar Slunga

Uppsala Universit}~ S-75236 Uppsala, Sweden, e-mail: slunga~foi.se

Tetsuo Takanami Institute of Seismolo~" and Volcanology, Graduate School of Science, Hokkaido University, Nishi 8, Kita 10, Kita-ku, Sapporo 060-0810, Japan, e-mail: t [email protected] Matti Tarvainen Finland

Institute of Seismology, PO BOX 26, 00014, University of Helsinki,

Shin~ya Tsukada Earthquake Disaster Prevention Technology Division, Railway Technic'a] Research Institute, Hikari-cho 2-8438, Kokubunji, Tokyo 185-8540, Japan, e-mail: [email protected]

XIV

Extraction of Small Seismic Signal by State Space Modeling Genshiro Kitagawa 1 and Tetsuo Takanami-" The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569 Japan. [email protected] 2 Institute of Seismology and Volcanology,Hokkaido University, Nishi 8, Kita 10, Kita-ku, Sapporo, 060-0810 Japa.u, [email protected]

A b s t r a c t . State space method for the extraction of small seismic signal from noisy observation is shown in this article. In the basic model, it is assumed that the observed time series is consisted of the three components, namely the background noise, seismic signal and the observation noise components. Autoregressive models are used for the background noise component and the seismic signal component and they are estimated from the observed time series by the maximum likelihood method. The observation noise is assumed to be a white noise sequence. In this state space method, the estimation of the time-varying im~ovation variance of the seismic signal model is crucial. In this article, two methods based on the piecewise modeling and the self-organizing state space modeling are shown. To illustrate the method, the results of the analysis of the foreshock of Urakawa-Oki earthquake were shown.

1

Introduction

Ground movement due to earthquake is conventionally recorded by a seismometer. The earth's surface is actually in continuous movement due to a variety of natural forces such as the continuation or ringing effects of past earthquakes, and by wave, wind and tide effects for seismometers located near ocean shores and by a variety of human induced sources. We consider the sum of these background effects to be a stationary" process. If the amplitude of the earthquake signal is very small, it will be quite difficult to distinguish it from the background noise. In this article, an observed time series is decomposed into several components such as the background noise, seismic signal and the observation noisel To obtain reasonable estimates of these components, we assume that the background noise and the seismic signal follow independent AR processes. If they are known, the decomposition an be performed by the Kalman filter and the fixed interval smoother. However, in actuality, they are unknown and have to be estimated from the observations. Another source of difficulty in modeling this earthquake plus background noise data is that if we consider the microearthquake to be represented by an AR model it will have to be one with a time yawing innovations variance. A conventional approach to modeling nons~ationary covariance time series is to segment the series and to model each segment separately. If the segment duration is short enough to follow the change of variance it might not be large enough to yield a statistically reliable

12 6 0 -6

-12

i

0

Fig. 1

I

500

I

1000

1500

I

2000

f

2500

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Seismog-ram record, Urakawa-Oki earthquake, March 21, 1982.

estimate. Here, a local likelihood approach and the self-organizing state space model are taken to model the changing variance. These approaches eliminate the messy problem of choosing segment lengths. For the estimation of the unknwon state of the self-organizing state space model, a recently developed sequential Monte Carlo filter and the smoother are utilized.

2 2.1

The Model and

the

Space Representation

State

T h e M o d e l s for t h e E x t r a c t i o n o f S e i s m i c S i g n a l

For the extraction of small seismic signal from background noise, we use the following model y~ = r~ + s~ + ~ ,

(1)

where r~, s~ and ~ represent the background noise, the seismic signal and the observation noise, respectively. To separate these three components and to extract the seismic signal from noisy data, it is assumed that both r~ and sn are expressed by the autoregressive models rn

~- i

sn

=

airn-i ~ ~n

l ~ , b i s ~ - , + v~,

(2)

i---I

where the AR orders m and g and the AR coefficients a~ and b~ are unknown and u~, v~ and e,~ are mutually independent white noise sequences with u,~ ~ N(0, ~-~), v~ ~ N(0, ~-~) and ~ ~ g ( 0 , r respectively (Kitagawa and Takanami 1985).

2.2

The State Space Representation

The basic model in (1) and the component model in (2) can be expressed in the state space model form xn

-~ F x n _ l + G'wn

y~

=

H z ~ + g~,

(3)

where x~ is (m+/)-dimensional state defined by x~ = ( r ~ , . . . , r~-m+l, s ~ , . . . , s~_t+l) T, and w~ = (u,,, v~) T is a two dimensional system noise. F, G and H are respectively

(m + ~) x (m + f), (.rn 4- t) x 2 and 1 x (m + s matrices defined by al 1

. .. am

a2

' 1 0_) 0 0

0 ".

:

F:

bl

be

..-

b~

'

a:

~176 --O---i0

1

1 =

1

0

(4)

0 I t

~

0 H

:

.-.

0ll

0

...

ooJ

0].

The variance covariance matrix of the system noise w= is given by

It is noted that the innovation variance of the seismic signal ~ and thus the matrix Q~ depends on time n.

3 3.1

changes with time

Estimation of the M o d e l and D e c o m p o s i t i o n E x t r a c t i o n of t h e Signal by t h e K a l m a n F i l t e r a n d S m o o t h e r

If all of the orders m, g and the parameters 0 = (aj, b~, m~, m~, a2)T are given, the state vector x~ can be estimated by the Kalman filter. Denote the mean and the variance covariance matrix of the state x~ given the observations y I , . . . , y t by X=lt and l,~!t, respectively. Then the one-step-ahead predictor x~i~_t and the filter xal ~ and their variance covariance matrices can be obtained recursively by the following Kalman filter (Anderson and Moore 1979) Prediction Xnln-I = ~I'~- ~ =

Fxn-lln-1 FV~-~[ n - I F T + GQ~ GT,

(6)

Filter K,

=

Vnln_IHT(HVnln_IH T + R) -1

znb~ :

x~ln-, + Kn(y,~ - Hx,q,~_l)

v.,~

(I - A ' ~ H ) G - 1 t ~ - I

=

(7)

Here the initial values x%0 and ~!o are determined from the unconditional means and the autocovariance function of two AR models. Namely, they are given by

z010=

V010=

0 I C '~

(s)

where C ~ and C* are the TSplitz matrices whose (i,j) components are given by the autocovariances with lag i - j of r~ and sn, respectively. Note that the autocovariance

function C/, (i == 0 , . . . , g) can be determined from the AK model via the Yule-Walker equation 7tl

c~ = E ~c; + ~ j=l m

G

=

E~Jc;--J,

(i = 1 , . . . , ~ ) .

(9)

j=l

The autocovariance function for the signal component, C~, (i = 0, . . . , g), can be given similarly. Then the above one-step-ahead prediction and the filter steps are repeated as long as the observations are obtained. The final estimates of the state vectors X~IN, (n = N - 1 , . . . , 1) are obtained by the following fLxed interval smoothing algorithm (Anderson and Moore 1979): An X,~IN

"~ VnlnFTyn-+~n ---- X,,[,, + A~,(x,~+IIN - x~+li~)

V.I~- =

(10)

I.'~i~+ A~(t~+l;~- - I~+li~)A T.

Since the state vector xn contains both rn and s,,, it means that we can decompose the time series y~ and estimate the background noise component rn and the seismic signal component s~ by the Kalman filter and the fixed interval smoother. 3.2

Estimation of the Model Parameters

In actual situation, the orders m and g, and t.he parameters of the model 0 such as the AR coefficients and the innovation variance are unknown. Under the assumption of stationarity of the background noise, the parameters of the model a, and T~ can be estimated by fitting the AR model with observation noise Yn

---- rn "+ ~n

r.

=

(11)

~ air,~_i + u~, i-=l

to a part of data where the seismic signal apparently does not exist. The state space representation for this model can be obtained by considering the special case when g = 0 in (4). The log-likelihood of this AR(m) plus observation noise model is obtained by

N

1 N

1~

4

(12)

where e . = y . - Hx~,l,~_t and /3~ = Hv~,I,~_IH y + cr~- (Jones 1980). Tile AR order m for the background noise model can be determined by minimizing the information criterion AIC (Akaike 1973, Sakamoto et al. 1986): AIC

=

-2maxg(0,~) + 2(number of parameters)

=

Nlog2~r+

0n

e. Iogfl~+y]~+ n~l

n==-i

2(0 + 2).

(13)

Then, by fixing the estimated parameters for the background noise model, the parameters of the seismic signal model bi and ~'~ are obtained by fitting the model (1) and (2) to a subinterval of the data where the seismic signal apparently exists. Note that at this stage, ~-~= is assumed to be a constant over time. This two-step estimation procedure will be reasonable since the background noise can be considered stationary for a certain time interval. Further, if the time series is obtained by the same seismometer and the epicenters of the earthquakes are very close, it will be reasonable to use the same parameters. At least we can use the parameters as the initial values for numerical optimization. 3.3

Estimation of the Time Varying Variance by Piecewise Modeling

The variance of the autoregressive model for seismic signal component is related to the amplitude of the seismic sig-nal and is actually time varying. Namely, the variance, T22, is almost zero before the seismic signal arrives, becomes large depending on the amplitude of the signal and then goes back to zero as the tail of the seismic signal dies out. This variance parameter plays the role of a signal to noise ratio, and the estimation of this parameter is the key problem for the extraction of the seismic signal. In this subsection, we briefly introduce a local likelihood method proposed in Kitagawa and Takanamai (1985). A more recent development will be shown in the next subsection. From the definition of the log-likelihood of the state space model shown in (12),

1{

, 4/

(14)

has a natural interpretation as the contribution to the log-likelihood of the model from the observation at time n. On the assumption that the true model changes quite slowly and smoothly, then correspondingly the log-likelihood should also change quite smoothly. This suggests that by smoothing the one-point log-likelihood (14), we can define a local log-likelihood. The time-varying variance is then estimated by finding the value of variance that attain the maximum fo this local log-likelihood. For estimating the local-likelihood of the model, we applied a method of estimating the time-varying variance (or volatility) of nonstationary time series, (Kitagawa and Gersch 1985, 1996, Kitagawa and Sato 2000). We define zm by

for m = 1 , . . . , n / 2 , then t~ is roughly approximated by a normal distribution with the mean and the variance of t~ are approximately given by F_,[t,~] ~_ log c~ + 7, V a r ( t ~ ) ~" 7r~/6 where ~ is the average of the true expected log-likelihood at time 2 m - 1 and 2m and ~' __ 0.57721 is the Euler constant. Upon approximating the distribution of t~ by a normal distribution and using the smoothness priors trend model, t,~ = 2t,~_1 - t,~ + v,~, v~ ~ N ( 7 , p2), we can obtain the smoothed value ~,~ of t,,,. The local log-likelihood of that model is then obtained by ~ = ~2~-~ = exp{{m}. For simplicity here, ~-~, the value of the innovations variance of the earthquake signal at any one instant in time, is only allowed to take on discrete values. Then, a summary of the procedure used here for the estimation of the changing variance based on the local likelihood method is as follows:

1. For each possible value of r~ = Co2 - k , k = 1,

., k , ~ .

(a) Compute gk,~, n = 1 , . . . , N . (b) Obtain the smoothed value ~k,~,n = 1 , . . , N. 2. For each time instant n, n = 1 , . . . , N (a) Find k* for which gk,~, k = 1 , . . . , k , ~ is maximum. (b) Set

= co2

3.4 E s t i m a t i o n of t h e T i m e V a r y i n g Variance b y S e l f - o r g a n i z i n g S t a t e Space M o d e l In the treatment shown in the previous subsection, the time-varying variance was estimated by defining the local likelihood which evaluates the goodness of predetermined candidates of variance and finding the best one for each time instance (Kitagawa and Takanami 1985). Recently, a self-organizing state space model was successfully applied for the estimation of the time-varying variance or volatility (Kitagawa 1998).. In this method, the original state vector x. is augmented with the time-varying parameter 0,~ as

zn =

On

'

where the parameter On, for the present problem, is defined by O. ----log10 Tff..

(17)

The logarithm of tile variance is used to assure the positivity of r ~ . We further assume that this parameter O~ changes according to the random walk model , = logl0 72.,~_ 2 t + ~, logto Tff,~

(18)

where r/~ is the Gaussian white noise with r]~ ~ N(O, ~2). The state space model for this augmented state is easily obtained from the original state space model for z~ and (18) as follows. =

/7/ =

[Ht0 ]

eO~! ~

]j,

(19)

(20)

Then by applying the nonlinear non-Gaussian smoother based on the Monte Carlo method (see Appendix), we can estimate the state z~. Since the augmented state z~ contains both xn and 0,,, this means that the marginal posterior density of x~ and 0,~ can be obtained simultaneously and that it is not necessary to estimate the parameter. 0~ by the maximum likelihood method that requires repetition of the filtering many times.

4 4.1

Analysis

of Urakawa-Oki

Earthquake

Data

E s t i m a t i o n o f t h e M o d e l s for D e c o m p o s i t i o n

To illustrate the proposed method, we show the results of decomposing the data shown in Fig. 1. The data is a record of the North-South component of a foreshock of the 1982 Urakawa-Oki earthquake observed at the Erimo station of the Institute of Seismology and Volcanology, Hokkaido University, Japan at 11:32 AM, March 21 1982, (Takanami 1991). The magnitude was M = 2.30, and the epicenter was about 50 km away from the location of the recording seismometers which in turn are located 0.5 km from the shoreline of the Pacific. The observed signal is miniscule relative to the background noise. The original record of 83.85 seconds duration was regularly sampled at 0.01084 second intervals (92.3 samples/second), and subsequently 2 consecutive observations were averaged to produce the observations shown in Fig. 1. As a result of this sampling scheme, the sampling error variance of this record is 1/24. Firstly, the AR(m) plus observation noise model shown in (11) was fitted to the first 1000 observations. For the maximum likelihood estimation of the parameters of the model, the ordinary autoregressive models are fitted by the least squares method (Program UNIMAR of the TIMSAC-78, Akaike et al. 1979) and the estimated AR coefficients and the innovation variance are used as the initial estimates for quasiNewton optimization procedure. The initial value for the observation noise variance is arbitrarily set to 1/24. As shown in Tab. 1, the model with rn = 5 attains the minimum of AIC and this model was selected as the AR model for background noise component. T a b . 1: AR process plus observation noise model fitted to the first 1000 observation models. The AR models with orders up to 8 are compared Order 1 2 3 4 5 6 7 8 AIC 1113.5 1082.8 1084.3 1082.5 1079.3 1081.2 1083.2 1085.2

Tab. 2: AR process plus observation noise model fitted to the first 1000 observation models. The AR models with orders up to 8 are compared Order 1 2 3 4 5 6 7 8 AIC 3893.9 3499.1 3422.1 3396.4 3392.7 3380.5 3373.9 3375.8

By assuming this observation noise model, the AR model for the seismic signal was fitted to the data n = 1301,..., 2300, where the seismic signal apparently exists. The AIC values shown in Tab. 2 indicate that the AR model with order 7 best fit to the data. Fig. 2 shows the power spectra of the estimated models. The left plot shows the power spectrum of the background noise plus the observation noise component in logarithmic scale. In this plot the straight line shows the observation noise level. It can be seen that the background noise component has a high power in low frequency ranges, in particular in the frequencies less than 10 Hz. it has almost no power in high fl-equency range.

4.

Noise

Background

Seismic Signal

2-

-2 O

i

i

l

I

5

10

15

20

-2 25

0

I

~

I

I

5

10

15

20

25

Fig. 2 Power spectra of the component models in natural logarithmic scale. Left: Background noise plus observation noise. Right: Seismic signal component.

The right plot shows the power spectrum of the seismic signal component. It can be seen that the power spectrum of the seismic signal has two peaks at around f = 4Hz and 10Hz which presumably correspond to the basic frequencies of the P-wa-~'e and the S-wave.

4.2

Decomposition by Piecewise Modeling

Fig. 3 illustrates the result of data shown in the top plot, by the piecewise modeling of time-var)ing innovation variance for the seismic signal component. The second and the third plots show the extracted background noise and the microearthquake signal, respectively. The seismic signal was clearly extracted by this decomposition. It is interesting that even after the arrival of the seismic signal, the background noise component was extracted. The bottom plot shows the estimated time changing variance. The variance was only permitted to take on discrete values, ~-~ = 40 x 2j, j = 0 , . . . , 39. The estimated innovation variance roughly capture the change of the amplitude of the seismic signal.

4.3

D e c o m p o s i t i o n by Self-organizing State Space M o d e l

Fig. 4 shows the results by the self-organizing state space model. In this method, the same AR models as the previous subsection were used. Then the augmented state space (15) was estimated by the Monte Carlo filter and smoother shown in Appendix. By this method, the background noise component and the seismic signal component were clearly extracted. The bottom plot shows the estimated time-varying innovation variance of the seismic signal component in logarithmic scale. It clearly capture the sudden increase of the variance when the seismic signal arrived at around n -- 1250. It is emphasised here that this variance parameter was estimated simultaneously and thus it is not necessary to estimate it prior to the analysis. Therefore this result is obtained only one pass of the Monte Calro filter and the smoother.

12

OBSERVED DATA

r

6

0 -6

-12

I

0 12

500

I

1000

I

1500

I

2000

I

2500

3000

Background Noise

6

0 -6

-12 0 12

I

I

I

500

1000

1500

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2000

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2500

3000

Seismic Signal

6

0 -6

-12 0 0.8

I

I

500

1(300

1

1500

I

2000

I

2500

3000

Time-varying Varian

?Ul'

0.4

O.O

0

I

I

I

500

1000

1500

t

2000

t

2500

3000

Fig. 3 Decomposition of observations by piecewise modeling. From top to bottom: Observed time series, estimated background noise component, extracted seismic signal and the estimated time-varying variance of the seismic signal model, respectively.

12

OBSERVED DATA

0 -6

-12

I

0 12

500

I

1000

I

1500

I

2000

I

2500

3000

Background Noise

6 0 -6 -12 0 12

I

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1000

1500

I

2000

I

2500

3000

Seismic Signal

6 0 -6 -12 0 2 0

I

I

I

500

1000

1500

I

2000

I

2500

i Time_yawing Variance (in IoglO scale)

3000 I

-2

-6 0

I 500

= 1000

1500

2000

2500

3000

Fig. 4 Decomposition of observations by self-organizing state space model. From top to bottom: Observed time series, estimated background noise component, extracted seismic signal and the estimated time-varying variance of the seismic signal model in log scale, respectively.

l0

5

Possible E x t e n s i o n s of t h e M e t h o d

The method described in this chapter can be directly generalized to decompose the observed time series into background noise, P-wave and S-wave. However, this decomposition is sometimes very delicate and requires very careful modeling. The seismograms are records of seismic waves in 3-dimensional space and three components, namely East-West, North-South and Up-Down components, can be observed. The signal extraction method shown in this section can be generalized to 3-dimensional case by using multivariate AR models. A more precise extraction of the seismic signal will be possible by using the explicit modeling of the characteristics of the P-wave and the S-wave. Namely, P-wave is a compression wave and it moves along the wave direction. Therefore it can be approximated by a one-dimensional model. On the other hand, S-wave moves on a plane perpendicular to the wave direction and thus can be expressed by 2-dimensional model. In this approach, the crucial problem is the estimation of time-varying wave direction.

A

Appendix: M o n t e Carlo Filter and S m o o t h e r

In the Monte Carlo filtering (Doucet et al. 2001, Gordon et al. 1993, Kitagawa 1996), we approximate each density function by many particles which can be considered as realizations from that distribution. Specifically, assume that each distribution is expressed by using m (m=10,000, say) particles as follows: {p(j),...,p(m)}

~

p(x,~lYn-.1)

{fn(1),..., f(nm)} "~ p ( z n [ ~ ) (i)

~(m) l

S,~!N,''',%tN~r

~

P(x~IYN)

{v(1),...,v(2)}

~

p(v,~)

Predictor Filter Smoother System noise

Namely, we approximate the distributions by the empirical distributions determined by m particles. Then it will be shown that a set of realizations expressing the one step ahead predictor p(x,~l~_l) and the filter p(x~ I~,) can be obtained recursively as follows. [ M o n t e C a r l o Filter]

1. Generate a random number f(oJ)..~ po(x) for j = 1,... ,m. 2. Repeat the following steps for n = 1 , . . . , N. (a) Generate a random number" v(nJ),~ q(v), for j -- 1 , . . . , m. (b) Compute p~) = ,.~/~j~_~,,(J)@)), j = 1, . . . , m.

(c) Co, p. te

= p(wlp

)) -for j = 1 , . . . ,

(d) Generate f(nj), j = 1,... , m by the resampling of

p(nl),..., p(nm).

An algorithm for smoothing is obtained by" replacing the Step 2 (d) of the algorithm for filtering by

ll

,, (J) o(J) AJ) ~T ' j = 1 , . . . , m } by the resarn(d-L) For fixed L, generate ((s,~_c!~,... , %-'1=' v=!~) , (j) ~(J) ,n(j)yr pling of ,liS,~_LI~_I, ~-1(~-1,e~ J , J = 1, m } with f ~ ) = o(J)

This is equivalent to applying the L-lag fixed lag smoother. T h e increase of lag, L, will improve the accuracy of the p(x=lY,,+L ) as an approximation to p(x,]}'~v), while it is very likely to decrease the accuracy of ~ (~) , 9 9 9 OniNJ ~ ~ as representatives ( Sn,N of p(X,,[]:~+L). Since p(x,~!Y~§ usually converges r~ther quickly to p(x,~[YN), it is recommended to take L not so large (Kitagawa 1996).

Acknowledgement Some of the work shown in this article is motivated by the joint work of the first named author with Professor Will Gersch of University of Hawaii.

References Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle: Second International Symposium on Information Theory, .atademial Kiado, Budapest, 267-281. (Reproduced in Selected Papers of Hirotugu Akaike, Parzen, E., Tanabe, K. and Kitagawa, G. eds, Springer-Verlag, New York (1998)) Akaike, H. Kitagawa, G, Arahata, E. and Tada, F., (1979), TLMSAC-78, Computer Science Afonographs, No. 11, The Institute of Statistical Mathematics. Akaike, H. (1979). A Bayesian extension of the minimum AIC procedure of autoregressive model fitting, Biometrika: 66,237-242. Akaike, H. and Kitagawa, G. (1998). The Practice of Time Series Analysis, Springer-Verlag, New York. Doucet, A., de Freitas, N. and Gordon, N. (2001), Sequential Monte Carlo Methods in Practice, Springer Verlag, New York. Gordon, N,, Saimond, D.J, and Smith, A.F.M., Novel approach to nonlinear/non-Gaussian Bayesian state estimation, IEE Proceedings-F, 140, 107-113. Gutenberg, B. and Richter, C.F. (1941). Seismicity of the Earth, Geol. Soc. Am., Spec. Pap., 34, 133. Harvey, A.C., R.uiz, E. and Shepard, N. (1994). Multivariate stochastic variance model, Review of Economic Studies, 61, 247-264. Jones, l%.H. (1980). Maximum likelihood fitting of ARMA models to time series with missing observations, Technometrics: 22,389-395. Kitagawa, G. (1996). Monte Carlo filter and smoother for non-Gaussian nonlinear state space models, Journal of Computational and Graphical Statistics, 5, 1-25. Kitagawa, G. (1998). Self-organizing State Space Model, Journal of the American Statistical Association, ~3, No.' 443, 1203-1215. Kitagawa, G. and Gersch, W. (1996). Smoothness Priors Analysis of Time Series, Lecture Notes in Statistics, No. 116, Springer-Verlag, New York. Kitagawa, G. and Sato, S. (2000), Nonlinear State Space Model Approach to Financial Time Series with Time-Varying Variance, Proceedings of the Hong Kong International Workshop on Statistics in Finance An Interface, eds. W.S. Chan, W. Keubg and H. Tong, Hong Kong, (2000) 23-44. Kitagawa, G. and Takanami, T. (1985). Extraction of signal by a time series model and screening out micro earthquakes, Signal Processing, 8, 303-314. Sakamoto, Y., Ishiguro, M. and Kitagawa: G. (1986), Akaike Information Criterion Statistics, D. Reidel Publishing Company, Dordrecht/Tokyo. Takanami, T. (1991). ISM data 43-3-01: Seismograms of foreshocks of 1982 Urakawa-Oki e.ar~hquake, Annals of the Institute of Statistical Mathematics, 43, No. 3, 605.

12

Multivariate Time Series Model to Estimate Arrival Times of S Waves 9

.

9

TetsuoTakanamiland Genshiro Kltagawa" 1The Institute of Seismology and Volcanology,Graduate School of Science, Hokkaido University; N10 W8, Sapporo, 060-0810; Japan ~rhe Institute of Statistical Mathematics, Minami-Azabu, Minato-ku, Tokyo 106-8569; Japan Abstract. Some eomputationally efficient procedures that were developed for the precise estimation of the changing point of multivariate locally stationary autoregressive (MLSAR) model are examined for their ability in determining the onset time of S wave in an online system. The details of Householder's method that is quite efficient in both accuracy and computation are described. The amount of computation is bounded by a multiple of Nm2 with N being the data length and m the highest model order, and dose not depend on the number of models checked. The tmivariate locally stationary autoregressive model (LSAR) for one vertical component is sufficient to determine the arrival time of P wave, but not appropriate to determine the arrival time of S wave. The procedure of multivariate AR model (2-V MLSAR) for two horizontal components is most useful for the precise estimation of the arrival time of S wave. Based on the AICs' of the fitted MLSAR and Akaike's definition of likelihood of the model, a method of evaluating the posterior distribution of change point of the AR model is also presented. 1

Introduction

In the past 20 years, the automatic processing of seismic signals for the detection of seismic activity has been developed due to the establishment of a well-equipped nation-wide seismological network system9 In practice, the analysis o f micro-earthquake causes two problems 9 Firstly, the seismic signals observed by seismometers a r e contaminated by various kinds of noises, such as microtremors, microseisms, and artificial vibration. Since the noise level is almost a constant independent o f the signal, the effect of the background noise becomes more severe, for earthquakes with smaller magnitudes. Therefore, if we want to analyze signals of micro-earthquakes, it is recluired to develop a more sophisticated procedure, which can handle very noisy data9 Secondly, the number o f earthquakes increases exponentially with the decrease of the magnitude according to the Gutenberg-Richter's law, l o g n ( M ) = a - b M , the incremental or cumulative number n(M) of earthquakes as a function of magnitude M9 For the processing of so many micro-earthquakes, it thus becomes necessary to develop a computationaUy efficient method that can automatically estimate the onset time of seismic wave with noise9 Many attempts have been made based on the AR modeling of the seismic signals (e.g. Tj~stheim, 1975; Hamaguchi and Suzuki, 1979, Hamaguchi and Morita, 1980; Yokota et all, 1981; Maeda (1985), and Hasegawa et al., 1986) The AR model is useful for the analysis o f stationary time series. Although, from the statistical point o f view, the main feature of the seismic signal is its nonstationarity, it might be reasonable to approximate it by an AR model on each properly divided time interval. In this way the use o f the locally stationary AR model (Ozaki and Tong, 1975; Kitagawa and Akaike, 1978) was motivated and it was shown that it is useful for the detection of the arrival time of P waves in noisy data (Yokota et al., 1981). A significant merit of the current time series method is that one can determine automatically the arrival time of P wave by just looking for the time point

13

that attains the minimum value of the AIC (Akaike Information Criterion) of the locally stationary AR model. The AIC was proposed for the selection of the best statistical model (Akaike, 1973). The CPU time of such a method used to depend on the number of data points, the order of the AR model and on the number of models checked, that is proportional the number of candidates of the arrival time. However, a more efficient procedure for the estimation of the arrival time of P wave has been developed based on the univariate locally stationary AR models (Takanami and Kitagawa, 1988). On the other hand, it is well known that the additional information from S wave improves the accuracy of the estimate of location (Buland, 1976). Further, to get elastic parameters such as Poisson's ratio, the velocity of the S wave as well as that of P wave is required. Therefore, in this chapter, a procedure for the estimation of the arrival time of S wave is introduced and is examined for its suitability as an online system. The objective of this chapter is three-fold. Firstly, we develop a eomputationally efficient algorithm for the fitting of the multi-variate locally stationary AR model so that it can be applied to the on-line processing of seismic wave. The procedure is, in particular, useful for automatic determination of the arrival time of S waves of micro-earthquakes with magnitudes (1 < M < 3). Secondly, we will present a method of evaluating the posterior probability of the arrival time. The posterior probability will be useful for estimation of the hypocenters of the earthquakes. The third objective of the paper is to demonstrate the usefulness of the proposed procedure by applying it to the foreshocks of the 1982 Urakawa-Oki earthquakes. The plan of this chapter is as follows. In Section 2, a procedure for the estimation of arrival time of a seismic wave that was developed based on a multivariate locally stationary autoregressive (MLSAR) model fitting is shown. In Section 3, a computationally efficient procedure for MLSAR model fitting is described. In Section 4, the posterior probability of arrival time of seismic wave is derived from the likelihood of MLSAR models. Section 5 is devoted to empirical study where the proposed procedure is applied to the estimation of the arrival times of the seismic waves. Especially, the main focus is put on the estimation of arrival time of S wave. 2

Estimation of Arrival Time and 3-D Locally Stationary AR Model to Estimate S-Arrival Times

Let y, = (y,E, y ~ , y,,u) ~, (n = 1 ..... N) be a three variate-time series, where yne, y,~, and y,~ express the east-west, north-south, and up-down components of the seismogram, respectively, y ' denotes the transpose of the vector y. Obviously, the characteristics of the series, e.g., the variances and spectra, change over time due to the arrival of a seismic wave such as P wave or S wave. However, it might be reasonable to assume that each of the seismogram before and after the arrival of the seismic wave are stationary and can be expressed by a single time series model. This will be verified by the time-varying spectrum analysis shown in section 6. For a stationary time series, an AR model usually fits well and allows computationally efficient procedure for the identification. Therefore we will use an AR model for the modeling of each stationary sub-series. In this modeling the arrival time of the seismic wave, ha, corresponds to the change point of the AR model. In the estimation of the arrival time of P wave, the use of univariate time series has been considered reasonable, since the P wave is a compression wave and a dominant part of the movement appears in the vertical component. However, since the S wave is a shear type wave, for the estimation of the arrival time of S wave, the analysis of the movement in the horizontal plane, namely of the east-west and north-south components, seems to be

14

necessary. In view of the fact that even after the arrival o f S wave, the coda of P wave remains and that S wave also induces the vertical motion, the use of two or three components seems to be desirable. We also have an anticipation that even for the detection of P wave, the analysis of three-variate time series will give more precise information about the arrival time. We are thus motivated to use a MLSAR model which consisted of the following two local models. B a c k g r o u n d noise m o d e l y, =

A,~y,_~ + w.1 ,

(n = 1 ..... ns).

(1)

l=l

Here ml is the AR order, Au is t h e k x k A R coefficient matrix for i-lag component, and w , l i s the innovation sequence with mean 0 and variance covariance matrix )2~. In our applications, k is typically 2 or 3 and y~ = (.v,a~ y,,u)t or y , = fy,~ y ~ , y,,u) t. This model expresses the d3aaamics of the background motion. It should be noted that in the detection of S wave, this "background noise" model expresses the coda of P wave together with the background motion. Signal M o d e l nh.

y , = ~ . a i 2 y , _ i + w,2 ,

(n = n~ + 1..... N).

(2)

t=l

Here m~ At2 and w,a are AR order, AR coefficient matrix and the innovation of the signal model, respectively. The variance covariance matrix of the innovation w2 is denoted by Z 2 . This model expresses the dynamics o f the seismic wave. Assuming the arrival time na = nB + 1 and the orders o f autoregressions, mt and m2 to be known, the distribution of the time series is given by y, - N(~AilY,.,,Z,),

( n = 1 .... ,nB),

i=l ~2

y, ~ N(yA,zy,_eE2),

(n = 1,...,N).

(3)

Therefore. given the observations Yl ..... y,~; the log-likelihood of the M L S A R model is given approximately as follows;

t ( A , , A2, Y., ,E 2) = - I / 2{k(N - m~) log 2~r + (n B - m,) loglX t ] +

(4) N

(N--nB)log~X2l+

t -, + w.,X, n=ml+l

where, A t

=(A~,,...,A,,,,

),A 2 =

(A,2,...,A,,:2)

by

15

, -, w.2} ~w.:X2 n=nll

and from (1) and (2), w,~ are obtained

I111

w~ = Yn - ~ Agy._i

(j = 1,2).

(5)

1=I

The maximum likelihood estimates ofA U and Yi, (i = 1..... ms;j = 1,2) are approximately given by maximizing (4). However, from the form of the log-likelihood function given (4), it can be easily seen that the parameters of the background noise model and the signal model can be obtained by mmtmtzmg nil t

-I

(rib-mt)logl E1 l+ ~-",w.f.L w~t, n=ml+l

N

( N - m B ) l o g [ Z 2 1+ ~_~wt.2Z2tw,2,

(6)

n=.n B +1

respectively. The eomputationally efficient procedure for the fitting of these models will be shown in the next section. The fitted model cart be evaluated by the AIC criterion defined by AIC = -2e(/~ t, A2,Y.1,Z2) + 2 (the number of estimated parameters).

(7)

where, A1 ,-42,E1, andE2 are the maximum likelihood estimates o f A j andZj (j = i, 2), respectively. In the estimation of the arrival time, the crucial problem is the estimation of the dividing point ha. This point can be determined by fmding the minimum of the AIC. 3

3.1

Computationally Efficient Procedure for Multivariate Locally Stationary AR Model Fitting Householder Method for Multivariate AR Model Fitting

We will first briefly review the procedure for the fitting of multivariate AR model developed for the program MULAR in TIMSAC-78 (Akaike et al., 1979). This program has been widely used since then. Assume that three-vadate time series {Yt..... y~r is given and we are going to fit multivariate AR (MAR) model ta A iYn-i + wn Yn = ~.+

,

wn

~

N(O, Y.) .

(8)

n=l

It should be noted that although an algorithm for fitting three-variate A R model is shown here, it can be readily extended to a general k-variate time series. The main idea of MULAR is to use an AR model with instantaneous response m

y,, = Boy,, + ~_+B,y,,_, + v+ ,

v,, ~ N(O, V ) .

n=-I

Here it is assumed that the coefficient of the instantaneous response is of the form

16

(9)

0 0

B o = b21

[b3,

(10)

b32

and the covariance matrix V is of diagonal form: 0"2 V=

0

0 o-22

0

0

0 0 2 0-3

(11)

Since m

y. : (I - B o)-1 ~ B,y,_, + (I - B o)-I v,,,

(12)

i=1

Thus the instantaneous response-orthogonal innovations model in (9) is equivalent to the usual MAR model in (8) by algebraic transformation

A, = ( I - B o ) - I B , ,

X=(I-Bo)-lV(I-Bo)

-~,

i = 1,2 ..... m.

(13)

It should be noted that these two models, (8) and (9), have the same number of parameters. The significant merit of the use of the AR model with the instantaneous response is that it can be obtained by independently fitting the univariate models for each o f the three components. This can be justified as follows. Since the covariance matrix is of diagonal form, N log ] V I +2., v,,tV_l v,, =

N log or;, + 1

n'=-t

I=i I .

i

v~2 , n=l

(14)

]

where v,, denotes the i-th element of vn. Therefore, if the 3 x 3 matrix B; is divided as bil ]

(15)

B, =]bi21,

[b,~] t

/

the parameter set ~bo,(i = 1..... m~),o-~ l, f o r j = 1, 2, 3 can be independently estimated by mmlmmmg kr

N log cr~ +L-~-X~,. 1 2 t.,j

(16)

n=l

For any given bo, (16) is minimized when O'j

--

V

17

,

(17)

and by substituting this estimate into (16), it can be seen that b,j are obtained by mmmammg N log a~ + N ,

(18)

or equivalently by minimizing o-j. This means that by using the special expression for the multivariate AR (MAR) model given in (9), the maximum likelihood estimates of the MAR model are obtained by solving the least square problem for each of the three component. Further, the log-likelihood and AIC of the MAR model are obtained as the sum of AIC's of three components models. We will next show an algorithm that can solve these three least squares problems quite efficiently. The least squares estimation of the MAR model can be realized by first making (N- m) • (3m + 3) matrix Y~ "'" t X = [-Y"~'~ "'" Lye-,

Y{

Y~+1 l Y~,§ "/

t

Y~

9..

(19)

J

and reduce this matrix to an upper triangular form by an orthogonal transformation (i.e., Householder transformation, Golub (1965), Sakamoto et al. (1986)

[

SI1

S=

"" 9

S3,3•.3

"'.

:

0

]

(20)

,

S3m+3,3ra_#3

The (3m + 1) • (3m + 1) upper left triangular matrix of S contains sufficient information for the fitting of the model for the first Component (e.g., E-W component in this case). In particular, the innovation variance o-~(j) and AICQ) of thejth order model l

y~ = ~bily

(21)

. + W,~ ,

J=l

where b~I = (b~ (1,1),b, (l,2),b, (1,3)) and y , = ( y , ~ , y~v , y , v ) t, are obtained by (kitagawa and Akaike (1980); Sakamoto et al. (1986)) 3m+l

1

=

-'

.

Uv - m ) i=3/+t

( / = o , t ..... m),

AIC~(j) = (N - m) log tr] (j) + 2(3j + 1).

(22)

Incidentally, the regression coefficients of the E-W component model with order j are obtained by.solving the linear equation

18

:ii

sl,3J

1

(23)

(1'3)J However, it should be emphasized that for the present purpose of the estimation of the arrival time, only the AIC values of the best model are necessary and we do not actually solve this linear equation. For the computation of the AIC of the second (North-South) component model, J

Y,N = b02(2,1)Y,a + ~ b,2Y.-, + W~v, i=l

(24)

we first transform the matrix (20) to the following form

". 1

:

:

:

S;m+I.3m

S;m+l,3m+2

5;m+l,3m+3

3m+2,3m*2

(25)

S3m§ S;m+3,3m+3

O This can be done by using an appropriate Householder transformation with only a little additional computations. Then the upper left (3m + 2) x (3m + 2) sub-diagonal matrix contains sufficient information for the fitting of the regression model for the second component, which has an instant response from the first (E-W) component. The residual variance and AIC ofthej-th order model is given by 3ra+2

1

cry(J) = N

t

2 ,

mi.3j.~_

AIC 2(j) = (N - m)log cr~ (j) + 2(3j + 2).

(26)

It should be noted that the (3m+l)-st column of the matrix S which was used as the vector of objective variable in fitting the model for the first component, is now used as the vector of a regressor corresponding to the instantaneous response from the first variable. Similarly, the model for the third variable (U-D component) can be obtained from

19

Sl,3m

arc

t? 821

9

r b'2,3m

$31

.o.

~r $3,3m

"..

:

Sl,3ra+l

Si,3m+2

SI,3m+3

tt

tt

82,3m+2

82,3m+3 SJf2,3m+3

f? 'S3ra+2,3m

w

S3m+2,3m+3 p?

S3m+3,3,,n+3

0

3m+3 Z (Si,3m+3) o'2 (j) - N -1 m ,=,j§

2

,

AIC 3(j) = (N - m) log cr~ (j) + 2(3j + 3).

(27)

The AIC o f the original MAR model is then given by AIC = rain AIC~ (j) + rain AIC z (j) + min AIC 3(j) J

)

(28)

J

By using the Householder transformation, we can further fit a more sophisticated model which, for example, allows that some part of the coefficients are zeros. The program for such model is given in the subroutine MARFIT of TIMSAC-78 (Akaike et aL, 1979). However, this will not be necessary for the present purpose.

3.2 Augmentation of Data In the previous section, we showed the algorithm o f the fitting o f MAR model. We will now show a method of modifying the AR model when the augmented data set {.vl..... yJv, Yu+l..... ym.p}was obtained. Here p > 1 is the number of the new data. This can be performed by first organizing the following (3m + 3 + p ) • (3m + 3) matrix R

t

R= Ly~c+p_l t

s

"'"

YN+I-m

"'"

YN+p-m

t

t

YN*I

1

(29)

t YN§ ]

with S being the upper triangular matrix given in (20) and then reducing to an upper triangular form. It should be noted that due to the orthogonality o f the Householder transformation, non-zero elements of the Householder reduced from o f R is one and the same as the upper triangular form obtained by the Householder reduction o f the following ( N + p - - m ) x (3m + 3) matrix:

20

f

3'~

"'"

:

"..

t

X=

Yu-1 1

YN

f

Yl : I

"'" "'"

t

Y~+t

Yu-, t

-

: l

Y~.I 1

(30)

Yu+t-~ YN+I

:

"..

:

:

Y,v.p-~

"'"

Y::+p-~

Y~,'+p

t

t

t

This means that the upper triangular matrix, which is necessary to fit A R models to the augmented data set can be obtained with only a few additional computations. By applying the same method as presented in the previous section to this matrix, we can get the AIC values of the best AR model fitted to this augmented data set.

3.3 Fitting Locally Stationary AR Model In order to determine the arrival time of a seismic wave based on the MLSAR model, we have to compare the goodness o f the fit of many MLSAR models obtained by assuming various arrival time. We assumed that we have N observations and that nB is no < nB < hi. Note that the arrival time na is given by n~ = nB + 1. It is also assumed that the required resolution is p points, thus we have to fit models for each dividing points no, n o + p , , . . , n o + g p = n~. Therefore, we have to fit g + 1 different MLSAR models. In this subsection we shall present a computationally efficient procedure for the fitting of many MLSAR models based on Householder method for MAR model fitting and augmentation o f the data. The procedure is constructed as follows: 1.

Fit an MAR model to the data { Y i , ' " , Y , , o } by the method presented in Subsection 3.1. AIC0N denotes the AIC of the best M A R model fitted to the data.

2.

For i = 1,--., g, successively augment the upper triangular matrix obtained in step 1 by the additional data {y~0+u_op~1,-..,y~0.~}and fred the minimum value of AICs'. This value is denoted by AICi".

3.

Similarly to step 1, fit an MAR model to the data {Y,I,'",Ys-}. The minimum value of the AIC for this data set is denoted b y A I C s .

,

For i = g - I , - - . , 0 , successively augment the upper triangular matrix obtained step 3, by the additional data {Y,0+ip.1,'",Y~0+(i+op}" The minimum value of the AIC of the MAR models fitted to the data set is denoted b y A I C s

.

Obtain the AIC of MLSAR model which assume the diving point to be n~ --'-no + ivby AIC, = AICi~ + AICf (i = 0,---, g). (3 i)

6.

Find the minimum of AIC0,-. -, AIC,.. If AICi is the minimum, then n A 1 is our estimate of the arrival time o f the seismic signal.

21

= nO + ip+

3.4 T h e N u m b e r o f Necessary O p e r a t i o n s

For the Householder transformation of n • k matrix to an upper triangular form, the amount of multiplications (and additions) is approximately evaluated as (Golub, 1965) k

(n + 1 - i)(k + 1 - i) ~ l n k 2 .

(32)

Therefore, the number of necessary operations for fitting an ordinary 3-V MAR model to entire data set is approximately 9Nm2/2, and fitting 3-V MLSAR model without recursive formula shown in Subsection 3.3 requires 1

f ~ l ( n o +ip)(3m+3)2 + i ~ _ o ~ ( N - n o - i p ) ( 3 m + 3 ) 2 ~ q N m 2 ( n l - n o ) . _ _ 2p

(33)

On the other hand, the necessary operations for the Householder transformation of the matrix (29) is k

~(p+l)(k+l-i)~

1

2.

(34)

I=1

Therefore, the total amount of multiplications (and additions) for the fitting of all possible 3D-MLSAR models by the present method is 1

n~

(3m+3)2+s ~:~ 2 l 1 + ~ -~p(3m + 3) 2 ___-9 Nm ~ + 9 m 2(n 1 _ no) <_9Nm 2 ~t z 2 2

(35)

This means that the total number of computation for the fitting of 3-V MLSAR model by the proposed method is less than 2p/(nl--no) of the conventional method, and is less than twice of that for the fitting single 3-V MAR model. Incidentally, fitting an I-V LSAR model by the same recursion requires (1/2)Nm 2 + ( 1 / 2 ) m 3 ( n l - n o ) . Summarizing, the necessary computing time by the present method is only twice that for ordinary 3-V MAR model, and is 9 times of that for 1-V LSAR model 4

Posterior Probabilities o f the A r r i v a l t i m e

So, it has been shown that we can determine the arrival time of the seismic wave by using MLSAR model and AIC, and that we can develop a computationally efficient algorithm for the computation of the AIC values, In this section, we will present a method that allows using more fully the information contained in the AIC values. In Akaike (1979), it was shown that exp{-(1/2)AIC}is considered as an appropriate definition of likelihood of the model whose parameters are estimated by the maximum likelihood method. In our case p(y[ j) = e x p { - 1 A I C : }

(36)

is the likelihood of the MLSAR model which assumes, that no + pj + 1 is the arrival time,

22

Therefore, if a prior distribution of the arrival time is ~ven, then the posterior distribution of the arrival time can be obtained by

P(J) P(J [Y) = Z jP(Y l J)j)p(j) " P(Y I

(37)

In the actual analysis shown in the next section, the uniform prior over the interval is used. It seems more reasonable to put more weight on the center of the interval. However, since the likelihood, p(y[/), usually takes significant values only at limited interval, only the local behavior of the prior is influential to the posterior probability. Therefore as long as very smooth functions are used, the choice of the prior is not so important for the present problem. One of the most important uses of the estimated arrival time is the determination of the hypocenter of the earthquake. Conventionally, this has been done by the weighted least squares method. However, the use of the likelihoods of various MLSAR models or the posterior distribution of the arrNal time may yield more precise inference on the hypocenter by using the maximum likelihood method or by a Bayesian modeling. This is a subject of the future study.

5 Application of the Multivariate Locally Stationary AR Model Estimating of Arrival Times 5.1 Data Source As in a previous section, let y~ = (.v,e, v.,~. y,u) t, (n=l ..... n) be a three variate time series where ynE,y~; and y,,v, and denote the east-west (E-W), north-south (N-S), and up-down (U-D, vertical) components of the seismograms, respectively. The characteristics of the series, for example the variances and the spectra, change through time because of the arrival of seismic waves such as P or S wave. The fitting of the multivariate AR model to nonstationary time series is applied here to the micro-earthquake data recorded at stations of the Research Center for Earthquake Prediction (RCEP) of Hokkaido University, which was reorganized as the Institute of Seismology and Volcanology (ISV) in 1998. The data we use in this chapter are seismograms of four foreshocks of the 1982 Urakawa-Oki Earthquake ( M j ~ = 7.1, 11:32 on 21 March, 1982, Urakawa, Hokkaido, Japan) recorded at six stations of the RCEP of Hokkaido University (Suzuki et al., 1986). The locations of the epicenters of the four foreshocks and six stations are shown in Fig. 1 and Table 1 summarizes the source parameters of these earthquakes. The epicenters are closely located compared with the spread of the stations. Table 1: Sourceparametersof the four foreshocks. Date

Time

Longitude

Latitude

Depth, km

M

Code

Start time

Mar.21 1982

07:4553.0

142.557

42.158

31.0

1.9

1F

7:45 31.46

Mar.2l 1 9 8 2

08:42 52.0

142.555

42.131

26.0

2.0

2["

8:42 30.44

Mar.21 1 9 8 2

08:49 20.7

142.561

42.158

33.7

2.1

3F

8:48 59.46

Mar.21 1982

09:33 15.0

142.574

42.133

31.1

2.3

41:

9:32 54.55

Mar.21 1982

1l:32 05.7

142.600

42.150

40.0

7.i

23

At each station, the East-West (E-W), the North-South (N-S) and the Up-Down (U-D) components of the ground velocity signal were measured by seismometers with a natural frequency of 1 Hz. They were digitized by 8 bit nonlinear AD converter at the rate of 92.3 samples per second (2,400 bps/26 bits), and transformed to PCM (pulse coded modulation ) data. Each record has 7740 observations (83.85 seconds time span). Fig. 2 shows the seismograms of event 1F (the first foreshock). The station Erimo (ERM) is located 0.5 km from the shoreline of the Pacific Ocean and the epicentral distances are about 50 km. The seismograms are strongly affected by the attenuation in the crustal structure along the ray paths, and the ratios of P wave signal to the background noise are reduced to about 0.5 (Takanami, 1982). Therefore, in the routine work, it is very hard to determine the arrival times of such week P waves record. The station Hidaka 0-IIC) is located 80 km from the epicenters of the foreshocks and is apart from town and traffic road and the amplitude of the background noise is usually less than two LSB (least significant bit). The seismic signal observed at HIC was also very weak and almost equal to one LSB of the digital signal and are comparable to those of the backgrotmd noise. The

0 ,

10

20

50krn

1

,

4~.00 ~

I

HIC 0

/

"~

~~

IWN

/

/

KMU

ESH

l%re=hock

1~

4

-

42.00 Q

Cape Erimo

141.00~

I

I o

142.00 ~

143.00

144.00 ~

Fig. 1. Locations of the epicenters of micro-earthquakes (e) and stations (o) of Hidaka seismologicalnetworkof HokkaidoUniversity. location Iwanai (IWN) is located about 65 km from the epicenters. The observation at this station has higher signal to noise ratios. The station Kamikineusu (KMU) is located about 27 km from the epicenters. On this occasion, the seismograms obtained at KMU were contaminated by a strong electronic hum noise with frequency of 50 Hz. The station Misono (MSN) is located about 30 km from the epicenters and is near a road. Therefore, seismograms obtained in this station occasionally suffer from traffic noise, e.g., MSN-3E The station Moyori (MYR) is about 60 km from the epicenters. Good seismograms were obtained from this station.

24

K/aEil,

......

:

r.ll~il,3, , m r - -

iii: ; iiii

J.

,JJ

.L

J.L

.....ii I

IWU1F

~

~

~

Fig. 2. Seismograms of the first foreshock (IF) observed at Hidaka seismological network of Hokkaido University (Station: ERM, HIC, [WN, KMU, MSN and MYR).

5.2 Determination o f P arrival Time

Although it is not o f our primary concern, we will first consider the estimation of the arrival time of P wave, which is supposed to be much easier than S wave. LSAR model and MLSAR model presented in the previous sections have been applied to the micro-earthquake data presented in the previous subsection. Fig. 3.1 shows a part of MYR-2F data. Fig. 3.2 shows the results o f the LSAR model for this data set. Three figures from top of this figure show the plot of AIC values versus assumed arrival time when LSAR models are fitted to E-W, N-S and U-D components. The minimum AIC estimates of the arrival time obtained by the LSAR model are nn = 3001, 3011, and 2992 for the E-W, the N-S and the U-D components, respectively. AIC values of the estimated models are also shown in the figure. Judging from the original seismogram, the point 2992 seems to be the most reasonable estimate of the arrival time of P wave. The estimates from E-W and N-S components are 9 points (0.098 seconds) and 19 points (0.206 seconds) later than that estimated from the vertical motion, respectively. This phenomenon can be typically seen in the estimation of the arrival time of P wave (see also Table 2). Further, the slope of the AIC value before and after the arrival time is the steepest for the U-D component.

25

41 2aO0

1m2!_. ~. E2F.:... ~ 2gO0

~1000

3100

2800

3200

2go0

,,....m2~...+'.F .......... 28~0

MYU2F

2900

3000

3LQG

....... 3000

. ......... 3"113<1

, ~2~0

"Z,,./ .................

3200

la

-~....m~.~y.. 1787

~.587

~ iooo .....................................

i

3xoo

lloo

3100

3200

3V-~ha'~

x4117 . 2800

2900

300~

r ~ 3.2 Fig.3.1. A part of seismogram of 2F observed at MYR. From top to bottom, E-W, N-S and U-D components. Fig.3.2. AIC values of LSAR and MLSAR models for the estimation of P waves of the MYR-2F data. From top to bottom, LSAR models for E-W, N-S and U-D components and the 3-V MLSAR model. This means that the vertical component o f the seismograms has more precise information about the arrival time o f P wave than the other two components. This can be understood from the fact that the particle displacement o f P wave is often parallel to the direction of wave propagation and the dominant part o f the movement appears in the vertical motion. The bottom one in Fig. 3.2 shows the trace o f AIC of the 3-V MLSAR model. The minimum o f the AIC, 1484, occurs at nA = 2992 which is exactly the same as the one obtained by LSAR model from the U-D component. However, the slope o f the AIC value is steeper than those of LSAR models indicating that the estimate by the M L S A R models is more reliable than the ones by LSAR models. As can be seen in Table 2, for about a half cases LSAR model for U-D component and the 3-V M L S A R model yielded the same estimates. We will next show eases when the LSAR and the MLSAR models yield different estimates. In all cases except for HIC-3F and MSN-3F, the estimates by the MLSAR model are later than the ones by the LSAR models. Fig. 4.1 shows the ERM-4F data. Fig. 4.2 shows the traces of AIC o f three LSAR models and 3-V MLSAR model for ERM-4F data. The estimate by the MLSAR model is 4 points (0.043 seconds) later than the one by LSAR model for U-D component. By a precise examination of the original record, it cart be seen that the LSAR model for U-D component has an ability to detect the slight change o f the slope of the data, which is probably caused by the frequency characteristics of the seismometers. On the other hand, the MLSAR model yields more conservative estimates. H o w e v e r , e v e n w h e n t h e signal to n o i s e r a t i o s a r e v e r y low, s u c h a s t h e ease

26

of H I C , t h e M L S A R m o d e l yields a r e a s o n a b l e e s t i m a t e . Later, b y t h e P ' S plot of t h e e s t i m a t e d a r r i v a l time, it b e c o m e s c l e a r t h a t in t h i s case t h e e s t i m a t e s by t h e M3_~AR m o d e l are m o r e r e a s o n a b l e . Table 2: Estimated arrival time of P waves. The first cohm-mshows the channel-code name of the data. The second to fourth columns show the estimates by LSAR models. The fifth column shows the results by the 3-V MSLAR models. The Last column shows the estimate obtained from the sum of AICs' of three models. Channel ERM-IF ERM-2F ERM-3F ERM~F

E-W 2881 2856 2870 2791

N-S 2869 2865 2873 2792

U-D 2867 2857 2846 2782

3-D 2867 2864 2854 2786

E+N+U 2866 2857 2854 2787

I-~C-1F HIC-2F HIC-3F HIC-4F

3393 3553 3479 3340

3399 3364 3406 3310

3320 3396 3318 3278

3399 3396 3317 3300

3399 3396 3317 3300

IWN-1F IWN-2F IWN-3F IWN-4F

3079 3076 3076 2980

3079 3083 3076 2991

3074 3076 3075 2986

3077 3076 3076 2986

3077 3076 3076 2986

KMU-1F KMU-2F KMU-3F KMU-4F

2636 2638 2630 2540

2637 2638 2637 2553

2622 2622 2614 2518

2626 2622 2615 2531

2624 2635 2615 2531

MSN-1F MSN-2F MSN-3F MSN-4F

2619 2623 2679 2558

26t6 2617 2636 2534

2609 2599 2616 2514

2612 2599 2615 2533

2613 2599 2615 2554

MYR-1F MYR-2F MYR-3F MYR-4F

2999 3001 2988 2909

3014 3011 2996 2916

2986 2992 2986 2902

2995 2992 2988 2902

2995 2992 "2987 2902

27

20QO

-tl .

27QG

.

.

21100

.

2900

.

2800

2700

2800

2900

3000

2600

2700

~

~

3000

-1.O18 tg

,, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-:1.118

-

1~

~

, ~ ,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . " "

,

.

2IM)O

2,700

l

NM'IN AICM

;

.......

= 2'791

= -1318

: ........

4.1

21100

2900

3000

F~ 4.2

Fig. 4.1. A part of seismogramof 4F observedat ERM. Fig. 4.2. AIC values of LSAR and MLSAR models for the estimation of P wave of the ERM-4F data. As a conclusion, for the detection of P wave, LSAR model is very sensitive to the slight change of the characteristics of the series caused by P wave and that the estimates by the MLSAR model can be used to check these estimates. 5.3 D e t e r m i n a t i o n o f S-arrival T i m e

We will examine the advantage of the use of MLSAR model for determining the arrival time o f S wave. The LSAR model and the MLSAR model used in the previous subsection are applied to a part o f the three components seismograms, where S waves presumably exist. Fig. 5.1 shows IWN-1F data. Fig. 5.2 shows the results o f LSAR model analyses. It can be seen that the minimum AIC estimates of the arrival time from the E-W, the N-S and the U-D component are 3929, 3906 and 3958, respectively. The discrepancy between the estimated arrival times by the three components indicates that it is difficult to determine the arrival time of S wave from only one component of the seismogram. Moreover the shapes of AIC traces are much gentle than the case o f P waves suggesting the difficulty of the determination of the arrival time of S wave. Last two panels of Fig. 5.2 show the results by MLSAR models. In this case, the estimates by the 2-V MLSAR model and the 3-V MLSAR model coincide and are identical to the one by the N-S component. Fig. 6.1 and 6.2 show the results for MSN-1F. The estimated arrival time by 2-V and 3-V MLSAR models coincide and are identical to the estimate o f the LSAR model obtained from the E-W component.

28

43

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

i~VE1F

3700 52

380Q

~

...........................

4 ~

4100

3700 3800 ~ 1~1'18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~'.', ........

Z 37DCr

3800

~l)O0

4000

410G

~

47"JS

...... . -

4000

4100

~.-.;..'Tw:

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~ . ~.1

37~Q

38Q0

~900

4000

4100

38a~

34~0Q

40OO

41G0

Fig. 5.1. A part of seismograa'nof 1F observed at IWN. From top to bottom, E-W, N-S, and U-D components. Fig. 5.2. AIC values of LSAR and MLSAR models for the estimation of S waves of the IWN-1F data. From top to bottom, LSAR models for E-W, N-S and U-D ~mponents, 3-V MLSAR model and 2-u MLSAR model. However, the slope of M C values in the neighborhood o f its minimum is steeper than the one by LSAR model. Many local minima are found on each M C curve o f LSAR models as has been inferred from the behavior of the partiele motion of S waves (Takanami, 1990). Therefore, it is usually hard to precisely determine the arrival time by using a single trace, especially only from the vertical component of the seismogram as seen in Fig. 6.2. Fig. 7.1 and 7.2 show the data and the results for MYR-2F. In this ease, the left halves of the trace of AIC of the LSAR models are almost flat indicating that this estimate is not reliable. The estimate by the LSAR model for E-W component is the earliest one. However, in the later analysis, it can be seen that this is not a good estimate. Even in this case, the M C o f the 2-V MLSAR model has a clear minimum. The estimate only from U-D component is more than 100 points (about 1.33 seconds) earlier than these estimates. This clearly indicates that the U-D component is inadequate for the detection of S wave. This can be understood from Fig.2, where in some eases such as ERM, KMU

29

IS6

. . . . . . . . . . . . .

' ......

~

/ ~E:F

4 1 1 5 ~ . .r . 9. ~. ..

. . . . . . . . . . . . .

./A

.....

;I

J

.

.

9.

.

.

.

.

.

.

.

.

.

.

.

.

.

~d[SEIF

.

~ '.'

#

.

.

.

N ~ 3102

.

.

.

.

.

.

.

.

.

.

ALIC ~ 3 8 1 5

4015

"290050 27

3<X30

..........

31~

33~00

~ ..............

9

.

.

.

.

.

.

33~0 .

.

.

.

3 1 1 6 ~I O F [1-G~ ]N .

.MSNIF

.

.

.

.

.

.

2816 .

.

.

.

.

.

.

3100 .

.

t _1

" -25 .

~

3t~lO0

.

.

.

.

.

.

.

.

.

.

.

32OO

33013

N * 3136L . . . . . AIC'" t .-. . . 11116~'~' [ .

.

t

~ .

.

2900

3414

.

.

3000

.

12130

2100

~, , ~ r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

:,J

~ - 3o,1 , ~ - 3114 I

/ ~st~xF l

L

3214

-

3 29G0

5

| ~ 3GO0

31GO

.....

~

;' .....

$114 . 2900

'.' 33Q0

.

.

.

30GO

.

~100

3200

N - 31113

9365

Ate

3300

- 906S

F ' ~ . 6,1

9O651 6718

.........

;

.

.

.

.

.

.

.

.

.

,

30OO 3t, OO .......................................

,

,

32fl@

Fig. 6.1. A part of seismogram of 1F observed at MSN. From top to bottom, E-W, N-S and U-D components. Fig. 6.2. AIC values of LSAR and MLSAR models for the estimation of S waves of the MSN-IF data. From top to bottom, LSAR models for E-W, N-S and U-D components and 3-V and 2-V MLSAR models. and MYR, the presence o f S wave is invisible. Fig. 7.3 shows the posterior distributions o f the arrival time obtained by these models. The posterior distribution obtained by the LSAR model is distributed over a wide region. Whereas the one by the MLSAR model is concentrated on nA = 3812. It is typically seen for many of the seismograms (see Table 3) that one o f the horizontal components (i.e. the minimum o f estimates from E-W and N-S components) coincides with the ones by MLSAR models and that the estimate by U-D component is slightly earlier than this estimate or completely different. Fig. 8.1 and 8.2 shows the analysis o f ERM-2F data. All o f three traces o f AIC values obtained by LSAR models are flat and none o f them yields reliable estimates. In this case, the AIC o f the two MLSAR models have reasonable minima and yield the same estimate. They are quite different from all o f the three LSAR models (see Table 3). 6

Discussion

Using the start time o f the record, ts given in table 1 and the estimated arrival time point, n~., given in Table 2 and Table 3, we can get the arrival time

30

-

7 3800

4

~ 3700

''~ 3800

....

:. . . . . . 3g~O

I 4000

3C~0

3700

3800

391XI

400@

34.23t MYN2F

N - 3~2 MC - 3223

34101 M ~ 2 F

N = 3(~1 AIC 311' ]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -. . . . .

32113 3110 3(=00 311SO0

3700

351X:l Fig.

3~1130

==

~ 3700

3800

3900

4000

4000

7.1

7972

"~ .............

9 ........

~72 ] 2V-M~LSAR

3700

,. . . . . . . . . . . . .

~ ~3

~

3BOO

~

Fig. 7.1. A part of seismogram of 2F observed at MYR. From to bottom, E-W, N-S and U-D components. Fig. 7.2. AIC values of LSAR and MLSAR models for the e~imation of S waves of the MYR-2F data. From to bottom, LSAR models for E-W; N-S and U-D components and 3-V and 2-V M_LSAR models9

O. 10

9

3718

37~

37S.B

3T~JI

3798

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J

,

3621

. . . . . . . .

;

"'t 0.~ 3782

.......

~ ........ 3&02

' 3822

; 3E42

3~c62

3772

. . . . .

:

. . . . . .

,

-

3

1

....... t 3792

,

.

3a~2

.

.

.

.

.

.

.

.

.

~12

.

.

.

.

.

.

.

38~2

Fig. 7.3. Posterior probabilities of the S arrival time for MYR-2F data. LSAR models for E-W (top left), N-S (bottom left) and U-D (top fight) components and the 2-V MLSAR model (bottom

right).

31

..............

.1.52.7.

? . ,i-'~-'~... . = ?. ,

.

: ........

3S00 41+11

=I++

)PalJJ2F

-11.2

3400

3~OD

37Q0

35~0

. . . . . . . . . . .

3400 3500

; ......

,,q

3700

3800

.7 :

3400

,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

384~r

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

118

42:3

10

.,+

'. "-.

3500

3600 9 -'.

3700

. . . . . . . . . . .

3(100

3800

". . . . . . . . . . .

3700

3~00

3800

F ~ 8.+.

24 t

2V-M:LSAR

N

-

3576

AIC

! -17e 3400

- -176 I

! 3500

31600

e~.

3700

3800

8.2

Fig. 8.1. A part of seismogram of 2F observed at ERM. From top to bottom, E-W, N-S and U-D components. Fig. 8.2. AIC values of LSAR and MLSAR models for the estimation of S waves of the ERM-2F data. From top to bottom, LSAR models for E-W, N-S and U-D components and 3-V and 2-V MLSAR models. 26 ta =t, +n A - . (38) 2400 e and t~ - t o Therefore, by denoting the arrival times o f P wave and S wave by t A respectively. Fig. 9.1 shows P wave travel time versus S wave travel time plot. Since the hypocenters of our foreshocks are very closely located, four points obtained from the same station should locate closely each other. Further, if the ratio o f the velocities o f P wave and S wave is a constant over the region, these points obtained for various stations lie on a straight line. However, in Fig.9.1, these points look rather scattered. To get freer relation between P and S travel times, we ftrst refined the origin times of the foreshocks given in Table 1. To do that, we compute the mean of the four travel times and then compute the deviations from the means. Then the mean of these deviations at five stations, excluding I-1IC, gives the bias of the origin time of each foreshock. Fig. 9.2 shows the same plot as Fig.9.1 obtained by correcting for the bias of the origin time. Here the arrival time, hA, is obtained by the MLSAR model.

32

Table 3: Estimated arrival times of S waves. Code name ERM-1F ERM-2F ERM-3F ERM-4F

E-W 3582 3622 3538 3382

N-S 3565 3515 3563 3553

U-D 3423 3733 3466 3623

E+N+U 3500 3577 3537 3543

3-D 3497 3577 3537 3458

E+N 3582 3577 3538 3358

2-D 3481 3576 3538 3458

I-tlC-1F HIC-2F HIC-3F HIC-4F

4462 4501 4477 4399

4484 4600 4423 4532

4376 4507 4426 4572

4484 4501 4423 4540

4505 4501 4612 4533

4484 450t 4602 4540

4484 4501 4423 4421

IWN-IF IWN-2F IWN-3F IWN-4F

3929 3927 3947 3855

3906 3911 3925 3864

3958 3898 3880 3843

3906 3919 3947 3843

3906 3887 3925 3843

3906 3919 3925 3850

3906 3919 3925 3854

KMU-IF K.MU-2F K_MU-3F KMU-4F

3156 3154 3130 3086

3174 3164 3168 3100

3116 3218 3207 3176

3156 3154 3146 3093

3117 3149 3130 3089

3156 3154 3146 3093

3156 3154 3130 3089

MSN-1F MSN-2F MSN-3F MSN-4F

3102 3106 3042 3014

3136 3074 3002 3002

3091 3108 3015 3033

3102 3105 3066 3032

3103 3067 3100 3033

3102 3105 3066 3002

3102 3106 3097 3002

MYR-1F MYR~F M'YR-3F MYR-4F

3819 3758 3775 3758

3843 3822 3763 3757

3939 3661 3756 3501

3812 3805 3778 3758

3812 3806 3778 3758

3816 3812 3763 3758

3816 3812 3781 3758

It can be seen that, four points corresponding to the same station, mostly locate closely than Fig.9.1. This shows that by the above method, better estimates of origin times were obtained. In these figures, horizontal variation corresponds to the estimation error of P wave, whereas the vertical variation does that o f S wave. Comparing these two figures, it can be seen that the points by M L S A R model with the correction o f the origin time are much closely located. One way to simplify the present procedure is to use the sum o f the A I C ' s o f three L S A R models obtained by fitting to each o f E-W, N-S and U-D components. This is equivalent to assume that these three components are independent. The estimated arrival times by the method are shown in the extreme right column o f the Table 2 and 3.

33

g

.....................................

148

...........

'..........................

ERE2F

-I,5 .

.

.

. 3400

3500

3600

3700

/

31S~ F.,RN2~"

N - 3S1~

A I C - 118

/ 3400 10

3500

3ai~

3790

3400 3500 3600 ;11700 3800 425 / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3I.S~ ERU2F N = 3733 A I c - IT.S I

34100

...................................... ]~RU2F

225

3400 3~ 3~ -8 .......................................

3400

35~

3600

124 I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 2 V - b ~ N - 3576

37~

3800

3700

38Gr

A I C ~ -176

/ 6 . "173400

.

. 3500

.

1800

37(]0

', 3800

F~. s.2

Fig. 8.1. A part of seismogram of 2F observed at ERM. From top to bottom, E-W, N-S and U-D components. Fig. 8.2. AIC values of LSAR and MLSAR models for the estimation of S waves of the ERM-2F data. From top to bottom, LSAR models for E-W, N-S and U-D components and 3-V and 2-V MLSAR models. In all cases, the sum of three (or two) AIC's are significantly larger than the AIC of the M L S A R model. This indicates that the series are actually not independent. However, as can be seen in Table 2 and 3, for many of series, the minimum points obtained from these two models coincide. Therefore, at least, for the seismograms with high signal to noise ratios, the use of this simplified procedure might be reasonable. It might be interesting to compare the estimates shown in Table 2 and 3 with ones obtained by experiences persons. Fig. 10.1 shows the histograms of the P arrival times read from the seismograms by 38 researchers of RCEP or students of Geophysical department of several universities. The mid points of the histograms show the P arrival times estimated by the LSAR model for U-D components. The number of unanswered person is also shown in the right margin o f each histogram. It can be seen that the estimated P arrival times are distributed around the center and generally have good coincidence with the estimates by LSAR model. However, for KMU data, the estimates by LSAR model precede 20 - 40 points. This is due to the presence of hum noise and the human operators could not detect small signal berried in the hum noise.

34

2~

2~

,,

~SAR 26-

IIlC

I-tiC

;14

24"

22-

22

(•IWN

VWN 20-

20

18-

18

'0 ERM

ERM 16-

16

14-

1-4

12- ~

KMI.r 12.

t0

'O

26-

MSN 10

12

14

10

6~e

FI~ 9.!

~ IO4U MSN s

x2 F~ 9.2

1~

l~ ' ~

Fig. 9.1. P vs. S arrival times for LSAK models. Origin times of the earthquakes were estimated by RCEP of Hokkaido University. Horizontal axis indicates the estimated P arrival times. Vertical axis indicates the estimated S arrival times. Fig. 9.2. P vs. S arrival times for MLSAR models. Origin times are modified by the method shown in discussion. Horizontal axis indicates the estimated P arrival times. Vertical axis indicates the estimated S arrival times. Fig. 10.2 shows the cases o f S arrival times. The mid points o f the histograms show the estimates by the 2-V MLSAR models. The histograms are scattered over wide region indicating the difficulty o f the estimation of S arrival time, On the other hand, however, from the S-P plot shown in Figs. 9.1 and 9.2, it was shown that the MLSAR model can yield reasonable estimates for most of the data sets. Thus the merit of the time series method becomes clear. Fig. 11 shows the changing spectra (Kitagawa, 1983) o f the three components of MYR-1F data obtained by the program TVCAR of TIMSAC-84 (Akaike et al., 1985). In the computation, the estimated arrival times were used to specify the change points of the spectra. Based on this information, the changes of spectra are clearly detected. It can be seen that after the arrival o f S waves, the spectra o f the series gradually change and go back to the original shape o f background noise. However, the significant change occurred only when P wave and S wave arrived. This supports our assumption that the seismogram before and after the arrival o f the new wave is reasonably expressed by a single A R model. The reader may wonder the relation between the proposed numerical algorithm and the Kalman filter. For simplicity, we consider the univariate case. For the application of the Kalman filter, we will use the following state space representation of the A R model:

35

~aa

.

.

.

.

:~ ...ll II

Fig. 10.1

Fig. t0.~

Fig. 10.1. The histograms of the estimated P arrival times by human operators. The center of each histogram indicates the estimate by the MLSAR model. Fig. 10.2. The histograms of the e~znated S arrival times by human operators. The center of each histogram indicates the estimates by the MLSAR model.

x, = x,_ I

(39)

Y,, = n n x n + w , ,

where, x, = (a~), -. 9, ,_(.)~, r_r = (y,_~ ,..-,y,_,,) andw, is the Gaussian white noise with , ) ,,~, mean 0 and the variance o-2 . By using this expression, the Kalman filter can yield tha L S A R model with the same order o f computations. However, the Householder method has the following two merits compared with the Kalman filter. Firstly, by the use o f Kalman filter, the necessary computation is approximately 4kZN, whereas by our method it is less than k~N. This difference appears since the Householder method can automatically use the merit o f symmetry o f the matrix and since in our method the variances o f the regression coefficients are not explicity evaluated. Secondly, by our method we can automatically get the minimum value o f the A I C ' s o f the A R models with orders less than or equal to m, whereas the Kalman filter can yield only the A I C o f the A R models o f order m.

36

Fig. 11. Changingspectraof MYR-1F data. 7

CONCLUSIONS

The objectives of this chapter were three-fold. Firstly, we have presented a computationally efficient procedure for the fitting of multivariate locally stationary autoregressive (MLSAR) models. By the proposed procedure, it becomes possible to fit all of the necessary MLSAR models for determining the arrival time of a signal only a few times as much as the computation for fitting single multivariate AR model. This makes it practical to use the MLSAR model in an on-line system for automatic detection of earthquakes. Secondly, we have shown a method of obtaining the posterior probability of the arrival time. It is expected that this posterior probability will be useful for the estimation of the hypocenter of the earthquakes. It was also used for the changing Spectrum estimation. Thirdly, the proposed method was applied to various seismograms of foreshocks of the 1982 Urakawa-Oki Earthquake. By this empirical study, it has been seen that 1. For the estimation of the arrival time of P wave, the information on the U-D component is usually sufficient. However, even when it is difficult to determine the arrival time only from the U-D component, the 3-V MLSAR model might give reasonable estimates. 2. For the estimation of the arrival time of S wave, 2-V MLSAR model for E-W and N-S components yields the most reliable estimate. In particular, even when the LSAR model yielded very flat M C values and was difficult to determine the minimum, the AIC of the 2-V MLSAR model had a clear minimum. In summary, for the estimation of the arrival times of S waves, the use of the 2-V MLSAR model is adequate and the fast algorithm presented in this chapter facilitates the application of this model in online systems.

37

Acknowledgments The present work was written under the permission of the Institute of Statistical Mathematics, using most of the parts of previously published paper (T. Takanami and G. Kitagawa, "Estimation of the Arrival Times of Seismic Waves by Multivariate Time Series Model", printed in the Journal "Annals of the Institute of Statistical Mathematics, Vol. 43 No. 3, 1991). We wish to express our thanks to the Institute of Statistical Mathematics for allowing its publication. References Akaike, H., 1973, Information theory and an extension of the maximum likelihood principle, in Petrov, B. N., and Caski, 17.,eds., Second International Symposium on Information Theory, Budapest, Akademiai Kiado, 267-281. Akaike, H., 1979, A Bayesian extension of the minimum AIC procedure of autoregressive model firing, Biometrica, 66, 237-242. Akaike, H., Kitagawa, G., Arahata, E., and Tada, F., 1979, TIMSAC-78, Compt. Sci. Monographs, No. 11. Akaike, H., Ozaki, T., Ishiguro, M., Ogata, Y., Kitagawa, G., Tamura, Y-H., Arahat~ E., Katsura, K., and Tamura, Y., 1985, TIMSAC-84 Part 1, Comput. Sci. Monographs, No.22. Buland, R., 1976, The mechanics of locating earthquakes, Bull. Seismol. Soc. Amer., 66, 173-187. Golub, G., 1965, Numerical methods for solving linear least squares problem, Numer. Math., 7, 206-219. Hamaguchi, H. and Modta, Y., 1980, Second order atttoregressive representation of short-period seismic waves, Zisirg Ser. 2, 33, 131-140 (in Japanese with English abstract). Hamaguclfi, H. and Suzuki, Z., 1979, Automatic detection of onset time of micro earthquake and its confidence, Report of grant-in-aid for scientific research project on natural disaster, No. 54-2, 62-83, Ministry of Education, Science and Culture, Japan. Hasegawa, A., Umino, N., Yamamote, A., and Takagi, A., 1986, Automatic event detection and location system of micro earthquake observation network, Zisin, Set. 2, 39, 381-395 (in Japanese with English abstract). Kitagawa, G., 1983, Changing spectrum estimation, J. Sound Vibration, 89, 433-445. Kitagawa, G., and Akaike, H., 1978, A procedure for the modeling of non-stationary time series, Ann. Inst. Statist. Math., 30, no. 2, 351-363. Kitagawa, G., and Akaike, H., 1980, On TIMSAC-78, Applied "Vtme Series Analysis II, 499-547, Academic Press, New York. Meeda, N., 1985, A method for reading and checking phase time in auto-processing system of seismic wave data, Zisixt, Set. 2.38, 365-379 (in Japanese with English abstract). Ozaki, T., and Tong, H., 1975, On the fitting of non-stationary autoregressive models in the time series analysis, in Proceedings of the 8th Hawaii International Conference on System Science, Western Periodical, Hawaii. Sakamoto, Y., lshiguro, M. and Kitagawa, G., 1986, Akaike Information Criterion Statistics, Reidel, Tokyo. Suzuki, S., Takanami, %, Motoya, Y., Kasahara, M., and Nakanishi, I., 1986, Automatic processing system for micro earthquake network of Hokkaido University, Proceedings of the Annual Meeting of Seismological Society of Japan, April (in Japanese). Takanaml, T., 1982, Three-dimensional seismic structure of the crust and upper mantle beneath the orogenic belts in the southern Hokkaido, Japan, Journal of Physics of the Earth, 30, 87-104. Takanami, T., 1991, A study of detection and extraction methods for micro-earthquake waves by

38

autoregessive models, J. Fac. Sci., Hold~aido Univ., Ser. 7, Geophysics, v. 9, no. 6, 67-196. Takanami, T., and Kitagawa, G., 1988, A new efficient procedure for the estimation of onset times of seismic waves, J. Phys. Eartk v. 36, no. 6, 267-290. Tjastheim, D., 1975, Autoregressive representation of seismic P wave signals with an application to the problem of short period dise6minates, Geophysical J. Roy. Astr. Sot., 43, 269-291. Yokota, T., Zhou, S., Mizoue, M., and Nakamura, 1981, An automatic measurement of arrival time of seismic waves and its application to an on-line processing system, Bull. Earthquake Res. Inst., Univ. Tokyo, v. 55, no. 3, 449-484 (in Japanese with English abstract).

39

Automatic Interpretation of Regional Short Period Seismic Signals Using CUSUM-SA Algorithms Zoltan A. Der ~ and Robert H. Shumway 2

1ENSCO Inc., Springfield, VA, U.S.A. "~Universityof California at Davis, Davis, CA, U.S.A. Abstract. Several simple methods for the automatic interpretationof short period regional seismogram were tested. Because of the emergent nature of most regional arrivals, the onsets of seismic phases are associated ~Sth gradual, rather than sudden, changes in the autoregressNe models and mean square amplitudes. We have found that amplitude contrasts between windows containing the seismic phase and the noise (background prior to the arrival) can be enhanced by filtering making use of autoregressive models and thus in the further analysis we utilize only the enhanced amplitude changes for defining onset times. The interpretationprocess consists of two steps; iterative segmentation of the seismogram to isolate time intervals where sudden changes occur and the onset time estimation performed on these segments. For segmentation, we have applied two main methodologies. One involves variants of the iterative segmentation method developed by Inclfia and Tiao (1994). The original Inctfin-Tiaoalgorithms were modified in several ways; for finding the preliminary onset times the minima of the cumulative sum of absolute trace amplitudes, rather than their squares is used. This is followed by the declaration of onset times using standard F tests. The iterative process was also modified in continuing the iterations, until a preset number of iterations were completed, even though some F tests detected no significant changes in the intermediate iterations. Besides the Inclhn-Tiao approach we have tested segmentation methods based on finding maxima of the leaky-integrated absolute values of the seismic traces by various methods, including simulated annealing, to define segment boundaries. We have found that the automatic process for estimating onset times for Pn performed nearly as well as a human analyst, though the onset times were, on average, about 0.1 second late. This is a systematic bias that can be estimated and corrected. Interestingly, the fluctuations in the errors made by both the automatic processes and the human interpreter were similar when presented with the same noisy data samples. Automatic segmentation and interpretation of complete regional seismograms has been accomplished by several methods, though some methods work better than others depending on the particular nature of the seismograms.

1 Introduction Automatic phase arrival time estimation is of considerable interest because o f the need for rapid location and identification of numerous seismic events by networks monitoring natural and man-made seismic activity. Times of seismic 'phase' arrivals can be defined as time instants, where some visible characteristic, such as amplitude, frequency content or wave polarization changes. Typically, regional arrivals are high frequency, broadband, emergent wave groups containing numerous cycles. Later arrivals generally have no clear, impulsive waveforms, are preceded by the codas o f earlier phases and their onset times can only be defined to within a few cycles. Besides locating events fi:om Pn times at multiple stations, onset time estimation is useful in facilitating location using multiple arrivals in the same seismogram and in automated application time and frequency domain discriminants.

41

Most statistical methods for detecting changes assume only one change in the time series. Original methods for binary, iterative detection of multiple change points, such as those proposed by Incl~n and Tiao (1994) and Chert and Gupta (1997) for general time series, do not seem to work well for regional seismograms without suitable adaptations to seismic data. Handling multiple changes requires the isolation of the segments of the time series where only one major change occurs. The need for segmentation of the seismic data is akin to similar techniques required for successful decomposition of even more complex signals in other fields, such as human speech and electrocardiograms. High fxequency recordings of seismic events typically contain multiple wavetrains of seismic energy with elevated amplitudes and subsequent decreases (codas) in amplitude. We are interested in the times of sudden increases in amplitudes - - onset times. Codas of seismic phases are of little interest in this context_ The segments that we need should include the time of sudden changes with sufficient quasi-stationary lengths of the time series preceding and following the onset time. We reduce the onset time estimation to detection of sudden changes in variance, rather than trying to detect changes in AR models of the time series. This can be accomplished in most cases by appropriate pre-filtering. Various kinds ofprefilters have been developed for enhancing the amplitude of signals. In this application causal versions of these must be used. For three-component and array recordings other possibilities for segmentation exist, based on polarization and slowness changes. Moreover, generalized polarization analyses developed for arbitrary sets of sensors (Der e t al., 1993) can aid in segmenting regional seismograms originating from limited source areas into distinguishable arrivals. In this paper we concentrate on finding arrivals in single traces.

1.1 General Statistical Baekground Onsets of packets of seismic energy associated with various paths, i.e. seismic phases, are usually associated with sudden changes in amplitudes, spectra, polarization and slowness. It is usually assumed that the time series are stationary before and after such a change and that the statistical distributions are multivariate Gaussian (e.g. Basseville and Nikiforov, 1993). A popular approach is to test for changes in single- or multi-channel autoregressive models to the data of the form where x(t) is the multidimensional time series, the constants in matrix A~ are regression coefficients and e(t) is a stationary noise vector process. The number of channels, p, in various applications may be one (a single seismic channel), three (three component station) or many (a seismic array). In this process, the autoregressive parameters Ak will have to be estimated (Pisarenko et al., 1987). x(t)=~-~ A kx(t - k)+ e(t)

(1)

k'=l

The determination of the onset times is based on residuals r of the autoregressive models computed by using the estimated autoregressive parameters Ak in (2). r(t)=-x(t)-~~ X kx(t - k)

(2)

k=l

Depending on the autoregressive models applied one may test for spectral and amplitude changes (single-channel model), slowness changes (multi-channel model applied to array sensor outputs) or polarization (three-channel model) as described by Kushnir (1996). In the purest form of such methods, the model fitting, can be performed 42

for each guess of the onset time (Taylor et al. 1992; Takanami, 1991) or, alternatively, a single fit to two fixed models fitted at each side of the possible aarival times may be used (Kvaema, 1966a,b). The minimum o f the summed squared residuals occurs when two models are fitted on either side with the boundary o f the fitting regions corresponding to the onset time. In any case, repeated application of autoregressive analysis may represent an unnecessarily heavy computational load that can slow the analysis. If the autoregressive analysis is performed only once for a signal and noise window, then the process will be similar to ours, as we shall show below. Common to all such methods is the assumption that the time interval where the phase onset occurs is known and there are sufficient segments o f the time series preceding and following the onset for effect the estimation models. The approach described above is quite general and is applicable to many kinds o f problems involving changes in time series. Regardless what kind of test statistic is used for detecting changes a step-like change can be detected easier if a cumulative sum (CUSUM) of it is computed (Der and Shumway, 1999; Iclan and Tiao, 1994; Basseville and Nildforov, 1993; Shumway, 1998), alter the application o f appropriate pre-filters. After imposing a linear trend to the CUSUM, repetitive onset time estimation is performed, locating the minima or maxima of various chosen functions, by simulated annealing (SA) or simply finding a minimum. The clustering in the multiple SA onsets time estimates provides a means to assess the reliability o f the process and t h e significance of each major arrival. The approaches based on the cumulative sum statistics are simple to apply and can be automated for applications in a Comprehensive Nuclear Test-Ban Treaty (CTBT) monitoring environment. I n c l ~ and Tiao (1996) developed a properly centered and normalized CUSUM test statistic and tabulated critical points for testing of significance. Furthermore, they developed a binary Itemtive Cumulative Sum o f Squares (ICSS) algorithm that allows sequential identification of multiple change points in a white noise series. In this work, we have tested their approach on a set of regional seismic data. Suppose first, that a single channel time series x~, x=l,2 ..... n is observed and we have a possible change point that is to be detected using a CUSUM type statistic. Assume that the time series x has been prewhitened and has a zero mean, so that the change in regime can be modeled simply by a change in the variance o f the white noise process. InclS.n and Tiao (1996) proposed using the centered and scaled cumulative sum o f the squared amplitudes. First they define the sum of squares function over the interval [1, k] of length points as k

c, =

(3) I=I

The scaled and normalized CUSUM statistic over the interval [1,7] at the point I
Dk=.Ck tc

(4)

The F statistic for testing for a change o f variance at time ~c is

(5)

eT . . . .

This is of course the standard power detector. With no change in variance in the time interval I<~
43

continuous equivalent D(t)) will have a maximum at the change point. If we assume that the xi are normally distributed with mean 0 and variances ~ then we can obtain the likelihoods for testing one change against no change and let NT=I represent one change. The likelihood for NT=O is

l(Nr=O;x~-~T~log(2z)-Tlog[Cr / rl, r z z 2

(6)

The likelihood function forNT=l, change at point t is

---Y-

(7)

The best estimate of the change point is where the likelihood ratio is maximized = tc T logL(Ic,o-~,o'2)~-max{-~-log(l+~-D.) T;tClog(X

T

T_tcD,~)}.

(8)

The function puts more weight on the middle of the time series. This is not a serious disadvantage since before applying the algorithm one has a good idea where the main regional phases are (from standard detection algorithms and F-K analyses). All the previous formulas assume that the time series were pre-whitened. In doing F-tests with bandwidth limited data the degrees of freedom used in the assumed F distributions should be appropriately reduced to account for the limited bandwidth. The paper by Chert and Gupta (1997) uses a corrected form of AIC, say

AIC(C(Ir

4(r~c- ~c2 - T) = - 2 log L(tr o-~,cr~) + (~_--~)(T---~-_--~)

(9)

for 2<~:
44

terminating the procedure when an F-test failed, we continue the iteration until the specified number of iterations is completed. When the function DQr has a maximum instead of a minimum (signifying a decrease in amplitudes) we use this for a new segment boundary. This way we are able to pick out additional significant arrivals. In addition, we ignore minima in the DQc) function where they are close to the segment boundary. Again, this allows us to pick out arrivals further down in the iteration process. In the earlier part of our work, we have also used the minimum of the trend-adjusted CUSUM of the absolute trace amplitude. The alternative to the CUSUM is

Zlx~

(10)

The trend-adjusted alternative to the D(g) function of Incl~n and Tiao (1994) is computed as before by Equation (2). We have found that the minimum of this function is a better estimate of the phase arrival time. We prefer versions of the procedure that use the minimum of this function, but apply the same F test as before, using the ratios of powers of the trace before and after the onset, for testing of the significance of an arrival.

1.2 Pre-Filtering Issues Subtle changes in the frequency content in noisy records often give clue to a human indicating the onset of a seismic phase arrival. When such human capabilities are needed, on the other hand, it simply indicates a failure of applying appropriate frequency domain pre-filtering that could produce an enhanced amplitude contrast between the noise and the arrival. Appropriate pre-filtering in frequency is a prerequisite for further onset time determination regardless of the method but the results do not depend much on the particular pre-ftlters used as long as they are 'reasonable' (Kvaerna, 1996a, b). Various schemes for optimum pre-filtering were suggested: most of these seem to work well in practice and the exact nature of filter is not critical as long as they are reasonably close to the optimum SIN2 shape (averages of signal amplitude spectrum divided by the squared noise amplitude spectrum). Minimum phase filters based on Kvaerna's definition of 'usable bandwidth' (Kvaerna, 1995, 1996a), as well as those shaped according to SIN2, where S and N are signal and noise spectral amplitudes respectively, or noise-adaptive predictive filtering all enhance the amplitude contrast between the noise background preceding the onset of the signal. Empirical fixed 'optimum' filters defined for a given region being monitored or path type seems to work as well. Such filters for regional signals will reduce the amplitude of the low frequency noise below 2 Hz, emphasize the band where the SIN is nearly constant, in the 3 -10 Hz range, and reduce the low S/N portions of the spectra at very high frequencies. This enhancement 0fthe signal amplitude always happens at the expense of decreasing the visible frequency contrast between the signal and noise. This is because both regional seismic signals and noise have similar spectral shapes in the 3 -10 Hz band, in which they both fall off with frequency. Following the application of such pre-filters we may utilize only the amplitude changes to locate the phase onsets. "Iqaese statements seem to be generally true for typical regional seismograms, especially in shield regions such as Scandinavia, where most of the seismic signal energy is concentrate in the 3 -10 Hz band regardless of phase.

45

1.3 Onset Estimation Toolkit Despite early successes in onset time picking by CUSUM-related techniques (e.g. Der and Shumway, 1999), we have always struggled with the problem of proper segmentation of regional seismograms prior to the application of statistical testing for changes in variance. Besides the CUSUM-based algorithms for detecting single changes in a seismogram segment developed by Basseville and Nikiforov (1993), Incl~n and Tiao (1994), Chen and Gupta (1997) and N'ddforov et al. (1986, 1989) we may apply additional methodologies for analysis of complete seismograms. These additional tools listed below, assist us to segment the complete seismograms to provide time windows to be probed for single arrivals using the methods above for defining single onset times.

1.3.1 Leaky Integration An alternative to the function D(t) described above is the outcome of the leaky integration of the absolute amplitudes of the pre-filtered seismic trace which we denote as L(t). The maxima of this function occur typically after the maximum amplitude of the phase arrival, in the early part of the coda. Thus the locations of these maxima can be used as segment boundaries. The leaky integration decay constant can be adjusted to capture arrivals of various durations.

1.3.2 Simulated Annealing Instead of finding an absolute minimum in the CUSUM-linear trend sum, the minimum can also be located by randomized search methods. In the work presented, we have used the method of simulated annealing (SA). SA was designed to find global minima of irregular functions where many local minima may exist. It tends to disregard minor local minima and converge to the lowest points. It uses the randomized Metropolis search algorithm, which is based on a thermodynamic analogy (Press et al., 1986). Initially, it allows a search using large steps in the independent variables, which may even be associated with increased values of the function. This allows the solution to "jump out" from local minima and resume searching for other minima. As "cooling" occurs such steps are accepted less and less and finally the solution will settle in broad global minima. Cooling rates and rejection criteria are adjustable for optimizing performance. Repeated application of SA with random starting points will give rise to populations of onset time estimates. Alternatively, the method can be used for finding the maxima of the function L(t) to define segment boundaries.

1.3.3 Cluster analysis The multiple application of SA searches automatically provides a means for assessing the stability and accuracy of the onset estimates derived from the SA method. Starting out with numerous randomly chosen positions for the onset time within a search window these will converge into positions of prominent CUSUM minima and form a varying number of fight clusters. Besides these there will be hopefully much fewer scattered 'solutions' that are obviously spurious and thus must be discarded. This approach has a considerable potential (Der and Shumway 1999). We apply the well-known K-means

46

clustering algorithm (Ton and Gonzalez, 1974; Theodoris and Koutroumbas, 1999) for fmding the clusters in a population of SA onset times or trace amplitude maxima in this report. We use the square of the distance as a metric in this 1-D clustering scheme

2

Practical Examples o f the Application o f Methodology Described

In the follow-ing we describe the results of the applications of the various algorithms outlined above to actual seismic data recorded at regional or near teleseismic distances. Although the exact source of events used is immaterial to this presentation, we shall identify the origins most example events utilized.

2.1 Performance of the CUSIsWI Procedure for Estimating Pn Onset Times In the following we show evaluations of the performance of the CUSUM minimum and the combined CUSUM-SA procedure for picking onset times of fu'st-arriving P n phases. The evaluation is based on comparing the performances of a) human analysts b) picking the absolute minimum of normalized CUSUM and keeping the arrival if the F tests is passed c) picking the median of multiple picks using SA on the CUSUM and taking the median of these, but discarding the result if the SA arrivals are highly scattered. Prefikering preceded all the data processing. The two kinds of pre-filters applied to the seismograms were 2 - 7 Hz Butterworth band-pass filters and minimum phase filters designed by taking the S / N 2 spectral ratio such that the maximum was set at unity and cutoffs were placed at the values at 0.24. The latter are similar to the filters that define "useful bandwidth." We have seen little difference in the performance of these filters in accordance with the comments made by Kvaema (1996a). The events used had originally very high S / N ratios, especially on the pre-filtered traces. To provide a "true" onset time the practically noise-free original trace was picked by the analyst after he has gone through all the noisy examples presented to him. Thus, the objective standard is this onset, not the analyst as it is ot~en assumed. In order to construct noisy data we have fitted a 15th order AR model to the noise prior to the signal arrival and this model was used to construct independent noise samples by filtering Gaussian white noise. In retrospect, lower order of noise AR models (down to 6) could have been satisfactory. The noise samples were added to the signal (mean removed) with various signal-to-noise ratios. In order to prevent the analysts from learning the exact position of the signal from previous examples by using the same signal, random delays were introduced in each frame, which were removed by differencing in the final step of the analysis. As a further measure to prevent such 'cheating' we have presented the noisy signals in the order of increasing signal-to-noise ratio. In the first low SNR examples one could not detect the signal visually at all. The differences between the 'true' onset value and the other onset time estimates were plotted for all the three methods against the logarithms of SNR values, with the random time shifts removed, of course. This is the same kind of evaluation method as the one used by Kvaema (1996 a, b), Yokota et al. (1981) and Maeda (1985). Examples of results from these procedures are shown in Figs. 1 and 2. Unlike in the original Inclfin-Tiao procedures, the D(t) functions used in the CUSUM in this examples were accumulations of the absolute values of the trace amplitudes, followed by conventional F tests (using squared amplitudes) to establish statistical significance.

47

Analyst 1131

101

d)

o~

z 03

CUSUM-minimum

CUSUIVI-SA

101

~)

0 0

0

O

I0~

-2

0

2

100 O 10~ -2 O 2 -2 Onset time error in sec

O

O

ao

Anal' rst

10 ~

CUSUM-minimum

,o

CUSUIV!-SA

101 oo

rr z co

o

o

o

Fo

o

10~2 "'

' 0

2

100 -2 0 2 Onset time error in sec

i0~ L -2

o

O

o

2

b~ Analyst

101 n," Z co

101

o

10o -2

o 2

c

10;

~o

~ 0

CUSUM-SA

CUSUb/I-minimum

c(

r

o

o

10o o I -2 0 2 Onset time error in sec r

Fig. 1. Comparison of the Pn onset picks with various S/N ratios. The picks on the left were made by an analyst, those in the middle were CUSUM minimum picks accepted only if the F-test was passed. Those on the right were made by a CUSUM-SA combination, and were accepted only if s of the trials were less than .5 see uear the median. Even though the analyst has the best performance, the second method come fairly close. Automatic picks tend to be somewhat later than the analyst. These picks were made for the events K2054, K2066 and K2110 listed by Der and Shumway (1999).

48

Analyst

101

'

lO

t0 ~

0

z

0

0

io

i 1110 -2

[J

CUSUM-SA

CUSUM-minimum

o 'C~ O 0

2

1

o~

Oo o ~ o

4

c

10~ o l 10 ~ -2 -2 0 2 Onset time error in sac

O

0

2

a. Anal, 'st o

101

101

CUSUM-minimum o

101

os

CUSUM-SA o

o o o

%

t.~ z r.z3

o

o

o

-2

o

0

2

o

10o 10o -2 -2 0 2 Onset time error in sec

o 0

2

b~

Anal' ~st 101

10 ~

CUSUM-minimum ) ) :1 10 o -,

CUSUM-SA c o C

,.j

o o

rt" z Go

1 -~

~o o

1 100 -2

0

2

10~ o, 10 ~ -2 0 2 -2 Onset time error in sec

0

0

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c. Fig. 2. Comparison the Pn onset picks with various S/N ratios. The picks on the let~ were made by an analyst, those in the middle were CUSUM minimum picks accepted only if the F-test was passed. Those on the fight were made by a CUSUM-SA combination, and were accepted only if s of the trials were less than .5 see near the median. Even though the analyst has the best performance, the second method come fairly close. Automatic picks tend to be somewhat later than the analy~. These picks were made for the events K2285, K4025 and I{4130 listed by Der and Shumway (1999).

2.1.1 Statistical Analysis o f the Three Onset Time Estimation Procedures In order to be able to m a k e m o r e quantitative statements w i t h regards to the a c c u r a c y o f the three m e t h o d s w e h a v e p e r f o r m e d statistical analyses o f the results o f n u m e r o u s repeated tests on a f e w o f the K o l a p e n i n s u l a e v e n t e x a m p l e s used before. A s before, we

49

have stepped through the analysis in the order of increasing SNrR many times, using different synthetic noise samples for each, and made histograms of the results. O f course, the results depend on the characteristics of the onsets themselves. For sharp, impulsive or step-like amplitude increases the estimates are more accurate, relative to the 'true' arrival time picked from the high SNR raw trace, than for emergent arrivals. It appears that the automatic processors tend to make the same kinds of mistakes as a human analyst. This is also seen in the individual examples shown in the preceding figures. The analyst was instructed to take a reading at the extreme left side of the display if he could detect no arrivals. This resulted in large errors, which were subsequently culled, from the population of the usable readings. Consequently, there is an increase in the size of populations as the signal-to-noise ratio (SNR) increases. The long noise samples were generated using a fifteenth-order autoregressive model fitted to the actual noise preceding the arrival. These were amplified and added to the high SNR raw signals to obtain the desired signal-to-noise ratio in the data that entered the onset time estimation process. First, we inspect the onset time residuals by an analyst at various SNR (Fig. 3). In general, these are late by about 0.1 - 0.12 second. These residuals are relative to the actual arrival picked from almost noise-free records. The standard deviations around the mean decrease strongly as the SNR increases. It appears that the first usable SNR is around 3, but the scatter really does not become acceptable below 4. This is in a reasonable agreement with the results of Kvaema (1996) who sets this limit at SNR=5. Inspection of the onset time residuals by the CUSUM minimum process at various SNR (Fig. 4) shows that in general these are late by about --49.2 second. These residuals are also relative to the actual arrival picked from almost noise-free records. The standard deviations around the mean also decrease strongly as the SNR increases as it would be expected. The first usable SNR is around 3, but the scatter really does not become acceptable below 4, just as in the previous case. The onset time residuals by the combined CUSUM-SA algorithm (Fig. 5) are very large at SNR=3. At higher SNR these are not late. This is because of the multiple SA picks we have a population of readings and we can assess the scatter. The estimated onset times by this method are advanced by one standard deviation to account for the bias described in various texts discussing the CUSUM method. This suggests that a similar strategem may be used to remove such a bias for the CUSUM-minirnum method. The standard deviation around the mean becomes more acceptable as the SNR increases to the value of 6. Fig. 6 shows histograms of the onset time differentials between a human analyst and the CUSUM minimum method for various SNR. The average bias between the two is -0.1 second, the automatic pick being relatively late. It is interesting to note that the scatter is small even at the lowest SNR relative to the scatter in the 'absolute' residuals themselves, basically confirming the observation that an human analyst and the automatic CUSUM-minimum algorithm tend to make similar mistakes at tow SNR (facing the same noise realizations), and thus these cancel out when the differences are taken. Note, however, that such biases are systematic because an analyst instinctively picks early anticipating the arrival based on larger amplitudes following it. Various strategems can be devised to correct for such biases (e.g. Basseville and Nikiforov, 1994). For instance, the rise time for a seismic pulse is roughly the reciprocal of the effective bandwidth which works out to be about 0.1 second for our -10 Hz bandwidth. This may be applied as a correction to advance the automatic onset time picks, which would remove any discrepancy between the analyst and machine-generated onset times.

50

~ ru,anll= I~..v,a rzt, S,'~,R= ..3 .

.

.

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b~

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10

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, ~, .~

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-1

I!

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Fig. 3. Histograms of onset time residuals by an analyst at various signal-to-noise ratios. The residuals are relative to onsets read at high SNR without superposed synthetic noise.

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ao

o ~.s 1 ,.2 2 ,~ h.

~t9 rz.uli=/,s b/e.C~c~ mln~mm. S~,,~= 9

lae= "Q.2AI~ ~ E~rnl ~ Z~1~ i~c

-2.5

-2

-I$

-I

41~

Co

Fig. 4. Histograms o f onset time residuals at the minimum o f trend-adjusted CUSUM at various signal-tonoise ratios. The residuals are relative to onsets read at high SNR without superposed synthetic noise.

51

iF

i

3O

S~gr~ = 5.3:~6E ~

19

I a .

.2.S

-2

-1~

.1

-05

5

[15

t

~5

2

~5

3S

~.

1

.

.

1.5

.

2

Z5

h.

5CI ~nuw~ ~

~tr

IS

'i

Fig. 5. Histograms of onset time residuals by the combined CUSUM-SA algorithm at various signal-tonoise ratios. The residuals are relative to onsets read at high SNR without superposed synthetic noise.

SiFng = ~

.c

,oL5 9

II

.

RLi

i.II

.

5J

1

I..__

I

n,

t.S

~

2.~

b.

a.

]

IJ

i O.S

,., !

1.5

, 2

25

C.

Fig. 6, Histograms of onset time pick differentials between the CUSUM minimum and an analyst at various signal-to-noise ratios.

52

2.2 Development Of Methods To Segment Complete Regional Seismograms The methodology presently used in nuclear monitoring for phase identification (in other words seismogram segmentation) is semi-automatic. After preliminary event location, the analyst brings up a display of pre-filtered seismograms with superposed predicted regional phase arrivals. Phase arrivals are declared (manually) based on the proximity of the amplitude increases to the predictions. Moreover, phase onset times are often adjusted to be closer to the predictions We have tested a number of procedures for the automatic segmentation of regional seismograms. At this stage we are not very concerned if the segmentation and the subsequent onset time estimation are not very accurate. We are merely attempting to find the approximate times for onsets; this is the most important first step and the most difficult problem.

2.2.1 Original Inclfin-Tiao Method The original iterative Incl~n and Tiao (1994) procedure works well with some types o f seismograms where the phase amplitudes are quite unequal and increase with time (Fig. 7). In such cases the first iteration finds the largest arrival, followed by the next largest, etc. The iteration stops in a segment as soon as the F test fails for the next minimum. Unfortunately, the latter feature causes the process to fail finding additional, statistically significant arrivals at iteration levels beyond that.

"T-V-,: "-'-:-

iIi

I

i

'I

t

i

,

!

1

!

i

i

i

!

Fig. 7. Results of the application of the original lnclfin and Tiao (1994) iteration procedure. The figure shows, below each other, the D(t) fimctionsfor successive segments in the iteration. The first segment is the whole seismogram.In the second step we have two segments bounded by the ends of the seismo~am and the arrival found previously. The third step searches minima in segments defined by previous arrivals and the ends of the seismogram.The minimum in each step is tested for a single arrival.

53

2.2.2 The modified Inel~in-Tiao Iterative Procedure As we mentioned above, the original iterative onset time estimation procedure of Incl~a and Tiao (1994) described above was modified by us in several ways to adopt it to seismic data. We continue the iteration until the specified number of iterations is completed regardless of the success or failure of the F tests in each step. When the function 13(0 has a maximum instead of a minimum (signifying an decrease in amplitudes) we use this for a new segment boundary. Of course, only the F tests that signify an increase in amplitudes are accepted as phase arrivals. This way we are able to pick out additional significant arrivals. In addition, we ignore minima in the D(t) function where they are closer than an adjustable fraction of segment length to the segment boundary. Again, this allows us to pick out arrivals further down in the iteration process, but avoids multiple picks near the segment boundary. The missed arrivals may be picked further down in the iteration process. Fig. 8 shows some examples of the picks produced by this modified process.

i

i,

,

::'

l'

L..i._

.

i

1

:

1

. l

2

'

7

,"

'

,I

~ 11]

~

30

40

Id~270 '

................

'

0

21

':' ! . . . . :-..~lilila

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le~Snnl

-2

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'i

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L

"i7

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2

'

......

.

~)

"~)

81)

lr2"llfl , ,

,

:

50

~

11~

,

. . . .

-2I 4

l~-at~

:i

i:

i:

:!

I

9 .

olg

T~B ;~ s ecoild~

Time il ser, o nlii

Fig. 8. Examples of the onset time picks produced by the modified Inclhn-Tiao method. The iteration proceeds regardless of the successes or failures of the F-test. In each segment, the successful F-test will result in the declaration of an arrival. Vertical short green lines show the segment boundaries as they develop. Five iterations were used. These picks were made for two Kola Peninsula events as listed in Der et

al. (1993).

54

The modified procedure removes the problem of missing arrivals due to the cessation of iteration when a non-significant F test is encountered. Moreover, the cumulative sum of absolute trace amplitudes is a better tool for finding arrivals with nearly equal amplitudes. Nevertheless, the process is apt to find more numerous arrivals than seems to be appropriate to a seismologist. Most o f these are real sudden increases in amplitude that a seismologist would dismiss nevertheless.

2.2.3 Methods involving leaky integration The binary segmentation methods proposed by both Incl~.n and Tiao (1994) or Chen and Gupta (1997) are too simplistic and often break down for actual regional seismograms. The Incl~n and Tiao method often picked the wrong windows and onset times, especially where the relative amplitudes of arrivals varied little. In some cases, shown above, they indeed picked the right arrivals. In Figs. 9 and 10 we have substituted leaky integrated trace amplitudes for the CUSUM. This takes the place of the function D(t). The approach seems to work much better in many cases. In order to fund the rapid increases in amplitude we have leaky-integrated the absolute trace amplitudes of the seismogram. The maxima of traces thus processed will be located at times later than the maximum amplitude portions of the respective phases due to the time delay introduced by the leaky integral low-pass filter. I f we segment the seismogram from beginning to end using these maxima as the intermediate point then the actual onsets will be interior to these segments. If we locate the minima of the functions D(t) within these initial segments then we shall have the approximate locations of the phase onsets. Now, if we create windows that are centered on this preliminary onset time with the end points at the maxima o f the leaky-integrated absolute amplitudes. We have tested two methods for finding the broad maxima. One method consisted of monitoring the amplitude differential (gradient) in the leaky-integrated absolute amplitude trace over a set time interval (typically tied to the time constant o f the leaky integrator), finding a maximum and setting the segment separation such that this gradient decreased by a set factor (typically 0.9). Automatic onset time picks for seismograms segmented this way are shown in Fig. 9. The examples shown are events in the Middle East as recorded at nearby digital seismic stations. All examples define the onsets quite well regardless o f the relative phase amplitudes. The weak point in this method is the definition of the end points of the segments. As long as each phase has a decaying coda, the end points can be defined as a certain part (such as 0.9 times in amplitude) of the maximum just previously found. If this value is reached the end o f the segment is declared. On the other hand, many seismograms contain increasing stepping-up in amplitude without decaying codas. In such cases, the end o f segments is never declared. Consequently, any search for onsets w-ill miss most o f them. The other method for finding the broad maxima was based on a cluster analysis o f multiple solutions produced by simulated annealing (SA). Since our SA program was designed for finding minima, we have simply reversed the sign of the leaky-integrated trace for such computations. The centers of the clusters for the picks of minima thus produced can be used as limits of the segments to be searched for single increases in amplitude. Note that this procedure is the same as the one we have applied for finding onset times previously (Der and Shumway, 1999). Illustrations of the results of such procedures are shown in Fig 10. We have found that this method was more robust than the previous one, although it is still sensitive to the same problem with the segmentation. The use o f SA algorithm for finding the maxima of the amplitudes in the seismograms eliminates the need for the criterion needed for finding the ends of the large amplitude 55

portions o f the seismograms The centers o f clusters o f picks for the minima o f the leakyintegrated absolute amplitudes provide a better definition. We have found that this approach works better in some cases. Subsequent to segmentation we have re-centered the fmal window for F-testing on the minimum o f the D(t) function (green lines below). Only arrivals that passed the F-test are declared (vertical red lines). In defining the clusters we have used the cubed distance as a metric in the K-means algorithm. aaeT162 BP .2-2

~V7162

bp .1-5

2

-L .I

I . ' i..,.,

'

*I

'

"

'

"''

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_!I l~n

-4 "'~

0.5

1

1.5

~'

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.......

'

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,,.\~,...._-~

.g

2 x IO 4

~ polrts BC.~CA 7 lOG BP .3-,3

2000

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1000(1 12000 'E4~C13 1 6 C ~

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KIV7100 ~.~ 3-3

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i

4000

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i

0

IOC00 'l~Ur~ Of points

0.5

I 1.5 bd~al;~f or p~n~

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2.5 xI04

Fig. 9. Examples of the decomposition of seismograms into segments bounded by the decreasing portions of the maxima of the leaky-integrated absolute amplitudes (second trace). This is followed by looking for the minima in the function D(t) of Inclgn and Tiao (1994) in each segment (third trace). This is followed by the redefinition of shorter segments designed to be approximately centered on this minimum and be bounded by the previous right side of the segment (shorter segments below). This is followed by an F-test around the minimum to determine whether the change in amplitudes is significant. An onset (vertical dashed lines) is declared if this is the case. Such onsets can be fiarther refined by actually defining the onsets as maxima ofF or the statistics of Chan and Gupta (1997). The first letters in the titles are the station names and the following digits are the event identifiers. 31aese data were sampled at 40 samples/sec.

3

Conclusions

CUSUM-based methods seem to be quite suitable for processing regional seismograms since these consist o f long wave trains and have emergent phase onsets. Since CUSLTM methods emphasize changes in the properties o f signals over several cycles this kinds o f methods can be used to segment regional seismograms. CUSUM-based methods to pick seismic phase onSet times can also be developed based on a variety o f statistics that are diagnostic o f polarization, slowness, and spectral changes Ourkevics, 1988; Der et al., 1993). Other candidates may include instantaneous relative phase differences among components, adaptive slowness estimates, or their combination.

56

+t-T--+7-+

~!

i

' ,

'

+ + ~ i

I; i

,L

'

'

'

+

il

ii

iLL__

,

i

i ++----[

2ii +

+

++ ++

-

+' ~P t ,

i++,: +:+w++'"

~

'

:

} i +s[

i

N~m~Jmf mf~++~is

!

?

[r

,

z 9 ,

!

!

,

N u m ~ g r ~f ~ + n t s

~+V+- ' j]

FI '

i

+t

.............!+I ... I

+2-

4~ +!

I+" '+'' 'I

I

}

I

:lI

....

NLlmbeiof~ i ~ + s

" + .............. =+ ....

]i

........................

Numb++r+~fpoi~l+~

Fig. 10. Examples of clustering. ExampIes o f ~ e decomposkion of seismograms (top trace) into segments defined by the cIusters (segment centers are defined as long vertical |ine segments at the top of each graph) of the SA picks (plus signs akernating in color for the various clusters) of the mimima o f the sign-inverted ieaky-integated absolute amplitudes (second trace below ~he time series), followed by rooking for the minima in the ihnction D(f) of Inclfin and Tiao (1994) in each segment (third trace). The next step is an Ftest aromnd the minimum to determine whether the change in amplitudes is sig~ificanL An onsets (vertical red lines) are declared if this is the case. The first letters in the tides are the station names and the following digks are event identifiers. These date.were sampled at 40 samples/sec.

W e have been successful in developing algoNthms that find the onset times o f first arrival P n quke efficiently compared to a human anMyst. AIthough there is a fairly consistent bias o f 0.t second in the machine picked onset times there m a y be ways to correct these.

We have been somewhat less successful in finding algorkhms that automatically decompose regional seismo~ams k++~o meaningful crustal arrivals that fall into the framework of arrivals that an analyst would always accept. The algoritbzns work in most cases in the sense that the picks are close to the above mentioned phase arriwJs. Nevertheless there are numerous missed phases and, more frequently, muttiple picks clustered around those avivais+ Part of the problem is that regional seismograms acmally contain more distinct,

Pg-S~-72g framework

stadstically significant a m p l k u d e increases than the c o m m o n Pe+would suggest (Vogfj6rd and Langston, 1990), and thus some o f

these discrepancies between our results and the simple model may not be failures at a11. During the course of previous work described in Der and Shumway (t999), and in the work summarized in this report, we have developed the essential building blocks for a practical implementation of an automatic seismogram_ inte~retation Mgoritlm~_+As stated above, not alt fne approaches that we have tried worked equally wet1 for segmentation of seismograms and onset estimation under the various scenarios encountered in practice. F o r seismograms ~aat contain step-like increases in the a~plib+~des o f the successive

57

phases, the modified binary iterative segmentation procedures o f InclS.n and Tiao (1994) and Chela and Gupta (1997), seem to work well. For seismograms containing phases with codas and variable amplitudes, the segmentation methods using leaky integration combined with SA work better, although some variants produce numerous duplicate arrivals. Once the segments are defined statistical approaches for the determination o f the onset times described above can be applied. It appears that reliable segmentation o f high frequency seismograms and the automatic determination of the onset times o f the various arrivals requires sophisticated algorithms. The algorithms need to have sufficient flexibility to recognize arrivals with quite different amplitudes, impulsive arrivals without codas, phases with long codas and phases where the seismogram essentially consists o f a series of increases in amplitude without much decrease until the Lg coda. The latter is typical of Kola Peninsula quarry blasts and the binary iterative segmentation procedures of Incl~hl and Tiao (1994) and Chert and Gupta (1997) seem to work well for these. For seismograms containing phases with codas, the segmentation methods using SA work better. In actual implementation o f such methods, more than a single approach may have to be employed in interpreting seismograms in the automatic mode. Any practical algorithm package for the automatic interpretation o f high frequency seismograms will have to possess sufficient intelligence to recognize various situations and chose the best algorithms. The stratagem used presently by analysts, the superposition of expected arrival times on the seismograms, could be modified to make an automatic algorithm reconcile these with the automatic onset times and discard the less significant onsets. In any implementation of such a scheme, the onset times should not be 'moved' and additional phases, such as that compatible with more complex generalized ray paths (besides the foursome o f Pn-Pg-Sn-Lg) should be allowed.

Acknowledgements This work was supported by the Defense Threat Reduction Agency under the contract DTRA01-98-C-0155.

References Basseville, M. and Nikiforov I.V.,1993, Detection of Abrupt Changes, Theoryand Application. Prentice Hall Informationand SystemScienceSeries,PrenticeHall, EnglewoodCliffs,NJ. , Chen, J. and Gupta, A.K., 1997, Testing and locating change points with applications to stock prices. J. Amer. Statist. Assoc., 92, 739-747. Der, Z.A., Banmgardt, D.R. and Shumway, R.H., 1993, The nature of particle motion in regional seismograms and its utilizationfor phase identification. Geophys.J. Int., 115, 1012-1024. Der, Z.A. and Shumway,R.H., 1999, Phase onset time estimation at regional distances using the CUSUMSA algorithm.Phys. Earth and Planet. Int., 113,227-246. Inel~in, C., and Tiao, G.C., 1994, Use of cumulative sums of squares for retrospective detection in the changes of variance. J. Amer. Statist.Assoc., 89, 913-923. Jurkcvics, A.,1988,.Polarizationanalysis of three-componentarray data. Bull. Seism. Soc. Am., 78, 17251743. Kushnir, A.F., 1996, Algorithms for ~d~ptivestatistical processing of seismic array data. In 'Monitoring a ComprehensiveTest Ban treaty', E.S. Husebyeand A.IVl.Dainty Eds., Kluwer AcademicPublishers. Kvaerna, T., 1995, Automatic onset time estimation based on autoregressive processing. Semiannual Technical Summary, 1 April-30 September 1995.NORSAR, Sei. ReportNo. 1-95/96,Kjeller,Norway.

58

Kvaerna, T., 1996a, Quality assessment of automatic onset times estimated by the autoregressive method. Semiannual Technical Summary', 1 April-30 September 1995. NORSAR, Sci. Report No. 1-95/96, Kjeller, Norway. Kvaerna, T. (1996b), Time shifts of phase onsets caused by SNR variations, Semiannual Technical Summary, 1 October 1995-31 March 1996. NORSAR, Sci. Report No. 2-95/96, Kjeller, Norway. Maeda, N. (1985), A method for reading and checking phase time in auto-processing ssystem of seismic wave data (in Japanese with English abstract), J. Seismol. Soc. Jpn., 38, 365-379. Nikiforov, LN. and Tikhonov, I.N., 1986, Application of change detection theory to seismic signal processing= trt "Detection of Abrupt Changes in Signals and Dynamical Systems "M. Bassevitle and A. Benveniste Editors. Lecture Notes in Control and Information Sciences, LNCIS 77, Springer, New York. Nikiforov, L.V., Tikhonov, I.N., and Mikhailova, T.G., 1989, Automatic on-line odeessing of seismic dataTheory and applications. Far Eastern Dept. of USSR Academy of Sciences, Vladivostok, USSR (In Russian). Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T., 1986, Numerical Recipes: The Art of Scientific Computing. Cambridge University Press. Pisarenko, V.F., Kuslmir, A.F. and Savinn, I.V., 1987, Statistical adaptive algorithms for estimation of onset moments of seismic phases. Phys. Earth. Planet Int., 47, 4-10. Shumway, ILH., 1998, An iterative cumulative sum of squares algorithm for phase onset estimation. ENSCO Teclmieal Memo. Takanami, T., 1991, A study of detection and extraction methods for earthquake waves by autoregressive models. J. Fac. Sci. Hokkaido, U., Ser VII, 9, 67-196. Taylor, D.W.A., Ghalib, H.A.A. and Kimmel, R. H., 1992, Autoregressive analysis for seismic signal detection and onset time estimation. ENSCO Inc. Technical Report DCS-92=90 prepared for AFTAC. Theodoris, S., and Koutroumbas, K., 1999, Pattern Recognition, Addison-Wesley. Tou, J.T., and Gonzalez, R.C., 1974, Pattern Recognition Principles. Addison-Wesley. Yokota, T., Zhou, S., Mizoue, M., and Nakarnura, I., 1981, An automatic measurement of arrival time of seismic waves and its application to an on-line processing system (in Japanese with English abstract), Bull. Earthquake. Res. Inst. Univ. Tokyo, 55, 449-484. Vogfj6rd, K.S., and Langston, C.A., 1990, Analysis of regional events recorded at NORESS. Bull. Seism. Soc. Am., 80, 2016-2031.

59

Application of Autoregressive Processing to the Analysis of Seismograms Mark Leonard AGSO, PO BOX 378, Canberra City, ACT2601, Australia. mark.leonard(~ga.gov.au

Abstract. The application of Autoregressive processing to the analysis of seismo~ams has been of value to seismologists for several decades. Work in the 1960s and 1970s focused primarily on using AutoregTessive (AR) filtering and other error predictive filters for improving the si~lal to noise ratio of small seismic signMs. In the eighties aald nineties most interest has been in the application of AR filtering to onset time estimation. Onset time pickers which utilise AR filtering have proved to be very effective for a wide range of seismic signals including, local and telezeismic events. A key advantage of them over other methods is that they are robust even for phases with a small signal to noise ratio. The accm-acy of automatic AR picks compare well with those of experienced seismic analysts.

1

Introduction

Autoregressive (AR) processing is one of the predictive filtering techniques and its applications to seismolo~" include chaJ-acterisation, error predictive filtering (improving SNR by removing noise), power spectrum estimation and onset time estimation. This paper describes the AR method and briefly describes these applications. I consider the accurate estimation of the onset time of seismic phases using AR processing to be the most useflfl application of AR processing to contemporary seismology. The application of predictive filters to seismograms has been part of the science of seismology since the 1960's. Early applications were in nuclear monitoring, particularly in the field of array processing. Nuclear monitoring applications focused on Maximum Likelihood filtering to improve the signal to noise ratio (SNR) of small signals (Green et al. (1965), Claerbout (1968), Capon (1971) Lacoss (1975), Bungum et al. (1971)). Maximum likelihood was used because it does not distort the phase and so information on whether the phase is compressional or dilational is preserved. It has long been recog~ised that the P phase from nuclear explosions recorded at teleseismic distances is always compressional, which remains one of the major methods of discriminating between an earthquake and an explosion. The complexity and computational requirements of the Maximum Likelihood method meant that it has never been widely used by the seismological community. The much simpler method of bandpass filtering and delay and sum processing of array data, which is almost as effective, has been used instead. Burg (1967) described a method for obtaining the power spectrum without needing to calculate the Fourier Transform. This method never gained popularity and the F F T and more recently wavelet processing have been the methods that almost all seismolo~sts have used to calculate power spectra.

61

/\ 1 m

l

Fig. 1 . Autoregressive processing uses samples 1 to l of a time series to calculate m point AR filter. This m point AR filter is then used to filter the data from samples m + 1 to n. Whilst the data has the same AR model as samples 1 to 1 the resulting time series will consist of low amplitude white noise (noise with a constant power spectrum).

2

T h e Autoregressive M o d e l

In the following equations x t is the input white noise time series. Yt is the output time series of a linear filter. c~ are the moving average model coefficients. ai are the autoregressive model coefficients. n autoregressive (AR) model of order m is defined as: Yt = a l y t - 1 + a 2 y t - 2 + "." + a,,~yt_l + x t

By introducing the backshift operator

Bye = Yt-1

equation

(1) 1 can be described

by: (1 -

alB

- a2B 2 .....

a,~B'~)yt = xt

(2)

Or

= x,

(3)

which implies that > = a -l(B)x,

(4)

Hence an autoregressive process can be thought of as the output y, from a linear filter with transfer function a -1 (B) when the input is white noise xt. Equation 1 describes an Autoregressive model (AP~) of order m abbreviated as AR(m). Filters based on this process are called autoregressive or feedback filters. The AR(1) process is called a Markov process. At any time t the output of the filter yt is the weighted sum of the past m output values plus the current value of the white noise time series xt. Rearranging equation 1 gives: xt

=

Yt - a l y t - 1 - a 2 y t - 2 . . . . .

=

Yt + ~ a ~ Y t - i

a,~yt-1

(5)

i=1

The aim of autoregressive, or error prediction, filtering is to determine the values of al - ' - a,~ so that equation 6 can be applied. The output of the autoregressive filter is then a white noise time series and a deviation of the output time series x~ from a white noise time series indicates that the input time series yt model has changed.

62

One method of deriving the AR coefficients is the least squares method. The following derivation of the autoregressive filter is from Aki and Richards (1973) (chapter 11) which is based on the work of Robinson (1957) and Robinson (1963). Since the filter that generates yt from the white-noise input has minimum delay, the filter coefficients ai can be found from the autocorrelation function which contains only amplitude information Robinson (1963) and xt is a random time series. As z t is purely random (white noise), the present value of xt is not rela~ed to the past values of y~. So the correlation < xtys > = 0 while s < t. < YsYt > t ~

ai < y j Y t - m > = 0

s < t

i=l

re = < Y~Yl > is the autocorrelation function, ~air~_~=

(6)

-rk

i=I FO

'r' 1

7" 1

ro

...

:

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To

rl

7"[

r0

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rl

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am

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rm

-

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rm

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: .

(7)

1

r.m

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:

=

al

?'m - 2 ...

r'm.-- 1

E~

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'1"0

(s)

am

ro + r l a i -r r2a.2 + " . + r,na~, = < yix~ >

(9)

--~

< X. i : > : = 0 2

(lO)

-

the variance of the white noise.

(11)

Equation 7 can also be derived by minimising the mea~l square of tYt Li=l aiyt-,) with respect to a~. See Claerbout (1968) for this derivation. The square matrices in equations 7 and 8 are Toepliz matrices and so can be efficiently solved using the Levinson recursion. In the multichannel case each clement in the Toepliz matrix, i.e. ro in equation 8, becomes an n * n matrix where n is the number of channels. Each submatrix has the form:

(

?,i(i)

r,(i)

..-

'r n(i)

'2 (0

r,~l(i)

(12) ""

run(i)

Where i = 1, m and r12(i) is the cross-correlation of channel one with channel two at offset i. The multicomponent versions of equations 7 and 8 are solved via a modified Levinson recursion, described by Wiggins and Robinson (1965) and RobinsQn (1966).

63

Table 1. Location information of the two events used for examples Event Fiji Eurelia

Date 19/05/2001 20/05/2001

Hr:Min 17:40 15:46

Lat -19.8 -32.5

Long 177.5 138.7

depth(km) 365 1

Mug 6.0 2.0

There are representations of time series data other than an AR model, most commonly Moving Average (MA) and Autoregressive Moving Average (ARMA) representations (Box et al. 1994). In the MA representation the data is represented by the next m values, as opposed to the AR model where it is represented by the previous m values. The ARMA model is a combination of the AP~ and MA models,

3

The Data

Table 1 lists the two events, the data from which are used as examples in this paper. The data were recorded by a Guralp broadband (CMT3) seismometer located at the seismic station STKA (-31.9 141.6). The Fiji data is a composite seismogram consisting of the data from the Fiji event divided by 150 and then added to the 15 minutes of noise preceding the event. This was done in order to obtain a small amplitude event for which the arrival time was known. The five minutes of pre-event noise which was divided by 150 had counts ranging from +3 to -3, so has negligible effect on the pre-event noise of the composite signal. Fignre 2 shows the power spectrum of the input pre-event noise and event signal which have been divided by 150 and the composite pre-event noise and event signal. All Fiji examples in this paper use this composite waveform. The data for the Eurelia event is aa recorded at STKA and has not been modified.

4

Characterisation of a Seismogram using an AR Model

The AR coefficents provide a relatively simple way of characterising a time series. Changes in both the order and the value of the AR coefficients are diagnostic of the differences between noise and signal, and can be exploited to characterise seismic data. Leonard and Kennett (1999) used the AR coefficients to characteris.e data by generating diagrams akin to Vespagrams and Spectragrams which they called AR-grams. Whereas Vespagrams displ<~" slowness and Spectragrams display the power spectrum on the ordinate and time on the abscissa, AR-grams display the AR coefficients on the ordinate. In this work AR-~ams use tile first 13 AR coefficients for single component seismog~'ams (see figures 3 and 4). The AIGgrams are generated by calculating the 13 AR coefficients every 2 seconds using a 5 second window. Each pixel plotted is 2 seconds wide. The scale is white at zero grading to black for higher absolute values. In the absence of a signal, it is expected that all but the first few coefficients will be white or light grey. When a signal is present, the values up to the order of the signal will darken.

54

I

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10 4 10 3

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10 2 10 ~ 10 0 10 4

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10 4

101

Hz Fig. 2 . FFT power spectrum of pre-event noise and P phase of the Fiji event. The first AR coefficient, of a single component AR-gram of broadband data is always positive and is about one. In the presence of some microseisms (figure 4) the absolute value of the second coefficient is less than 0.1, the third less than -0.15, the fourth about 0.1, and ibr all the others the absolute value is less than 0.1. The number at which all further AR coefficients have an absolute value less than 0.1 could be considered the order of the AR model. The AR order varies with the type of microseisms. In figure 3 the AR order of the noise is only 2, although there are periods where the order increases to 10. Most events have an AR order of about 10-15. Both the teleseismic Fiji event and local Eurelia event have orders of 12-15. The AR-gram of the Fiji event (figure 4) shows the event very clearly even though the signal is small on the broadband station. The effect of the P phase on the AR-gram is short lived, reflecting the isolated nature of most teleseismic P phases. The AR-gram of the Eurelia event clearly shows the long coda of the local P phase. The sustained high order of this coda is due to the high frequency content of the seismogram.

5

Power

Spectrum

Estimation

The AR coefficients can be used to calculate the power spectrum of the waveform directly without the need for a Fourier Transform. The AR method has the characteristics of: (1) needing only a short data segment, (2) producing a smooth power spectrum, (3) not needing to sample the spectrum in uniform frequency steps, (4) ability to sample in detail particular frequencies of interest. Using an F F T to estimate the power spectrum of broadband data, which typically has a frequency range of over three orders of magnitude (ie. 0.02 Hz - 20 Hz), requires a data segment of 100 seconds, which at 50 samples per second is 5000 samples. A single estimate of the power spectrum has a standard deviation of 100% (Press et al. 1986). Averaging the power spectrum of k 50% overlapping data segments reduces

65

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66

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Fig. 5 . Power spectrum estimates of the Eurelia eveat. The power spectrum is calculated on the vertical channel only using two 50% overlapping 20 second data segznents smoothed with a 5 point filter for the FFT estimate and a single 10 second data segment for the AR estimates. The two pairs are displaced three orders of magnitude which helps in interpretation. the variance by 9 k / l l (Welsh 1967). Averaging 11 estimates reduces the variance to 10%, but requires 550 seconds of data. This length of data is acceptable when calculating the power spectra of background noise but is unrealistic for estimating the power spectra of seismic phases which are often only a few cycles long9 Generally F F T power spectrum of a single data segment is smoothed, typically with multiple passes of a three point Harming filter. Burg (1967) showed that the Autoregressive coefficents can be used to calculate a smooth power spectrum using a single data segment which need be no longer than the duration of the phase. Gutowski et al. (1978) showed that the AR method works very "*-ellfor modelled data when that data has been generated by an AR process and the number of AR coefficients is the same or slightly higher than the AR model used to generate the data. When the data is generated by a Moving Average (MA) or an Autoreg~essive Moving Average (ARMA) process or when the order of the AR model is significantly different to the actual model, the spectral estimate is not as accurate. Typically it picks the position but not the width of the peaks. Figures 5 shows the F F T and AR power spectrum of vertical component for the Eurelia event. There are two pairs of power spectra. One pair was calculated via a F F T and the other by the AN. method. Each pair coi~sists of the power spectrum of the pre-event noise and the P phase. Two 50% overlapping data segments were used to calculate the power spectrum, which reduces the variance to 60% (Press et al. 1986). The very scattered power spectrum has been further smoothed by 2 convolutions of a 3pt triangular filter. This smoothing makes the difference between the power spectra of the signal and the noise clearer, but has detrimental effects such as broadening of peaks and tro~ghs, aJld does not remove all statistical fluctuations.

67

The order of the AR model (the number of AR coefficients) used to calculate the power spectrum affects the calculated power spectrum. If the order used is too low, detail in the F F T will be missed but if the order is too high false peaks might be introduced. An order of between 3 and 9 is generally adequate for describing noise. In the case of the noise prior to the Eurelia event (figure 5) the model of order 3 describes the main feature of the power spectrum - its log linear decrease. The model of order 11 describes all the features of the power spectrum. Models of order 21 add no more detail and appear to introduce spurious peaks. To adequately describe P phase the order of 10 - 20 is generally needed. For the Eurelia event (figure 5(b)) the order 5 model describes the nmjor features of the power spectrum: the peak at 3-4 Hz and the log linear decrease. The order 11 model resolves all the features of the power spectrum. The order 21 models better resolve the frequency at which signal and noise merge, but introduce false peaks at high frequences.

6

Error Predictive Filtering for Signal to Noise Improvement

AR filtering uses the previous m samples to predict the (m + 1) th sample and subtracts this predicted value from the actual sample. The filtered signal then becomes the residual (error) after this subtraction. In an ideal case the noise becomes a low amplitude random noise and the signal passes through undistorted and without attenuation. This will result in a significant improvement in the signal to noise ratio (SNR). However the signal, particularly of small events, will look different. With the removal of the log linear noise below 1Hz, the peak frequency of the signal will normally be shifted to a higher frequency. Figure 6 shows the power spectra of the pre P phase noise and the P phase for the Fiji event. There are two pairs - one is after the data has been AR filtered and the other has been band pass filtered between 1 & 3 Hz. Both the bandpass and AR filtering produce similar SNR improvements. The change in the dominant frequency of the P phase to higher frequency can be seen in this example. Whilst the noise power spectrum is reduced by AR filtering, the signal power spectrum is also reduced. When comparing the log log power spectra, the gap between sig~nal and noise remains constant. In the frequency domain the SNR could be defined as the ratio of the value of the signal power spectrum to the noise power spectrum. The optimal bandpass is then simply the range of frequencies for which the ratio of the power spectrums is highest. A method which subtracts the noise power spectrum away from both the signal and noise power spectra, would result in a lowering of the noise power spectra and the signal power spectra by the same amount. As they have been lowered by the same amount their ratio will increase hence resulting in a significant increase in SNP~. On a log log power spectrum plot the gap between the noise and signal would increase. The AR filter, instead of subtracting away the noise, reduces the power spectra by a constant fraction. This constant fraction is the amount required, at each frequency, to reduce the power spectrum of the noise to a fiat power spectrum. This can be seen by comparing the power spectrum pairs of the unfiltered Fiji data in figure 2 and the AR filtered power spectrum in figure 6. In the time domain, the AR filtering is a convolution followed by a subtraction. If the dominant process was subtraction this

68

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would result in a subtraction in the frequency domain. The power spectrum results suggest that the convolution process is the dominant process, as a com~olution in the time domain is equivalent to multiplication (or division) in the fl'equency domain. A filter which did subtract a power spectrum from the signal and noise power spectrum would result in an improved SNR. It would not need to be the noise power spectra, but for example, a negative sloped log linear function would be very significant.

7 7.1

Onset Time Estimation Introduction

Current applications of AR filtering to seismology have been mostly in the area of automatic onset time picking of previously detected phases. Three different, but quite similar, approaches have been proposed ((GSE/JAPAN/40 1992), (Kushnir et al. 1990) and (Takanami and Kitagawa 1993)) ibr use with short period data, and mostly with local and regional events which have large SNR. All the approaches involve calculating an AR model of the seismogram before and after the start of the phase. These two models will be most different when one contains only seismic noise and the other contains mostly signal. Since the two models have a common point, when the models are most different, the dividing point between the two models is considered the onset time. The Akaike Information Criterion (AIC) (Akaike 1973) is a commonly used method of measuring the difference between the two models and is the method used here.

69

7.2

Akaike Information Criterion

The Akaike Information Criterion (AIC) for a scalar N-point time series, is defined as:

AIC = =

- 2 ( maximum log likelihood )

(13)

+2(number of coefficients), - 2 N l o g u 2 + 2ra,

(14)

where

('v,---

am -9, j----1

represents the variance of the component not explained by the autoregressive process. The Akaike Information Criterion (AIC) is one method for determining the length of an AR filter. Normally the AIC of the filtered data will decrease as m increases until a minima is reached and AIC increases with increasing m. Tile m corresponding to this minima is considered the order of the AR system. Typically the AIC initially decreases rapidly, decreases slowly near the minima and then increases slowly after the minima. This suggests slightly underestimating or overestimating the order of the AR filter will have little effect on the final result. In its application to onset time picking the function AIC~ is calculated from the AR filtered time series in the interval m + 1 to n and the location of the minima determined. The location of the minima is considered the onset time. This is the approach in approach 3 discussed below. The joint AIC of two time series can also be calculated. This function, AIC(F e B)k, is defined as:

AIC(F • B)k = - ( k - 1 ) loguF, - k + 1)log4

+

+

(15)

where, in this case, u~ is the variance of the forward model, u~ is the variance of the backward model, mF is the number of AR coefficients used to calculate the forward model and nB is the number of AR coefficients used to calculate the backward model. Ideally AIC(F)j and AIC(F | B)j will linearly decrease from m + 1 to k then increase from k + 1 to n - m . Therefore both AIC functions will result in a "V" shaped fnnction with the minima at k, where k is the onset time. 7.3

S u m m a r y of Approaches

Conceptually there are three approaches which researchers have taken to calculating onset times using AR filtering. Figure 7 schematically describes the three methods. In each case they can be applied to both single component and three component records. Approach 1 This approach describes the whole time interval by two AR models. One AR model (F model) is calculated, in the forward diection, on the interval 1 to k - 1 and another

70

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Fig. 7 . The three approaches used in the AR onset time estimation methods. A1, A2, & A3 refer to the three approaches described in the text. F model refers to the forward model and B model refers to the backward model. (B model), in hte backwards direction, on the interval n to k. The joint Akaike Information Criteria (AtC(F@B)) is then calculated. This process is then repeated for all k from 1 + m to n - m, where m is the order of the AR model. The value of k for which ( A I C ( F ~ B ) is a minimum is chosen as the onset time. This approach, which divides the time series into two stationary time series, is conceptually the simplest of the three methods but is very computer intensive as n - 2 m sets of AR coefficients need to be calculated.

Approach 2 In approach 2 the time series is divided into two error prediction series(WF & Ir The F model is calculated on the interval 1 to l and tile B model on the interval n - l to n. The F model AR filters are then used to calculate the W ] error prediction series on the interval 1 + m to n - m where m is the order of the AR model (m < l). The B model AR filters are then used to calculate WB on the interval n - m to 1 + m (i.e. backwards). The variance of the prediction errors is calculated at each time point and is used to calculate the AIC(F| The two AR models are still calculated only once. Whilst the time series of the seismic signal is regarded as stationary in a limited interval (local stationarity), it is not a continuation of stationary series of the same nature, but changes slightly both before and after the merging of a'sigmal. The division of the interval is made by inferring the covariance matrix of prediction errors from F model and B model. The use of only two models with an update of the variance at every time point, corresponds to the assumption that the F and B model spectra stay almost the same but the amplitude changes with time. For seismic noise and short time segTnents of seismic phases this is a reasonable assumption.

Approach 3 In this approach the AR model (F-model) is calculated once in the first part of the time series. The prediction error series of the F-model is calculated in the forward

71

direction. When a phase emerges, the prediction error of the F model becomes larger. The AIC(F) is calculated at every point and its minimum corresponds to the arrival time. Approach 3 assumes that the signal and noise have different spectra. C o m p a r i s o n of Approaches GSE/JAPAN/40 (1992) found that the accuracy, stability and confidence of the time estimation using approach 2 is similar to, or better than using approach 1, and is much faster than approach 1. For short impulsive phases, where the assumption of stationarity of the B model in approach 2 does not hold, approach 3 is more accurate than approach 2. Approach 2 is superior to approach 3 when the power spectrum of the phase is similar to the noise. The work by Kushnir et al. (1990) is very similar to approach 1 described in the previous section. There are two differences. One is that instead of calculating the AIC(F| a closely related Maximum Likelihood parameter is constructed which has a maximum at the onset time. The second is that auto-correlations are calculated up to offset m (the order of the AR model) and then the Toeplitz matrix is solved via the Levinson-Durbin recursion (Levinson 1947). The approach of Takanami and Kitagawa (1988) is similar to approach 2 described above, but instead of calculating the AIC from the AR filtered time series, they calculate it directly without needing to calculate the AR coefficients or AR filter the data. Takanami and Kitagawa (1988) applied a single component method to P phases and Takanami and Kitagawa (1991) expanded the method to three components and applied it to S phases with a large SNR. Takanami and Kitagawa (1993) found that summing the three single component AIC time series performed nearly as well as the three component method~ but they were concerned about the implied assumption that each component is independent of each other. They found that when using the multi-component method for estimating the onset time of S phases, utilising the two horizontal components was slightly superior to using all three components. Figure 8 shows the broadband, bandpass filtered and AR filtered seismograms and the approach 2 and 3 AICs for the Fiji event which has a clear but low SNR P phase.Approach 2 has a minima 0.1 second after the P onset time and approach 3 is 0.4 seconds late. For such events the minima of the AIC is typically 0.05-0.2 seconds after an expert analyst's pick. To adjust for this Leonard (2000) proposed an adjusted AR-AIC picker (AAR), which calculates the average slope of the AIC in the first 0.35 seconds after the minima and if the slope is greater than 1500 per second, 0.05 seconds is subtracted from the onset time. If it is between 1000 and 1500, 0.1 seconds is subtracted and if less than 1000, 0.15 seconds is subtracted. This modification moves the average pick value close to that of an expert analyst and results in the time picks being more normally distributed about zero. The pick in figure 8 would then be 0.1 seconds earlier than the minima, which is close to the analyst's pick.

7.4

Picking P Phases

The AAR picker has three stages. Stage one picks an optimal filter band and bandpass filters the data with a second order causal Butterworth filter. The cutoffs for the filter band are calculated by subtracting the log of the power spectrum of the pre-event noise from the log of the power spectrum of the event. The upper and lower filter

72

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Fig. 8 . The broadband, bandpass filtered and AR filtered seismograms of the Fiji event and approach 2 (AIC_2) and 3 (AIC_3) Arc plots. bands are chosen where the resulting peak merges with the background level. The second stage is to filter the data with an autoregressive (Error Prediction) filter. A fouth order filter is adequate for both the forward noise filtering and the reverse signal filtering. The third stage is to calculate the Akaike Information Criteria along the time series and determine its minima. The minima of the AIC is taken as the onset time. For very large SN• events, stages one and two could be bypassed and for large SN• events stage one could be bypassed. For this study all three stages were used for all events as the main advantage of' bypassing the early stages is to save computation time which is not an issue. For many events the AR filter could be replaced by a severe (order g~'eater than 4 Butterworth) bandpass filter and the AIC calculated from this. The disadvantage of this is twofold. One is the AR filter produces white pre event noise resulting in a linear AIC, which does not have the si~lificant false minima that a AIC calculated from bandpass filtered data will have. Second, to be effective, the bandpass filtering needs to be both narrow and severe, so miscalculation of the band pass will give a poor results. The AAR picker calculates two separate picks, one using Approach 2 and one using Approach 3, and then chooses the earliest of the two picks. The first pick is calculated as follows: 1. A 12 second segment of data starting 7 seconds before the initial arrival time is selected. 2. An order 4 AR model of the noise based on 4 seconds of noise starting 7 seconds before the initial arrival time is calculated.

3. A 4 point AR (error prediction) filter, which removes the noise, is then applied to the data.

73

4. An order 4 AR model of the signal plus noise based on 4 seconds of signal starting at the initial arrival time is calculated. 5. A 4 point AR (error prediction) filter is then applied to the data in the reverse direction. This removes the signal from the data. 6. The joint AIC is calculated from the two AR filtered time series. 7. The minima of the AIC is considered the onset time. In an ideal case, the first time series would consist of pure low amplitude white noise until the start of the signal after which it would consist of the signal with the noise removed. The second time series would consist of high amplitude noise until the start of the signal after which it consists of pure low amplitude white noise. The AIC, which is related to the cumulative variance minus the pro rata of the average variance, then becomes an effective means of determining when the filtered time series changes from pure noise to noise plus signal. The second pick is calculated using only the forward error prediction filtering of the noise and not the reverse error prediction of the signal plus noise. It then calculates the AIC from the single filtered trace. tn practice the method is stable and not significantly affected by changes in the starting time as long as the AR model of the noise is based on noise only and the AR model of the signal at least is calculated on the coda. The AAR picker is very robust and a starting onset time as picked by a simple Short Term Average to Long Term Average detector is sufficient to ensure that AAR picker performs correctly. The signal does not need to be seismic. The AR picker will determine the onset time of any signal which has a different AR model to the background noise. Figure 9 demonstrates the performance of the onset time picker for this small local event, with both methods 2 and 3 accurately picking the onset time. This example and the Fiji event (figure 8) demonstrate how accurate this technique is for both low SNR local and teleseismic events. Leonard (2000) showed that there was very little difference between the times picked by an experienced analyst and those of the adjusted AR picker. Figure 10 summarises the difference in picked times between four seismic analysts and the AAR picker. The average difference between the analysts and the modified AR picker is 0.043 seconds with a standard deviation of 0.19 seconds. The average difference between the four analysts was 0.067 seconds with a standard deviation of 0.15 seconds. The data used by Leonard (2000) consisted of small to medium SNR teleseismic phases which had previously been identified as an iP phase. The author expects the difference between the automatic and manual picks for eP phases to again be similar to the differences between analysts. This similarity suggests that for most applications there was no advantage in using manual instead of automatic picks.

Picking S Phases Single component AR filtering can be used to calculate the onset time of an S phase. Leonard and Kennett (1999) found that the best results are obtained when the two horizontal components are processed as described here for the P phase and the AIC of the two horizontal components summed. As with P phase picking, two times are calculated, using methods 2 and 3, and the earlier time is considered the onset time.

74

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75

Slightly better results are obtained for S phases when a three component AP~ filter is applied using both methods 2 and 3. Again the two horizontal component AICs are summed and the earlier of the two picks is used. The energy of S phases, particularly regional and teleseismic S phases, is more evenly distributed over the three components than the energy of P phases. This reduces the SNR on each component. For S phases this results in the cross-correlation AR values, those which use component X to predict the next sample on component Y, being significant. This suggests three component AR analysis will perform better than single component AR analysis. This is thought to be the reason why three component AR filtering and composite AICs will outperform the single component method used for P phase onset picking.

8

Conclusion

Methods for characterising three component broadband data, where small phases are not discernible on the unfiltered trace, can be simply done via the use of an AR-gram. As well as being sensitive to the presence of seismic phases the AR coefficients also register changes in data quality. These AR coefficients can also be used to calculate the power spectrum of a seismogram with the following properties: (i) small data segments, which unlike for a FFT don't need to be a factor of two in length, can be used, (2) it is possible to sample in detail frequencies of interest, (3) do not need to be smoothed to produce realistically smooth power spectrums. The application of autoregressive filtering for signal to noise enhancement does work but has little advantage over conventional bandpass filtering with an appropriately selected bandpass. Autoregressive techniques are a very robust and simple way of determining the onset time of seismic phases. For large events and events with their energ3z concentrated on a single component, such as teleseismic P, single component AR onset time picking is very effective. For events which have their energy spread over two or more components, such as S phases, three component AR onset time estimation has superior performance. The inherent variance in manual onset time picking of iP phases, as measured by comparing analysts, is similar to the variance between the AR pickers and the analysts. When the adjusted AR-AIC (AAR) method is used the averages are very similar. The average difference between the four analysts is 0.067 seconds compared to 0.043 for the difference between the analysts and the AAR picker. The respective average standard deviations are 0.15 seconds and 0.19 seconds. The precision of the AR-AIC onset picker indicates that for many routine applications the automatic picks need not be modified. Applying the modified AR-AIC onset picker prior to review by an analyst will mean that the timing of most events will not need to be modified. When used in a location routine, the locations using the automatic picks and the location using manual picks will typically have overlapping error ellipses. The source code for the adjusted AR-AIC picker is freely available to researchers. To obtain it contact mark.leonard~.ga.gov.au.

76

Acknowledgements This paper is published with permission of the Chief Executive Officer of Geoscience Australia.

References Akaike, H., 1973, Infbrmation theory and an extension of the maximum likelihood principle, In B. Petrov and F. Csaki (Eds.), 2nd International Symposium on Information Theory, pp. 267-281, Budapest Akademiai Kiado. Aki, K. and P. Richards, 1973, Quantitative seismology: Theory and Methods, Volume 1 and 2, Sail Francisco: Freeman and Co. Box, G., G. Jenkins, and G. Reinsel, 1994, Time series analysis : forecasting and control (Jrd ed.), Prentice Hall. Bungum, H., E. Rygg, and L. Bruland, 1971, Short period seismic noise structure at the Norwegian seismic array, Bull. Seism. Soc. Am., 61(2), 357-373. Burg, J., 1967, Maximum entropy spectral analysis. In Proceedings of the 37th Meeting of the Society of Exploration Geophysicists, In Childers, 1978. Capon, J.~ 1971, Signal processing and frequency - wavenmnber spectrum analysis for a large aperture seismic array, In Methods in Computational Physics, Volume 13, Academic Press. Claerbout, J. F., 1968, A summary, by illustrations, of least-squares filters with constraints, IEEE transactions in information theory, IT-14(2), 269-272. Green, P., R. Frosch, and C. Romney, 1965, Principles of an experimental large aperture seismic array, I.E.E.E., 53(12), 1821-1833. GSE/JAPAN/40, 1992, A fully automated method for determining the arrival times of seismic waves and its application to an on-line processing system, Paper tabled in the 34th GSE session in Geneva GSE/RF/62, G.S.E. Gutowski, P., E. Robinson, and S..Treitel, 1978, Spectral estimation: Fact or fiction, IEEE Trans. Geosci. Electron., GB16, 80-84. (In Childers 1978). Kushnir, A., V. Lapshin, V. Pinsky, and J. Fyen, 1990, Statistically optimal event detection using small array data, Bull. Seism. Soc. Am., 80(6b), 1934-1950. Kvaerna, T., 1995, Automatic onset time estimation based on autoregressive processing. Norsar scientific report, NORSAR. ~Lacoss, R., 1975, Review of some techniques for array processing, In K. Beau& (Ed.), Exploitation of seismic networks, Series E Sci. App. No 11. Noordhoff-Leiden. Leonard, M. and B.L.N. Kennett, 1999, Multi-component autoregressive techniques for the analysis of seismograms, Physics of the Earth and PlanetaD ~ Interiors, 113(2), 247-264. Leonard, M, 2000, Comparison of Manual and Automatic Onset Time Picking, Bull. Seism. Soe. Am., 90(6), 1384-1391. Levinson, N., 1947, The Wiener RMS (root mean squared) error criterion in filter design and prediction. In N. Wiener (Ed.), Extrapolation, Interpolation, and Smoothing of Stationary Time Series with Engineering Applications, Chapter Appendix B., John Wiley and Sons. Press, W., B. Flannery, S. Teukotsky, and W. Vetterling, 1986, Numerical Recipes : The art of scientific computing, Cambridge: Cambridge University Press.

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Robinson, E., 1957, Predictive decomposition of seismic traces, Geophysics, 22, 767-778. Robinson, E., 1963, Mathematical development of discrete filters for the detection of nuclear explosions, J. Geophys. Res., 68, 5559-5568. Robinson, E., 1966, Multichannel z-transforms and minimum delay, Geophysics, 31, 482-500. Takanami, T. and G. Kitagawa, 1988, A new efficient procedure for the estimation of onset times of seismic waves, J. Phys. Earth, 36, 267-290. Takanami, T. and G. Kitagawa, 1991, Estimation of the arrival times of seismic waves by multivariate time series models, Ann. hist. Statist. Math., 43(3), 407-433. Takanami, T. and G. Kitagawa, 1993, Muhivariate time-series models to estimate the arrival times of S waves, Computers and Geoscienees, 19(2), 295-301. Welch, P. The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms, IEEE Trans. Audio and Electroacoust., AU-15; 70-73, 1967. (In Childers 1978). Wiggins, R. and E. Robinson, Recursive solution to the multichannel filtering problem, J. Geophys. Res.~ 70(8), 1885-1891, 1965.

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Hi-net: High Sensitivity Seismograph Network, Japan Kazushige Obara 1 t National Research Institute for Earth Science and Disaster Prevention, 3-1, Tennno-dai, Tsukuba, lbaraki, 305-0006, Japan. [email protected]

Abstract. The high sensitivity seismograph network in Japan (Hi-net), composed of around 600 seismic stations, is a part of the project made by 'The Headquarter for Earthquake Research Promotion' after 1995 Hyogokeu-nanbu Earthquake and has been constructed and operated by National Research Institute for Earth Science and Disaster Prevention (NIED). Seismic stations are distributed homogeneously covering whole Japan Islands with an average spacing of 20-30kin. Three-component short period velocity seismometers are installed at the bottom of boreholes with depth of 100 m or deeper. Seismic data are digitized by 24-bit A/D converters and decimated to 27bit data with the sampling frequency of 100Hz. Stations are connected to the Hi-net data center, N1ED in Tsukuba by a frame relay network service. TCWIP and SNMP are used for data transmission and network management, respectively. The data are continuously transmitted to the data center and local offices of Japan Meteorological Agency for routine monitoring of seismic activity. The data receiving, monitoring, processing, and archiving system is controlled by a database management system in the data center. Event detection, phase picking, hypocentral determination, spectra analyses, and extracting waveform parameters are processed automatically. Event information and continuous waveform data are available through the world-wide-web.

1 Background After the disastrous 1995 Hyogoken-nanbu (Kobe) Earthquake, the Headquarter for Earthquake Research Promotion was established by Japanese government and set up the project o f 'Fundamental Survey and Observation for Earthquake Research' on August 29, 1997. According to the project makers "the purposes o f the project are to estimate earthquake occurrence based on the understanding o f earthquake phenomena and to evaluate the strong motion through understanding o f generation mechanism o f the strong motion. The concrete measures to promote the earthquake research selected with a hig,h priority are as follows, (1) Seismic observation (~) High sensitivity seismic observation (microearthquake observation) (~) Broad band seismic observation (2) Observation o f strong motion (3) Observation o f crustal movement (continuous GPS observation) (4) Survey o f active fault in land and coastal regions."

2

Overviewof Hi-net

The purpose o f the Hi-net is to get precise information for earthquake activity and the underground structure. Especially, the depth o f earthquakes is one o f the important

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parameters. Basically, inland earthquakes occur in the upper crust at the depth of shallower than 15-20km except those associated with the subducting plate. The magnitude of major inland earthquake is related to the length and the width of the fault geometry and the dislocation during the faulting. Even if there is no information about the length of the fault, the lower limit of the inland earthquake depth helps us to estimate the maximum width of the fault, that is the maximum size of possible earthquake at the area.

In order to determine the focal depth of earthquake with higher resolution, we need the seismic network with a spacing of the same scale length corresponding to the focal depth, 15-20kin. Before the 1995 Kobe earthquake, Japan Meteorological Agency (JMA), universities, National Research Institute for Earth Science and Disaster Prevention (NIED), and other organiTations have been operating high sensitivity seismograph networks individually. Total number of seismic stations was about 500 at that time. In order to set up the seismic network with spacing of 15-20 km, we need about more 500 seismic stations. Based on the experience on constructing the Kanto-Tokai network (Hamada, et al., 1982; Okada, 1984), which is the NIED's original high sensitivity seismograph network operated in the central part of Japan, NIED was selected to be in charge with the construction and operation of the new seismic networks. At the end of 2000 fiscal year, 520 Hi-net stations have been constructed (Fig. 1). "Freesia net", which consists of 50 broadband seismometers (Fukuyama, et al., 1996), "K-NET", which consists of 1000 strong motion meters (Kinoshita, 1998), and "KiK-net", a strong motion meter network, the twin of Hi-net as described later, are also operated by NIED.

3

Hi-net Station and Sensor

In order to detect microearthquakes and fred hypocentral distribution with higher resolution, the signal to noise ratio of the data should be as high as possible. The sites of the seismic stations are selected in relatively noise-free and geologically better. To improve the detection capability for microearthquakes, every Hi-net station is set in a borehole of 100m or deeper to eliminate noises caused by human activities. The depth of the borehole is decided considering with the geological environment and noise level at the site. Generally, the quality of the data is good if the sensor is installed in hard rock layers. In Japan, some large cities, such as Tokyo, Osaka, are covered with deep soft sediment layers. In these cases, boreholes deeper than 1000m were constnlcted (Fig. 2). During the drilling of the borehole P and S wave velocity, material density, temperature, and other physical parameters are measured for further analysis. The seismic sensors are contained in an anti-pressure vessel and installed at the bottom of the borehole. The Hi-net system is required to keep stable observation for several ten years, so the anti-

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pressure vessel containing sensors is mechanically fixed in the borehole arid can be pulled tip again for maintenance and/or improvement. Fig. 3 shows the anti-pressure vessel and sensors. Inside the vessel, a set of three-component velocity seismometers and a set o f three-component strong motion meters are installed. The natural frequency and the sensitivity o f the velocity seismometer are I H z and around 200V/m/s, respectively. Another set o f three-component strong motion meters is also installed at the top of the borehole on the ground surface in every Hi-net station. The strong motion data are collected by KiK-net system (Aoi, et al., 2000), which uses dial-up method, different from Hi-net system.

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4

Data Acquisition

Fig. 4 shows a schematic view of a station. The analog signals are transmitted from the velocity seismometers at the bottom of the borehole to an A/D (analog to digital) converter through the signal cables. Then these signals input to the A/D converter are digitized using the delta-sigma method. The sampling frequency and the resolution of the A/D converter are 2kHz and 24bits, respectively. Because the A/D converter is easily affected by temperature, it is installed at the base of the undergrotmd pit with depth of 0.5-1m, constructed inside of every Hi-net station. The 2kHz sampling data is sent to a computer, which is operated on UNIX, and decimated to the data with the sampling frequency of 100Hz and resolution of 27bits. The digitized data, divided into small data packet by one second time window, are compressed and transformed to the WIN32 format, which is slightly different from the original WIN format introduced by Urabe and Tsukada(1992). The data packet is attached to the absolute time information retrieved from the GPS antenna, which is set up on every station. Data with 100Hz sampling rate are transmitted to the data center continuously by using protocol TCP/IP. On the other hand, lkHz-sampling triggered event data are recorded for monitoring of sensor and acquisition system if the amplitude level of the seismic signal exceeds a threshold, which is controlled by remote access. The computer in each seismic station has a memory and/or hard disk enough to keep continuous waveform data for one day in the case of the problem on the telephone line. Each computer is connected to the data center by our computer network. Working staffs can login to a computer in any station for maintenance and improvement. Sensors are regularly checked by the test coil response at a pre-set time. The sensor check can be carried out manually, too. Trouble information and warning messages are saved in the computer at each station as MIB(management information base), and major trouble information will be sent to the monitor center with SNMP(simple network management protocol), immediately.

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5 5.1

Data Flow of Hi-net Network

The is a computer network that is composed of stations, relay points, sub-centers, monitor center and data center (Fig. 5). All machines installed in these facilities are connected with each other by Internet protocol (IP). The wide area network (WAN) is netted by the frame relay service. The frame relay is a kind of packet exchange service and we can reserve a part of the frame relay as private leased lines. The cost o f the access line to the frame relay network is cheaper than that of leased line because it depends on the capacity of access line and is independent from distance. On the other hand, the fraane relay allows a delay for packet transmission and the delay time depends on network traffics. I r a seismic station is located in the service area of the frame relay, the station is connected to the frame relay network directly. In the non-frame relay area, data are first transmitted to a relay point using a leased line. At the relay point, modems and a router are installed to transfer the data packet from station to sub-center. The flame relay service becomes popular rapidly, and it is easy to change from the non-tPame relay type to the frame relay type. At the beginning o f the less than 20% stations were connected to the frame relay directly, now, more than 80% stations are connected (by September of 2001).

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As for data transmission, TCP/IP is adopted in the WAN between station and sub-center and between sub-center and Tsukuba data center. In the local area computer network (LAN) inside a sub-center or the data center, the multicast protocol is used for distributing data packet to the assigned computers for monitoring and processing. If the system has trouble and data packets are lost, the backup process starts to recover the lost data automatically. In the case of short-time packet loss, TCP/IP has a function for data re-sending. At the sub-center and the data center, data packets are always checked. If a packet loss for a specific station is recognized by the sub-center, the station is required for re-sending the data. I f a packet loss is found by the data center, the sub-center is asked whether the data exists or not. If the data exists in the sub-center, the sub-center re-sends. If no data, the data center asks the station directly. From each station, 100Hz-sampled continuous data, lkHz-sampled event trigger data, and their re-sent data are transmitted to the data center with priorities based on their importance. Continuous data transmission is given the highest priority and event trigger data are transmitted with very slow rate.

5.2

Sub-Center

The main jobs of the sub-center are data transferring and data back up. Now, we have two sub-centers, the West sub-center in Kyoto and the East sub-center in Tokyo. One

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sub-center receives the data packet from the half of Hi-net stations. Data of neighboring stations are transmitted to different sub-centers (Fig. 6). Consequential, in case of one sub-center has trouble another sub-center keeps data of at least a half density of the network. Data are transmitted not only to Tsukuba data center, but also to Japan Meteorological Agency for routine monitoring of seismic activity and universities (from the end of 2001 fiscal year) for earthquake research work. In order to prepare against a trouble in the data center, each sub-center has a disk server to store one-week continuous waveform data. Data will be recovered automatically by re-send function when the data are lost in short time. If the data center has trouble for longer than one day, data will be saved to magnetic tapes at sub-centers and then restored to the disk server in the data center. The sub-centers, which is the most important facility in the Hi-net data transmission system, are located in buildings which have stable power supply and data transmission environment with high-grade maintenance. Moreover, very important machines, router, computers for data receiving, and so on, are composed of dual machines. Sa~llite C.ommt.~k:atkm

Fig.6. Data flow of the Hi-net system.

5.3

Monitor Center

At the monitor center, the < Hi-net System> is watched for 24 hours by the network monitor system and human eyes. Whenever instruments and computers send alarm signals with SNMP, working staffs in the monitor center will login to any machine to get more detail information. All of actions including f'mding the trouble, processing, and final result are recorded in a database, which can be shown by the Internet browser.

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The monitor center and sub-centers are operated using outsourcing services.

6

Data Center

The system for data receiving, monitoring, processing, archiving, and the data public use is controlled by a data base management system in the data center. The data receiving system always checks the data packet loss and requests for re-sending to the sub-center or the station ira packet loss is recognized. It distributes data packets to computers in the data center by the multicast protocol. The monitoring system displays the quasi-real time waveform data. The data processing system is composed of the event detection, phase picking, hypocentral determination, and some other automatic processes based on Horiuchi et a1.(1999). The ratio of STA (short-term average) to LTA (long term average) is calculated for the event detection. When the STA/LTA at some neighboring stations exceeds a threshold at the same time, the event detection is declared and the following process is started. Just after the declaration of event detection, the first arrival data are picked from the first 20 stations then the hypocenter location and the focal mechanism are determined by the immediate picking process. On the other hand, the data are monitored to fmd the end point of the seismogram in order to retrieve the event waveform data. The waveform data is used to pick up clear phases, at most 10, for each station by the AIC method. These picked phases are classified into groups, then, the hypocenter location and the focal mechanism are determined again. In the case of no picking data on a trace, the waveform data, which gives the smallest logarithmic-likelihood, is selected as the P or S wave onset time within a time window expected from the hypocentral parameters calculated at the first step. After the hypocentral determination, the waveform parameters, which include spectra information, particle motion, coda parameters, and so on, are extracted from each seismogram. These hypocentral parameters and waveform parameters are stored in the data base system. The arrival time data picked up by automatic process are checked and corrected by human eyes and the manual picking data is used for the final calculation of the hypocenter of the event, mechanism and waveform parameters. Event waveform data and continuous waveform data are stored in a disk server, which is able to store six months continuous waveform data (500 stations). All data are saved in DLT tape library system as a backup. Continuous waveform data and the hypocentral parameters are opened for non-profit public use through the Internet.

7

Summary

The Hi-net is a new seismic observation system in Japan using the latest computer technology, such as, multicast, TCP/IP, SNMP, and so on. The landline is chosen for data transmission because it is good on the following aspects: high ratio of performance and cost; applicability for further technological development; and the sufficient back up system. Indeed, the optical fiber network is rapidly covering whole Japan, and the instrument must be applicable for the new media.

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Acknowledgments The author would like to acknowledge Tetsuo Takanami for his encouragement and valuable comments. Anshu Jin helped improve the manuscript by valuable comments.

References Aoi, S., Hori, S., and Kasahara, K., 2000, New Strong-Motion Observation network : KiK-net, Programme and Abstracts, Seismol. Soc. Jp~L,P010. Fukuyama, E., Ishida, M., Hori, S., Sekiguchi, S., and Watada, S., 1996, Broadband seismic observation Disaster Prevention, 57, 23-31. Hamada, K., Ohtake, M., Okada, Y., Matsumura, S., YamamiTaa,F., Sato, H., Imoto, M., Tatsukawa, M., Ohkubo, T., Yamamoto, E., Ishida, M., Kasaham, IC, Katsuyama, Y., and Takahashi, H., 1982, KantoTokai observation network of crustal activities -National Research Center for Disaster Prevention-, J. Seismol. Soc. Jpn.(Zisin), Set.2, 35, 401-426 ( in Japanese with English abstract). Horiuchi, S., Mtsuzawa, T., and Hasegawa, A., 1999, Automatic data processing system of seismic waves that works even at times of huge seismic activity, J. Seismol. Soe. Jpn.(Zisin), Set.2, 52, 241-254 ( in Japanese with English abstract). Kinoshita, S., 1998, Kyoshin net(K-net), Seismol. Res. Lett., 69, 309-332. Okada, Y., 1984, First results from Japanese network for earthquake prediction, Nature, 312, 500-501. Urabe, T., and Tsukada, S., 1992, win- A workstation program for processing waveform data from mieroearthquake networks, Programme and Abstracts, Seismol. Soc. Jpn.,No.2, 331.

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A PC-Based Computer Package for Automatic Detection and Location of Earthquakes: Application to a Seismic Network in Eastern Sicily (Italy) Domenico Patan61, Ferruccio Ferrari ~, Elisabetta Giampiccolo l'a and Stefano Gresta a l lstituto Nazionale di Geofisica e Vulcanologia; Piazza Roma 2; 95123 Catania; Italy. [email protected] -~Dipartimento di Scienze Geologiche, University of Catania; Corso Italia 55; 95129 Catania; Italy

Abstract. Few automated data acquisition and processing systems operate on mainframes, some run on UNIX-based workstations and others on personal computers, equipped with either DOS/WINDOWSor UNIX-derived operating systems. Several large and complex software packages for automatic and interactive analysis of seismic data have been developed in recent years (mainly for UNIX-based systems). Some of these programs use a variety of artificial intelligence techniques. The first operational version of a new software package, named PC-Seism, for analyzing seismic data from a local network is presented in Patan~ et al. (1999). This package, composed of three separate modules, provides an example of a new generation of visual object-oriented programs for interactive and automatic seismic data-processing running on a personal computer. In this work, we mainly discuss the automatic procedures implemented in the ASDP (Automatic Seismic Data-Processing) moduIe and real time application to data acquired by a seismic network running in eastern Sicily. This software uses a multi-algorithm approach and a new procedure MSA (multi-station-analysis) for signal detection, phase grouping and event identification and location. It is designed for an efficient and accurate processing of local earthquake records provided by single-site and array stations. Results from ASDP processing of two different data sets recorded at Mr. Etna volcano by a regional network are analyzed to evaluate its performance. By comparing the ASDP pickings with those revised manually, the detection and subsequently the location capabilities of this software are assessed. The first data set is composed of 330 local earthquakes recorded in the Mt. Etna area during I997 by the telemetry analog seismic network. The second data set comprises about 970 automatic locations of more than 2600 local events recorded at Mt. Etna during the last eruption (July 200 I) at the present network. For the former data set, a comparison of the automatic results with the manual picks indicates that the ASDP module can accurately pick 80% of the P-waves and 65% of S-waves. The on-line application on the latter data set shows that automatic locations are affected by larger errors, due to the preliminary setting of the configuration parameters in the program. However, both automatic ASDP and manual hypocenter locations are comparable within the estimated error bounds. New improvements of the PC-Seism software for on-line analysis are also discussed.

1

Introduction

The advent of digital recording systems in the late 1960s changed real-time earthquake monitoring. Today, automatic and interactive analysis of seismic data is a practical need because o f the growing amount of data produced by the increasing n u m b e r o f seismic stations. There are several papers (e.g. Allen, 1982; Chiaruttini et al., 1989; Bache et al., 1990; Chiaruttini, 1991; Takanami, 1991; Fletcher et al. 1992; Tarvainen, 1992; Bache et al., 1993; Ruud et al., 1993; Ruud and Husebye, 1993; Earle and Shearer, 1994; Evans and Pitt, 1995; Tong, 1995; Tong and Kenneth 1996; Wagner and Owens, 1996) that examine the tasks of automatic detection and processing of seismic signals at a single

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station or an array. Conventional automatic network algorithms for event detection and location generally use detectors based on short-term average (STA) and long-term average (LTA) and/or on some characteristic functions (CF) (Mlen, 1982). Their use allows finding triggers on each seismic channel while a multi-channel time window criterion is usually applied for event detection and location determination. In general, regional and local seismic networks automatically compute preliminary epicenters and magnitudes for most of the moderate-to-large earthquakes within a few minutes after their occurrence. Estimated preliminary parameters used both for monitoring and surveiUance purposes are sent to a number of scientific and civil organizations. However, today, an analyst's review is still a practical necessity in many cases, in order to achieve reliable focal parameters. For hypocentral location, one of the fundamental parameters which is poorly detenmned automatically is the focal depth due to: i) the sparseness of stations in regional or widely spaced local networks; ii) the lack of three-component stations to recognize clear S-phases. It is well known that the availability of seismic signals recorded by three-component stations increases the reliability of earthquake locations and, in general, the quality of analysis in "seismological studies" (Ruud et al., 1988; Kedrov and Ovtchinnikov, 1990; Roberts and Christoffersson, 1991; Tarvainen, 1992; Patan6 and Ferrari, 1997). The integration and a wider utilization of three-component stations in regional and local networks give the possibility of a better characterization of the P-phase and enables the detection of S arrivals, on the basis of physical differences between the Pwave and S-wave. Today, a relatively large number of methods have been proposed (Flinn, 1965; Montalbetti and Kanasewich, 1970; Vidale, 1986; Jurkevics, 1988; Takanami, 199l; Cichowicz, 1993; Der et al., 1993; Klumpen and Joswig, 1993; Patan6 and Ferrari, 1997) dealing with the polarization properties of the seismic signal, with detailed analysis of the S-wave. Algorithms developed to investigate seismic polarization properties are generally aimed at detecting phases, recognizing P- and S-phases and at giving estimates of the direction of propagation (azimuth) of the sig-nals. Azimuth estimates can be used in conjunction with phase picks from a seismic network to improve the source location estimate. Another typical problem in routine data processing at different seismological observatories is the automatic discrimination of the different types of seismic signals. Recent applications of artificial neural networks and spectrogram computations by continuous seismic signals spectral analysis indicate that these techniques can be efficiently used in event discrimination. Their use can be trained to distinguish earthquakes from artificial events, such as cultural noise, chemical explosions and quarry blasts (i.e. Ursino et al., 2001), and volcano-tectonic earthquakes from long-period events, explosion-quakes and tremors in volcanic areas (Falsaperla et al., 1996). Artificial neural networks have also been trained to detect seismic signals and to estimate their onsets (Joswig, 1990; Wang and Teng, 1995; Dai and MacBeth, 1995). In the future the main effort in network and seismic array design must therefore take into account a wider utilization of: i) three-component seismic stations based on digital tecl~lology with colmnunication ability; ii) intelligent software to handle the increasing quanti.ty of seismic data; iii) more robust automatic signal processing techniques both for precise identification of the seismic phases and, in the case of designed seismic arrays with a particular geometry, to .give precise measurements of the vertical and horizontal slowness of the wavet~ont p~sing the single elements of the array. In recent years, much more attention has been given to these problems in the design of permanent seismic networks, which are also deployed for local seismicity studies in active regions. Furthermore, the development of personal computers and visual-object

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programming language allows realizing acquisition systems of digital data and userfriendly software management at very low costs. Several software products for seismic data analysis include digital seismic network data acquisition software, interactive time series analysis for display, manipulation, filtering, spectral analysis and earthquake location (e.g. Bache et al., 1990; IASPEI Software Library, Tottingham and Lee, 1989; Bodvarsson et al., 1996; Harris and Young, 1997; SNDA, Haikin et al., 1998; MATSEIS). The current PC capability and the recent technology development in seismic instrumentation have motivated Patan6 and Ferrari (1999) to design a new PC-based software for automatic seismic data processing, in order to achieve the higher efficiency possible in automatic phase picking and in earthquake detection and location. In this Chapter we illustrate the main architecture of PC-Seism software, in particular of the ASDP (Automatic Seismic Data Processing) module, and report some details of the implemented procedures. The object-oriented design of the program allows users to easily acquire, modify and administer data and control parameters directly on-line, without stopph~g the acqtfisition. The software has been planned to process local earthquakes. Some tests of ASDP have been carried out on local earthquakes and seismic sequences occurring in the volcanic area of Nit. Etna (Italy) in two different periods.

PC-Based Seismic Monitoring and New Visual ObjectBased/Oriented Software Most older computerized seismological networks use radio and/or dedicated telephone lines for continuous transmission of relatively tow-dynamic range (maximtwa 72 dB), narrow bandwidth analog data to a central recording site. In the 1980s, some networks were designed using micro- or mini-computers for digitization and data detection at the station sites, but the relatively high cost of these systems has limited their application in permanent networks for several years. The recent availability of low cost digital stations with a higher dynamic range (equipped with 16- or 24-bit gain-ranging digitizer), accttrate timing (GPS receiver) and transmission capability will allow the modernization of older computerized seismic networks. Today, several new digital seismic networks, like the UPSAR network in California (Fletcher et al., 1992) and the SIL network in South Iceland, (Bodvarsson et al., 1996), and networks with satellite telemetry, like the GOES system (Mueller et al., 1995) and the ARGOSSN project of European Community (Calderoni et al. 1997) have been installed in different seismic areas in the world, and are operative with a high degee of automation. As such, networks with satellite telemetry, today offer many advantages (i.e. digital data transmission) if compared to the older analog networks based on traditional techniques using telephone cable transmission or radio transmission. Moreover, they are devised to work in extreme emergency conditions, as for instance during strong earthquakes. All the above-mentioned computerized systems are mainly developed for UNIX or UNIX-derived systems. Exceptions to these systems are the local seismic networks developed in recent years, which use a less expensive PC-based seismic data acquisition system. Today, the PC's capability of handling rigorous and advanced mathematical models in conjunction with the availability of new operating systems and programming languages (visual object-based or oriented) allow to overcome the limitations of the procedural pro~amming, with remarkable benefits and performance for the development of software for atttomatic monitoring.

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To promote the use of personal computers in seismological investigations, the International Association of Seismology and Physics of the Earth's Interior (IASPEI) published a software package in collaboration with the Seismological Society of America (Tottingham and Lee, 1989). Since 1994, a new version of automatic detection and location software (XRTP-IASPEI) has been available. In 1992 the IASPEI software library included the program PITSA. This program, written by Scherbaum and Johnson (1993), has become widely known for its potential in the interactive analysis of digital seismic data. It is available both on DOS and UNIX platforms. The major limitation of PITSA in its DOS version is the operating system itself. Recently, among the several software developed by Scientific Organizations and Commercial Manufacturers, one of the most used software is the "Earthworm" by U.S. Geological Survey. This project started in 1993, mainly in response to the most common needs of regional seismic networks. The program has been developed in order to achieve a high degree of modularity, system independence, scalability, connectivity and robustness. The "Earthworm" system consists of a set of modules which communicate through a standard TCP/IP network broadcasts. Each module performs some coherent task (such as data acquisition, phase picking, etc.) and receives various messages such as packets of trace data, phase picks, etc. Today, there exists a standard target desktop environment which developers can create applications for. In fact, if we look at the introduction of the PC and consider the progression from the first generation PC-chips to more powerful processors, the shift from command-based operating systems to more user-friendly interfaces and efficient programming packages, the development of very powerful and user-friendly software for the automatic processing of digital seismic data is now possible. Without doubt, new operating systems have brought 32-bit computing to the PC technology. The 32-bit applications in these operating systems enjoy improved multitasking and application stability. Therefore, the state-of-the-art approach in PC environment to create an application is to use some other client/server and multithread application development systems. Object-oriented programming (OOP) languages refer to an entire approach to application development in which the source code is a collection of objects. Several fundamental principles are defined to qualify an object-oriented language. These principles include encapsulation, inheritance and polymorphism. Although some programming languages, such as VisualBasic or VisualC, do not yet meet all the requirements, newer versions continue its evolution toward becoming an objectoriented language, allowing the realization of more complex applications as needed in multi-parameter monitoring systems. The PC-Seism software package described here provides an example of a new generation of visual object-oriented programs for interactive and automatic seismic data processing run on a personal computer. It has been developed with VisualBasic and, in order to improve performance and overcome some language limitations, several dynamic linked library (DLL) has been used. A rearrangement of the PC-Seism program package and of the related modules following the latest version of VisualBasic is still in progress. One of the most important elements of this package is the ASDP (Automatic Seismic Data Processing) module in which a visual object-based interface is used. This allows reducing the paradigms of procedural programming, and adopting simple and fast modular techniques. At any time, the object-based interface permits users to interactively modify the setup parameters in all the procedures and to recall the output results also when the program is in running mode.

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3

PC-Seism Architecture

The realization of PC-Seism (Patan~ and Ferrari, 1999) represents a by-product of research and software engineering, principally directed toward finding an optimal way to process three-component array data. However, even thougia it was designed for handling and analyzing records of three-component stations, the general use of the program in local and/or small regional networks equipped with only one-component stations is not prevented. The input data are record files in PC-SUDS format, adopted from IASPEI in 1989. This format shows high flexibility, diffusion and possibility to include different types of information. PC-SUDS is currently available on personal computers running MS-DOS, although versions for other platforms are available. The PC-Seism software package consists of three separate modules: Seismic Network Manager (SNM), Interactive Data Analysis (IDA) and Automatic Seismic Data Processing (ASDP). The first module SNM runs in combination with IDA and/or ASDP and represents the database manager of the seismic network and/or of a temporary array. The module IDA implements some similar procedures to those of the PITSA software and groups a number of tools and utilities for digital seismological signal processing. The automatic seismic monitoring module ASDP works in near real-time on an off-line unit. A local area connection between the on-line and off-line units is required, so that the off-line unit can access the SUDS files on the on-line system without stopping data acquisition. Recently, new modules have been added in order to automatically analyse volcanic tremor, in terms of frequency content (spectrograms) and polarization.

3.1

Database Management

In the management of a seismic network, care must be taken in recording all modifications to the station array. Station parameters obviously need to be routinely checked and information on observed modifications must be saved. The software module SN~%I (Seismic Network Manager) has been developed in order to devise a relational database able to manage information about the seismic network and recordings of seismic events (data type, stations, kind of instrumentation, phases, event location, etc.). The database structure in SNM shows strong analogies to PC-SUDS and has been devised using the SQL language and the Access software. It is aimed at improving the performance of the operating array and allows to: i) create different station database files for different networks, also when temporary modifications at the array configuration occur; ii) maintain detailed information of each station in the seismic network (location, instrument type, site characteristic, etc.); iii) exchange the available information at each station with the two modules ASDP and IDA. SNM was designed to store information on the processed seismic data (sampling rate, etc.) and tO allow users to add new recording stations and related characteristics into the network. The database and all the contained information can also be changed when ASDP is in operative mode. It is noteworthy that some parameters are automatically modified in SNM as a function of some signal environment conditions (level of noise, presence of spikes, etc.), which are processed in ASDP. For exanlple in the case of malfunction of one or more stations the program is able to identify anomalous events (e.g. loss of power supply) and to discard the related traces.

93

The organization of the program allows the integration of data coming from different pemaanent or temporary networks, recorded by different seismometers. S N M manages and updates some fundamental information (like instrumental transfer functions, the 1D crustal models, etc.) to process recorded data. In order to apply the appropriate instrument correction to recorded signals, a calibration section containing system response information for each station is included. The geophone transfer response can be defined by: i) a Frequency-Amplitude-Phase file, containing the frequency response o f the sensor (amplitude and phase) at discrete frequencies; ii) the geophone parametric characteristics (magnification, natural period, damping), which are used to obtain the resulting complex function and the amplitude and phase response of the system; iii) the poles and zeros of the analog transfer ftmction and gain.

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Instrumental corrections are performed during signal processing in frequency domain. The overall (instrumental) transfer function of a digital seismograph in SNM can be obtained, at each station of the array, combining several instrumental responses (seismometer-transducer-amplifier-system, anti-aliasing filter, digital high-pass filter).

94

When signals are processed in time domain, for fast computations (i.e. event detection procedures) the deconvolution for the instrumental response is not performed, under the assumption that through some multiplication constant it is possible to obtain the true ground amplitudes (displacement or velocity or acceleration). For location computations it is possible to insert different I D velocity models in SNM. They can be selected and used in relation to the extension of the seismic monitored area. For example it is possible to choose a general crustal model for the global network and/or more detailed velocity models for sub-arrays or for different sectors of the monitored area. In the database each selected crustal model is associated with one station or different groups of stations. The adopted velocity model in hypocentral computation will depend on the first recording station. Other processes also allow to display and manipulate digital maps (in bitmap or vectorial format). Fig.1 shows a t?~pical screen display of the SNM module form, after the choice of a particular station with a related map.

3.2

Automatic and Interactive Signal Processing

In off-line mode PC-Seism presents a wide variety of procedures for earthquake analysis and some of these are similar to those available in the PITSA software (Scherbaum and Johnson, 1993).

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95

The IDA (Interactive Data Analysis) module enables data visualization and processing, and provides different analysis tools. It can be used for traditional phase readings, measurement of amplitude and periods, and localization of events. Other procedures are used for filtering, spectral analysis, polarization and particle motion analysis, component rotation, attenuation estimate by spectral ratio and coda-Q, site effects evaluation, etc. Fig.2 shows a typical screen output of IDA module, related to the polarization analysis as applied to a three-component seismogram record. An extensive help guides the users through each form and makes the operation easy. With menus, forms and controls, users can accomplish a wide variety, ranging from simple to complex, of seismic data analysis tasks . Performance has been optimized through the use of a dynamic linked library (DLL). Many of these routines are also used in the ASDP module. 3.3

Automatic Signal Analysis and Event Location

The ASDP section of the program provides a complete organization of data, procedure and setup paranaeters, and display processing, presentation and storage. It thus separates tasks best performed by the automatic ASDP module fxom those best performed by seismologists. ~Iqaebasic architecture of ASDP is shown in Fig.3. Automatic analysis includes procedures of seismic signal at single channel and threecomponent stations followed by a Multi-Station Analysis (MSA) for earthquake detection and location. All the procedures of seismic signals at each channel or station can be applied through specific windows. The operator can define the execution of each procedure. As a first step, the correction of the offset in the traces and a continuous analysis of the noise level amplitude are done for each channel. The purpose of this part of the program is to perform simple computations of recorded signals in order to quickly discard noisy traces and disturbances. The second stage of the program, based on a single-station detection processing, enables the following procedures: 9 signal analysis by STA/LTA- and CF-based detectors, in order to check the beginning and the end of a seismic event; 9 improving time picking for phases with emergent onset; 9 spectral analysis: this procedure is used in order to confirm the begimaing and the end of a seismic event and to identify non-seismic events with low spectral content (e.g. longperiod events and explosion-quakes in volcanic environment) and to exclude them in earthquake detection analysis; 9 filtering performed by IIR or FIR digital filters; 9 polarization analysis of three-component data; [] identification of the P-phase; 9 rotation of the signal in the LQT system; [] identification of the S-phase by using a characteristic function, which includes the results of the polarization filter, spectral analysis and a STA/LTA application on rotated signals. De.tection and automatic phase pickers are mainly provided by three algorithms working in cascade mode, based on: i) the STA / LTA and CF detector routines (Allen, 1978). Modifications and optimizations of these routines, applied individually to each seismic data channel component, have also been performed to better identify emergent P-

96

arrivals; ii) the spectral analysis (performed at different stages of the automatic process) and temporal imaging of spectral energy. This type of analysis allows to recognize known patterns of earthquakes and reject false triggers and noise bursts, not well detected during the pre-processing stage; iii) the polarization filter in time domain, based on the Covariance Matrix Decomposition (i.e. Montalbetti and Kanasewich, 1970; Patanb and Ferrari, 1997). This is applied when a 3-C station is available to recognize P- and S- wave arrivals, to rotate seismograms, and automatically compute the direction of polarization, the back-azimuth and the angle of incidence tbr the P-wave.

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In the following sections, these main procedures used by the program in this stage are briefly described. 3.3.1

STA/LTA-and CF Based Detectors

The short-term average and long-term average ratio (STAJLTA) is a simple and efficient technique for detecting energy changes even though it is difficult to distinguish among cultural noise, wind, and other non-seismic noise sources. Signal detection is accomplished by comparing the STA with a threshold value, which is defined as the multiple of a LTA of a characteristic function (CF). If the STA exceeds the threshold value and is confirmed for a selected length of time a trigger is declared. The characteristic function can be designed simply as the absolute value of the input series or it may be quite a complex fimction, depending on the type of signal expected and the performance required of the picker. The CF of Allen (1978), designed to enhance changes in both amplitude and frequency, is used here. For further details see Appendix A. These procedures provide a first arrival time estimate, which is correct in most cases. Some limitations of the algorithm performance and piek_ing occur for emergent arrivals, whereas impulsive arrivals are picked accurately. In fact, in the case of weak events and emergent arrivals, the pick at the onset is missed entirely since the threshold is generally set too high and the trigger is given on the following stronger pick. In order to obtain a more correct picking for this kind of events some modifications on the algorithm of Allen (1978) have been made. Briefly, the routine enables the computer program to examine the STA/LTA ratio in the signal portion preceding the declared trigger, up to when this ratio is near to 1 (the value is definable). Then the process stops when the new value of STA/LTA is achieved. In this section of the program other parameters are also computed, such as the polarity, the duration (dominant frequency) and the amplitude of the first impulse, and the maximum amplitude of the seismogram. The original algorithm (Allen, 1978) has furthermore been modified to enhance recording of coda by the detection of the end of the event through a STA/LTAn detrigger threshold (LTAn is the long-term average of noise preceding the signal) and by the comparison of the spectral content of signal in a short time window after the declared de-trigger with that of the background noise of the trace (see Appendix A). Further details on the application of the spectral analysis to confn-m the onset and the end of the earthquake are reported in the following paragraph. The S-phase picking obtained by the STAJLTA procedure applied to vertical components may be affected by large errors (<0.5 s) since S arrivals are usually not clearly marked by large amplitude change. However, if three-component stations are available a characteristic function for S-phase detection and picking is computed. The parameters used in this function are obtained by the application of different kinds of analysis in the P-coda region. The STA/LTA procedure is computed on the rotated traces, in the LQT coordinate system, after the application of a polarization analysis. Both STA and LTA represent two new time series sets after the detected P arrival. When the STA exceeds the LTA, an S-phase arrival is declared and the result is considered to compute the CF. In the following paragraphs the application of the spectral and polarization analysis on the signal, which are used to obtain the further parameters for the S-phase recognition are discussed in more detail.

98

3.3.2 Spectral Analysis and Spectrogram Computation A wide variety of seismic signals are classified on the basis of spectral signatures. In volcanic environments the nature of the spectral character of the signals, or their change, may also be an important indicator of impending eruptions (i.e. Stephens et al., 1994, Rogers and Stephens, 1995). In areas of mining activity (for hard rock quarrying, coal exposure and mineral recovery), where blasting is applied, the necessity to distinguish explosions from earthquakes is a practical need in many seismological observatories. Even though a remarkable spectral complexity usually characterizes artificial explosions, several authors (i.e. Stump et al., 1996; Kim et al., 1997; Ursino et al., 2001) suggest that the spectral analysis and discrimination through amplitude ratios may be an efficient method to discriminate explosions from earthquakes. In a system designed to detect local and/or regional earthquakes, signals h~ the frequency bands between ca. 3 and ca. 20 Hz are given greater weight than those in other bands. In fact, with respect to the teleseismic earthquakes which have little energy content in the spectra (ca. 3 Hz), regional and local microearthquakes generally have broadband spectra extending respectively to about 15 Hz and to even higher frequencies. It is noteworthy that cultural and natural noises tend to have less frequency variation (almost monochromatic contents) than seismic signals and have their maximum energy, at a higher frequency. Therefore earthquake energy, in a background of seismic noise, can best be detected by frequency-domain techniques. Fig.4 shows different types of seismic signal and related spectrograms, such as an earthquake, a long-period volcanic event and some examples of cultural noise. We can clearly observe that the spectrograms of earthquakes have different characteristics from the spectrograms of non-earthquake signals. Recent detector algorithms based on pattern recognition and/or on Artificial Neural Networks use the moving window spectnun and spectrograms in solving problems in signal discrimination and classification. A spectrogram is a two-dimensional image that includes both temporal and frequency information. Pattern recognition and Artificial Neural Network analysis apply this technique to recognise known patterns of earthquakes and to reject known noise-disturbances (i.e. Joswig, 1990; Wang and Teng, 1995). For a seismic signal a temporal image of spectral energy is computed, using a moving window spectrogram as input to detect earthquake signals. The detection capability and timing accuracy will depend on the sample rate, since a long moving window produces a large error in arrival time and a short window will offer poor spectral representation. To analyse spectral content of background noise, to detect abrupt changes in spectral content of the seismogram and to recognise earthquakes, in the ASDP module, some automatic routines for spectral analysis (FFT, DFT, Average Periodogram by power spectrum, spectrogram) have been implemented. Spectrograms produce a continuous monitoring of the signal spectral features. Obviously, a continuous spectral computation on a high number of channels implies an increased computational time and in this case a DSP (Digital Signal Processing) board or a dedicated computer is preferable. ASDP offers the possibility to obtain a continuous spectrogram for a defined number of channels. Furthermore, in order to recognise an earthquake (P-phase detection) and to discard other false triggers not well identified previously, the progam applies a spectral computation by the use of an FFT (Fast Fourier Transform) or a DFT (Discrete Fourier Transform) in a short window, of a few seconds, after a declared trigger identified previously by STA/LTA and CF-based routines. ~[lae direct calculation of the DFT has the advantage that only the required spectral points need to be calculated. Thus, in some spectral analysis implemented in ASDP it is simpler and preferable to use a simple DFT algorithm instead of an FFT. 99

The signal spectral character is compared with the background noise one. In greater detail, the operation performs some distinct computation steps. The first one produces the spectra in a selectable time window after the trigger. Then, two integrals in different bands o f the spectra are computed and their ratio is evaluated. The former integral is calculated in a pre-definable frequency band (i.e. 3 to 10 Hz), wherein the earthquake energy is presumably confined, and the latter one for the overall spectrum. A similar procedure is also performed for the average noise spectrum. The noise spectra are calculated separately for day and night and then averaged. The second section performs the detection process which involves the comparison between the integral ratio for the signal and that obtained for the average noise spectrmn. The detection is confirmed when the comparison exceeds a selectable threshold.

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1130

This strategy is also applied to other portions of the signal to confirm both the end of the earthquake (after the declared de-trigger obtained by the STA/LTA procedure) and the S-phase arrivals (if three-component data are available). In choosing the band of signal integration some factors must be considered: i) the sampling frequency; ii) the system filtering; iii) the spectnma of the signal of interest; iv) the noise spectrum. In general, if we compare results with the conventional STA/LTA detector we find a more efficient way of discriminating events and non-events, either with low signal-to-noise ratios or with spike-like noises (Fig.4). 3.3.3

Polarization Analysis by Covariance Matrix Decomposition (CMD) Method

In seismology, polarization analysis is widely used to devise filters capable of distinguishing elastic body waves into compressional (P) and shear (S) phases and of discrinainating surface Rayleigh and Love waves. In fact, it is well known that the different waveforms making up a seismogram have distinct polarization patterns (e.g. Aki and Richards, 1980) and that both compressional and shear waves show a high degree of linear polarization. In the hypothesis of isotropic media the particle motion of the P-wave shows its larger principal axis oriented in the direction of propagation. This direction can be defined by two angles: i) incidence angle, measured from the normal to the horizontal plane; ii) back-azimuth, which is measured from station to epicenter. After computation of the back-azimuth and incidence angle each seismogram can be rotated in a new system of coordinates, L, Q and T, where L is the longitudinal component of the particle motion along the P-wave direction, Q is the component in the SV-wave direction and T is the component in the SH-wave direction. A polarization filter based on the Covariance Matrix Decomposition (CMD) is generally applied to the seismograms in order to investigate the possibility of automatically computing the direction of polarization for Pand S-waves (see Appendix B). When a 3-C station is available ASDP uses the CMD algorithm which works both in time and in frequency domain (i.e. Montalbetti and Kanasewich, 1970; Samson, 1977; Jurkevics, 1988; Patan~ and Ferrari, 1997). This algorithm is applied in addition to other detector algorithms to increase the reliability of P- and S-waves detection and arrival time estimate. In order to recognize the P-phase the program applies the CMD computation starting at the time of the trigger previously obtained by STA/LTA and CF-based routine. After the CMD algorithnl is applied, a complete set of different output parameters (rectilinearity, azimuth, angle of incidence, coherence) is available for a selected time window following the first P arrival (Fig.2). After the automatic computation of both back-azimuth and incidence angle for the Pphase, the algorithm rotates each seismogram in the new L, Q and T coordinate system, oriented along the seismic ray direction. Since a parameter that exploits only one feature of the seismic signal can fail, a characteristic function is used in order to recognize the Sphase, when the P-phase has been previously identified. The advantage of the use of this function is that it includes several attributes of the S-phase (Cichowicz, 1993). In this case, even small simultaneous increases in each parameter cause a significant increase in the characteristic function. For S-phase, detection and picking parameters of the CF are computed by: i) CMD polarization analysis (degree of polarization, direction of polarization with respect to the P-wave); ii) spectral analysis (degree of spectral variation with respect to the P-wave); iii) a new estimate of the STA/I,TA in the P-coda region. Two time series are computed by the stun of the absolute values of each transversal

101

component. When the STA exceeds the LTA value, an S-phase arrival is declared and the result is used to compute the CF. 3.3.4

Multi-Station Analysis (MSA) for Event Identification and Location

Infmxnation on single trace furnished by the second stage of ASDP, including the arrival time of P- and S-waves, the end of the signal, the amplitude and period of the first phase and of the wave with maximum amplitude, are used as input data in the third stage of the ASDP automatic process. Here, the application of the Multi-Station Analysis (MSA) for phase grouping and earthquake identification provides information on all detected earthquakes, including estimates of location and magnitude (Patan6 and Ferrari, 1999). Alert reporting (graphics and tables) is automatically presented on the screen in case of changes in parameters derived from the single- and multi-station analysis. The process starts with the event identification. In order to select pickings that belong to the same earthquake, ASDP performs an extensive selection on the overall set of triggers. The identification of the recorded earthquake and the selection of the related first trigger/phase are also made on the basis of the signal spectral content, used to discard false triggers. This first trigger/phase and the overall set respect some selection criteria (Fig.5). On the basis of the event duration, the program computes the maximum probable distance in km (hypothetical ray of"influence") starting from the first recording station. This value represents the hypothetical distance at which the earthquake could be recorded. Then, MSA adopts some selection criteria on the overall set of trigger/phase available. In detail, these criteria are based on: i) verification that the trigger was not used in a previous location and was not included between P and S arrival times; ii) check of the signal spectral contents; iii) check of the time interval between the triggers. Traveltime computations are made using the velocity model available in the area where the first recording station is located; iv) check of the stations that recorded the event, as a fimction of network geometry. This part of the routine evaluates the least number of weighed recording stations, which are within the estimated ray of "influence", and establishes if this number is sufficient to declare an earthquake. A weight (varying between zero and the length of the ray) is associated with each available picking and greater weights are related to nearby stations. If the total weight exceeds an established threshold an earthquake is declared; v) check of decreasing P-phase amplitude, in a selected number of stations, for increasing station-location distance. The majority of false triggers do not pass through these selection criteria because they are removed in the previous stages of the program. The grouping rules consider (optionally) other basic seismological constraints on timing and require that phases have azimuths (when available) and amplitudes consistent with phases from the same eat~daquakes. During the trigger/phase association procedure the many weak unassociated pickings are singled out if they do not pass all the selection criteria in MSA. These adopted procedures are very useful especially when seismic swarms occur with earthquakes having onsets on the coda of the previous shock (no separation from between two events by portions of noise). Earthquake locations in ASDP can be computed using either external programs or a simplified least-squared internal location routine, called VBH (VisualBasicHypo). The latter uses arrival time estimates with their error estimates in a least-squares inversion algorithm. To evaluate the hypocenter parameters, the algorithm divides the calculation into two steps. In the former one, the hypocenter is computed using an approximate

102

method. Once convergence is achieved, the routine reconfigures itself, switching to the exact method, and computes the hypocen~er again using the parameter found in the first step as input. In this way, the computing time can be substantially reduced without affecting the accuracy of the solution. The inversion method is based on Marquardt's algorithm (Marquardt, 1963). The output includes the location solution (latitude, longitude, depth, origin time and related errors); it is reported both in a table and in graphic form.

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103

parameters setup, necessary to run the Hypo71PC program (Lee and Waldes, 1985). This form allows to: 9 insert the values in the Reset List (reset values of the test variables used in the program) and in the Control List (option values used in the program), to create the input file *.INP; 9 select referring planes, used in the automatic computation of the elevation time residuals. Modifications to this form enable the possibility to use other external programs (e.g. Hypoellipse, Hypocenter) for computing hypocenter location. Some specific forms for the interactive display and editing tools to review and correct the picking computation as obtained by the ASDP process are provided by the analyst review part o f the program which is partially integrated in ASDP. Figure 6 shows a typical screen display after the analyst has selected a specific earthquake for review and correction. Furthermore, several options are available to provide and download the information needing for monitoring the network status and individual station. Automatic and revised locations can be plotted on a selected map and therefore different detailed scales are possible. When the analysis has been completed, the user can choose to maintain the automatic ASDP solution in conjunction with the revised one. The hypocentral location may be printed with an appropriate graphical printer output, including numerical parameters, map display and wave forms.

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4

The Eastern Sicily Seismic Network by INGV-CT

The permanent seismic network (Fig.7) at the moment run by the Catania Section of the National Institute o f Geophysics and Volcanology (hereafter, INGV-CT) derives from the

104

integration o f two seismic networks running separately until 2000 by Istituto Internazionale di Vulcanologia (IIV) and Sistema Poseidon. The former network was composed of 14 seismic stations deployed on Mount Etna (10 one-component analog stations and 4 three-component stations) and 14 stations deployed in the Aeolian Islands (8 one-component analog stations and 6 three-component stations). The Sistema Poseidon network was composed of 56 stations, spread out over all Eastern Sicily, whose distribution defines three contiguous sub-networks (Fig.7). The first one is located in the northeastern part of Sicily and consists of 8 analogic three-component stations; the second one is mainly used for monitoring the seismic activity at Mount Etna and is made up of 39 analogic stations, all but four (threecomponent stations) equipped with one-component sensor; finally, the third sub-network is located in southeastern Sicily and consists of 9 digital three-component stations. Most o f the stations are equipped with short-period sensors (1 see). In all the subnetworks some broadband and very broadband stations exist.

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105

recorded on drtun recorders and digitalized at a sampling rate of 100 Hz in continuous mode, and at a sampIing rate of 200 Hz in trigger mode.

5

Seismic Signals in Tectonic and Volcanic Areas

Earthquake activib' in tectonic areas is typically linked to shear fracture mechanisms, which produce short-period events. In Fig.8 a typical example of earthquake recorded in the tectonic active area of Southeastern Sicily is shown. Conversely, in a volcanic environment, such as Mount Etna, seismic activity is due partly to tensile failure under low confinement pressure near the surface, and partly to shear failure trader compressive stresses (e.g. Patan~ et al., 1994). Seismicity often relates to unstable magma bodies and to the stress changes they induce on the embedding rocks, the interaction of gas with fluid, and fluid with solid providing the occurrence of particular tensile failures that generate peculiar seismic signals such as the "lowfrequency" earthquakes and/or the volcanic tremor. Such a class of events, usually displaying a low-frequency content, is conventionally labelled as "volcano-tectonic", a definition that aims at distinguishing these events from the much broader category of "tectonic" earthquakes (e.g. Patan~ et al., 1994). Such definitions bear little quantitative significance because the theological properties of the medium, the type of equipment, and the respective position of seismic source and stations concur in determining the appearance of seismograms.

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Fig.8. Example of "tectonic" earthquake recorded at two 3-componentstations deployed in Southeastern Sicily.

106

In Fig.9 an example of "low-frequency event" and relative spectrum is shown together with a typical earthquake associated to a shear-mechanism, recorded at the same station at Motmt Etna. For both events the spectrnm has been performed starting from the first P arrival for a 4096 point-samples window (sampling rate 160 Hz). Different views of the rote played by source and medium in determining the character of volcano-tectonic signals are reported in literature on active volcanoes. They range from the assumption that the poor high-frequency content of seismograms must be largely ascribed to shallowness of the source (Minakami, 1974), to models for dynamic sources based on the excitation, to resonance of cracks filled with viscous fluid (Aki et al., 1977; Aki, 1984; Chouet et al., 1987, 1994). The former viewpoint best accounts for the fact that wave fields propagate in highly absorptive shallow layers typical of volcanic edifices; the latter, for melt uprising or propagating in the brittle upper crust through nests of fractures. The structural complexity of the crust in Eastern Sicily, and in volcanic environments (i.e. IVlt. Etna, Vulcano, Stromboli) in particular, did not allow the earthquakes of the past to be easily defined as "volcanic" or "tectonic". Recent advances in the quality and quantity of seismological data available on Mount Etna have allowed to infer that the dynamics of the volcano might be tectonically controlled (Ferrucci and Patan6, 1993; Patan6 et al., 1994) and no apparent difference seems to exist between short-period earthquakes recorded in this area and those recorded in tectonic regions (Patan6 et al., 1997).

i,

, ,t,J.,,

,

ti

lrtk, ,

Fig.9. Comparison between a "tectonic" earthquake (up) and a "low-frequencyevent" (down) recorded at Mount Etna. The relative spectra starting from the first P arrival for a 4096 point-samples window are also reported.

107

6

Application

of ASDP

Software:

A Case

Study

at Mount

Etna

The application of the ASDP software has been tested on two different data sets recorded at Mr. Etna during 1997 and during July 2001, respectively. In this section we will describe the results obtained by Patan~ et al. (1999) while in the paragraph 7 we will discuss the recent on-line use of the software ASDP, implemented on the whole INGVCT seismic network. The first data set considered here (Patan~ et al., 1999) is composed by 330 local microearthquakes (1.7<M<3.8) recorded during 1997 at 14 seismic stations o f the Mt. Etna permanent network, integrated with data acquired by the Aeolian Islands network (Fig.7). In Figure 10 an example of two earthquakes recorded at six stations o f the Mt. Etna network and at one station of the Aeolian network is reported.

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Fig.10. Example of two Etnean earthquake recordings (latitude: 37~ longitude: 14~ depth: 5.22 kin). Seismograms relate to six stations (ECP, CIS, PDN, CTS, CZM and SCV) of the Mt. Etna network and to one station of the Aeolian Islands network (VPL). Automatic P and S pickings are also shown.

The availability of seismic data in digital form, also from three-component stations, provides acceptable surveillance for characterisafion of seismic activity in the Mt. Etna area_ The crust structure has now been defined in detail beneath the volcano (e.g. Laigle et al., 2000; Chiarabba et al., 2000; Patan6 et al., 2001). Currently, the major seismological problems at Mt. Etna are related to: i) the abundance o f events with emergent phase onsets; ii) the high level of noise due to tremor sources which affect recordings at the stations near the summit of the volcano; and iii) the distortion in the signals caused by analog transmission of data to the network centre by the use of radio

108

and/or dedicated telephone lines. It is noteworthy that the focal depths of Etnean seismicity usually range between 1 and 25 km. The overall geometry of the Mr. Etna network integrated with the Aeolian Islands one and the type of equipment used allow us to put high-quality constraints on seismic activity at Mt. Etna occurring at all depths, with the exception of very shallow earthquakes (h
Automatic Detection Statistics

The accuracy of P and S onset-time estimation is an important issue and critical in the automatic analysis for earthquake location. To analyse the signal detection capability of the ASDP module, Patan~ et al. (1999) compared automatic signal onset time picking with manual picking. At Mt. Etna accurate determinations of microearthquake pickings are generally problematic mainly due to the high noise. In the histogram o f Fig.1 l a the P-waves picking time differences between ASDP and those manuatly revised, dtp = Tp(AUTO) Tp (MAN) are reported. After the manual revision it was recognised that these time differences decrease with increasing event magnitudes (for M _> 2.5). It was found that about 65% of the dtp's are within 0.05 s while in 80% of the cases the dtp's are within 0.15 s. The availability of three-component data improves the detection of S-arrivals on the basis of the differences in polarization characteristics, spectral content and a new estimation of the STA/LTA in the P-coda region. Therefore, for S-waves detection, a similar procedure to that described by Cichowicz (1993) has been adopted, even though the characteristic function has been computed in a different way. In the histogram of Fig. 11 b the S-waves picking time differences between ASDP and those manually revised, dts= Ts(AUTO) - Ts (MAN) are reported. On the overall set of automatic S-picks (129) performed by ASDP about 40% of dts's are within 0.1 s, while in 65% of the cases the dts's are within 0.3 s. It is noteworthy that the majority of the records on the 3 three-component stations available at Mt, Etna do not have detectable S-waves. If we consider that the bulk of seismicity used in this study occurred beneath the central-western pat"~s o f Mt. Etna and that the three-component stations are located in the south-eastern sector of the volcano, the presence of magma at depth in the central-southern part of the volcano may be responsible for the S-wave radiation attenuation.

109

al

<-1

4).8

4 3 . 6 -0.4

-0.2

0

0.2

0,4

0,6

0.8

>1 sec

b)

<-1

,-0.8 4),6

-0.4

-0,2

0

0,2

0.4

0.6

0.8

>1 sec

Fig.ll. For the 261 Etnean earthquakes automatically located by ASDP (79% of the overall data set), histograms reporting the differencesbetweenthe ASDP automatic and manual picking for the P-waves (a) and for the S-waves (lo). To identify S-waves a characteristic function (see the text for fflrther details) in which the application of the polarization analysis (CMD) presents a greater weight, has been applied. Therefore, the positive bias in the S-phase detection will depend on the choice of the fixed and moving windows used in the CMD analysis (Patan6 and Ferrari, 1997).

6.2

Automatic Location Statistics

The accurate determination of earthquake hypocenters depends on: i) the precision of P and S pickings; ii) the local velocity structure and iii) the network geometry. Conventional earthquake location estimates are based on a linear approximation to a set of non-linear equations and 1D velocity model. In recent years, new methods for hypocentral locations using a 3D velocity smlcture have been proposed (elg. Thurber, 1983; Eberhart-Phillips, 1986; Hole, 1992; Thurber and Atre, 1993) but they are not always usable in practice (e.g. Schwartz and Nelson, 1991; Hole, 1992).. The computation with 3D velocity models is in contrast with our need to obtain earthquake locations within a few minutes of their occurrence in the automatic analysis for surveillance purposes. At present, an ID model slightly modified from the one by Him et al. (t991) is used in automatic locations. However, we are testing the applicability of the available Mt. Etna 3D velocity models (i.e. Laigle et al., 2000; Chiarabba et al., 2000; Patan4 et al., 2001) in atttomatic locations. To automatically locate the earthquakes in the above data set with ASDP the standard HYPO71 routine (Lee & Lahr, 1975 revised by Lee and Waldes, in IASPEI Software Library, 1994) has been adopted. This choice allowed comparing ASDP results with those obtained using the XRTP-IASPEI software and with the locations obtained rominely by the analysts. Using the MSA procedure for phase gouping and earthquake

110

identification, a reduction of the Lmcertaiv2y, deriving Dom an incorrect association of time pickings, has been achieved. In Figs. 12a and b the 261 automatic locations provided by ASDP (79% of the whole data set) are compared with those maematly obtained by analysts. Encouragingly, 92% of earthquakes with M_>_2.4 were wet1 automatically located. For the Iower magnitude events (M<2.4) 62% of automatic locations were of high quali*y (Fig. 13@ Histograms in Fig. 14a-c give the differences be~-een mm~lal and automatic location parameters (latitude, longitude and depth).

e }~

,:

r

,. ,: i~......

e:,

Z =

b)

Fig.12. Comparisonbe'e~veenthe automatic ASDP (red ckcles) and the mamml(black squares) Iocations tbr the 261 earthquakes. Maps and cross-sections are related to the period January-Jmne 1997 (a) and JulyDecember 1997 (b) Maps also report some stations (with squares and triangles) of the Mt. E~aane~c*ork.

1tl

Regarding latitude, the differences are within 1 km and 2 km for 81% and 90% of the cases, respectively. For longitude the differences are wiflain 1 km and 2 km for 65% and 81% of the cases, respectively. Finally, for the depth the differences are within 1 km and 2 km in 58% and 71% of the cases, respectively. The slightly better precision of the latitude parameter is considered to reflect the geometry of the combined Etnean seismic network and Aeolian Islands stations. In the case of focal depth, events with M22.4 are well constrained by the favourable azimuthal coverage of the area, due to the relatively higher signal to noise ratio that allows a more accurate time picking. In general, in these results we do not observe a dependence of location errors on the magnitude (Fig. 13b-d), rather that earthquakes with maj or errors are related to locations computed with an inadequate azimuthal coverage. In Fig.15 a comparison between automatic and manual locations for a small shallow swarm is shown. In general computed automatic hypocenters are comparable to the manual ones within error bounds. Finally, in Fig.16 the location parameters (Hypo71 output results) for the whole data set obtained from the two automatic routines ASDP and XRTP-IASPEI are reported. At the ex-IIV centre, the XRTP-IASPEI software was routinely used for automatic locations of earthquakes recorded at the two seismic arrays of Mt. Etna and of Aeolian Islands. In the same figttre, the comparison of the ASDP and XRTP location parameters with those ~ revised manually is reported. It is noteworthy that minor RMS values and hypocentral errors obtained by XRTP-IASPEI do not represent true error limits, due to the minor number of phase readings involved in the calculus and to the related worst azimuthal coverage, In fact, the XRTP- IASPEI statistic includes much lower unreliable RMS values and errors, which are obtained by using only four (27% of the cases) and five (46% of the cases) readings, without S phases. A better performance of the ASDP module with respect to the XRTP software is clearly observed.

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Fig.14. Histograms reporting the differences between the automatic and manual location parameters (latitude, longitude and depth) for the 261 earthquakes.

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113

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Fig.16. Histograms reporting the comparison o f hypocentral parameters (Hypo71 results) for the 261 event locations obtained via phase manual pickings, via ASDP and via XRTP-IASPEI software. Statistics o f the solution quality of hypocenters (Quality class), number (NO) of station readings (only P for XRTP_IASPEI and P+S for manual and ASDP), largest azimuthal separation in degrees between the stations (GAP), root mean square error of time residuals in seconds (RMS), standard error o f the epicenters in kin (ERH) and standard error of the hypocenters in km (ERZ) are shown. It is noteworthy that minor RMS values and hypocentral errors obtained by X.RTP-IASPEI do not represent u'ue error limits, due to the minor number of phase readings (without S phases) involved in the calculus and the related bad azimuthal coverage.

114

On-Line Processing of INGV-CT Seismic Data: Preliminary Results by ASDP Application Since May 2001, ASDP is under test to be used for real-time analysis of earthquakes recorded by the integrated INGV-CT network. The preliminary results obtained from the analysis of data acquired in the period July 12-18, 2001 at Mount Etna are here shown. More than 2600 earthquakes were recorded between 12 and 18 July with Mmax=3.9, heralding one of the most important eruptions at Mt. Etna in the last decades. It has been characterized by an unusual eruptive style, with several lava flows along a complex fi'acture system (Fig.17), frequent and powerful strombolian explosions (sometimes culminating in lava fountains) and abundant gas emissions from adventive vents. Volcanic tremor had a key role in monitoring the evolution of this eruption. Paroxysmal phases such as lava fountains and powerful strombolian activity were associated with remarkable increases of the tremor amplitude. Although with some fluctuation, high amplitude values continued after the opening of the eruptive fractures, reaching a maximum on July 25.

Fig.17. Eruptivefractures(white line) and lava flows of the July-August2001 eruptionat Mt. Etna.

Among about 2600 earthquakes identified on drum recorders, a set of 416 events has been manually localized by the analysts, whereas 973 shocks have been localized by the automatic ASDP module. In total, 147 automatically "well localized" (erh < 1 km and erz

115

_<2 kin) events are availabie. In Fig. 18, these automatic locations provided by ASDP are compared with those obtained manually by analysts on the same data set.

4~

4~

4~

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Figo18. Comparisonbetweenthe automaticASDP (blue circles)and the manual(red squares) locations.

h Fig, 19 the comparison between the location parameters obtained by phase manual pickings and by the automatic routine ASDP is shown. It is to be noted that, with respect to the application of ASDP to the off-line analysis described in Section 6, the on-line application shows automatic locations affected by larger errors. This is due to the fact that the program is, at present, still being tested and fine setup of parameters is at a preliminary stage. In particular: i) the same configuration of triggem,ag and detection-phase parameters is used for all the stations; ii) higher reject-location thresholds for automatic recog-nition are selected.

ii6

A study on the best triggering and detection-phase parameters to be considered for each station is in progress. In Fig.20, the comparison between the nmnber of the automatic locations and the earthquakes identified on paper-drums, as a function of magnitude, is reported. It is shown as the number of earthquakes recognized by the analysts is higher than the automatic locations.

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Fig.19. Histograms reporting the comparison of hypoeentral parameters (Hypo71 outputs) for the earthquakes used, obtained via phase manual picking and via ASDP. Statistics of the number (NO) of station readings, largest azimuthal separation in degrees between stations (GAP), root mean square error of time residuals m seconds (R_MS), standard error of the epicenters in km (ERIt) and standard error of the hypocenters in km (ERZ) are shown.

117

Finally, the histogram in Fig.21 gives the differences between manual and automatic location parameters (latitude, longitude and depth). For earthquakes with M _> 2 the differences are less than 1 km for 65% in latitude, 63% in longitude and 31% in depth. The worst precision of the depth parameter is mainly due to: i) the high level of noise due to tremor sources which affect recordings at the stations near the summit of the volcano; ii) the shallowness of earthquakes which does not allow a reliable automatic detection of both P-waves at farthest stations and S-waves at 3-component ones. 450

g] Automatic 9 Readings on paper

400 350 300 250 200 150

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Fig.20. Comparison between the number of the automatic locations and earthquakes identified on paper, as a function of the magnitude.

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5

>5 K m

Fig.21. Histogram reporting the differences between the automatic and manual location parameters (latitude, longitude and depth).

118

7.1

First Application of Automatic Polarization and Spectral Analysis

The automatic application of the polarization filter routine by Covariance Matrix Decomposition (CMD) has been tested for the first time on the data a~qtfired at three 3component permanent stations (TDF, M N T and ESP) and at nine 3-component temporary stations deployed on Mt. E m a during the July-August, 2001 eruption. The results related to ND,IT and ESP are shown in Fig.22. The polarization of the tremor wave-field, recorded simultaneously at 12 threecomponent digital stations, equipped with short period (ls) or broad-band (20s) sensors, is analyzed by C M D in different frequency bands (0.1-1.5, 1-3, 3-5 and 5-7 H z for broadband stations; 1-3, 3-5 and 5-7 Hz for short-period stations). C M D has been automatically applied on recorded signals, considering a time window o f 0.3 seconds. The obtained values o f azimuth, incidence angles and rectilinearity have been averaged on the whole length o f each recorded file ( m a x i m u m 2 minutes). In Figs.22 and 23, for each station the cumulative direction (rose diagrams) o f azimuth during the whole analysed period is reported together with the azimuth, incidence angles and recfilinearity.

_+F

.iF

SA

_F

F ..................... E ......................

~ . . . . :'-...............

I 7

6

8

9

t0'1i'12

13'14 1 5 1 6 ' 1 7 " 1 8

19 20

2 1 ' 2 2 23r 24' 25 26 27 28 29 30 31' Ju}Y

,,, [~

T

~

~

.

"

.

"

.

~

.

_,.,

.

'

'

'

-

'

Rectltinea~ilV

---

_

-

-

'

~

Rectilir;egrib/

F: Lava fountain 8A: S~ombolian activily S: Seismic swarm E: Erup~on

--MNT

=%-

5 lug 2001

18 lug 2001

21 luQ 2001

--ESP

Fig.22. For ESP and MNT the on-line application of CMD polarization analysis during July 2001 is shown. Data are analyzed in the 0.15-1.5 Hz frequency band. The plot of azimuth (0 ~ - 360 ~ N), incidence angle (0~ - 90~ and rectilinearity (0 - 1) of the polarization vector is reported together with the rose diagrams of the cumulative direction of polarization on the horizontal component. At ESP stations a variation from ca. EW to ENE-WSW of the direction of polarization, starting from the eruption onset (July, 17), is evident. At the bottom the comparison between spectra computed at these two stations (ESP: black, MNT: grey) in three different periods (July, 5, 18 and 21) is shown. At the top, the RMS amplitude of tremor, calmalated on 30 second windows, is also reported.

II9

Preliminary results indicate that, before and during the July-August 2001 Mr. Ema eruption, significant variations in time o f direction o f polarization, incidence angle and linear content o f the tremor wave-field occurred. These variations are mainly observed on the broad-band recordings in the frequency range between about 0.5 and 1.5 Hz. This is in agreement with time variations o f the activity observed during the pre- and the eruptive period. Although we observe a complex polarization pattern, the behavior o f the polarization shows a steady horizontal, near-linear, approximately west-east pattern, at several stations (TDF, MNT, ESP, ERS, EC11). Such a behavior excludes confinement o f the source to the only active vents and suggests the possibility that a vertical extended source with overall north-south alignment might radiate SH waves, in the direction normal to the source.

Fig.23. Map showing all .stations used for the polarization analysis. For some stations, the plot of azimuth (0~ - 360~ N), incidence angle (0~ - 90~ arid rectiimearity (0 - 1) of the polarization vector is also reported. On the left, we show the rose diagrams of the cumulative direction of polarization on the horizontal component for the whole period (short-period stations July 18-24; broad-band stations July 30-August 13). The grey lines in the map represent the eruptive fracture system. The main vents activated during the eruption are also reported.

120

Other than automatic polarization, spectral analysis in continuous mode has been p e r f o ~ e d during 9,e pre- and the eruptive period on tremor recorded at some stations. .An example o f spectrograms obtained at TDF station, using a moving wi~adow FFT of 4096 point-samples (sampling rate 125 142z), is shown in Figo24.

TDF

l~scc

25

?

20

l~cs

15

i:~

i0

A,U.

~! 5coo

5

{ 2:;

25

20000

i} .....

20

!SCCO

i5

!ti

I0

I~GCO

~co

5

15~0 25 2O

~;ococ

35 ~0 ;>(3

2a I T 20 | 10 5

bl 25 20 15 10 ............... ~,, ~, ~Y;~

:.,~, .

SA

F = Lava tountoin SA = S t r o m b d i a n o c t M ~ S = Seismic s w a r m E = Eruption

F

F

................... i .

09

.

.

lO

.

.

.

II

.

....':,: =. . . . . . . .

.

12

i,~

14

;5

}6

.......... i7

18

]9

iremor

amplitude

/ 30 s

2Q JLi~

Figo24. (a,b) SpectroN'ams calculated at station TDF by the applicaion of FFT on 4096 point-sampWs windows. (b) specn-ogams obtained by normalization of spectra at the maximmn ampiitude value. On the bottom, the RMS ampkitude of tremor, calcu[ated on 30 second wL~dows, is a!so reported for the period 0920 J~@.

121

It is clearly observable that predominant energy falls into 1-7 Hz frequency band. In the same figure, the RaMS anaplitude of tremor, calculated on 30 second windows, is reported. The highest amplitude values are observed in correspondence of paroxysmal phases such as lava fountains and Strombolian activity. This observation is confirmed also by the variations of predominant frequency as a function of eruptive and/or seismic activity. Moreover, variations in frequency content are highlighted in spectrograms of Fig.24b, obtained by the normalization of each spectrum at the maximum amplitude value. It is noteworthy that, detailed analysis and studies on the acquired data during this eruption and on the source mechanism responsible of the recorded tremor are still in progress.

8

Concluding remarks

The deployment of advanced local and regional arrays, the associated development and implementation of atttomatic and increasingly powerful data processing techniques, represent some of the major advances in the field of seismic monitoring in recent years. Furthermore, the recent increase and integration of three-component digital stations in local networks provide more reliable phase identification and azimuth estimates which are particularly useful in locating weak events. In general, on the basis of acquired experience, we retain that the aim of future advances in seismic processing software must be the development of new strategies in processing seismic data, including multi-algorithrn approach using classical procedures in time and frequency domains and pattern matching and neural networks techniques. That in order to enhance automatic detection and classification among earthquakes (local, regional and teleseismic) and volcanic events (tremor, low-frequency events, explosionquakes) recorded both by short-period and broad-band sensors. The PC-Seism software and, in particular, the ASDP module here described have been developed to solve the problems of automatic detection, discrimination and phase recognition among different seismic signals recorded by a local network. In origin, the strategy adopted was the realization of an intelligent multi-algorithm software, working also on a PC-based remote station, which could operate the discrimination, the selection of waveforms and also produce phase log data to be transferred automatically to an acquisition centre (where a multi-station analysis and more sophisticated algorithms can be implemented). Today this is possible thanks to the advances in electronic miniaturization and PC capabilities. In this work we have discussed the f~rst operational version of the ASDP module (Patan~ and Ferrari, 1999) which represents a new generation of object-based programs for automatic seismic data processing on a personal computer. In f~ict, this and other similar programs may represent an essential key in advanced processing technology to handle data acquisition, quality control, database organization, automatic interpretation and interactive computer graphics which will be required in a modem monitoring system. A PC-based system is clearly characterized by more limited resources (only one CPU) with respect to a multi-processor-based system. Therefore, the choice of the implemented algorithms in ASDP and their use has been governed by the requirement to achieve the best results ha continuous on-line processing of local earthquakes acquired by a seismic network on a personal computer. ASDP module adopts most of the seismic data analysis procedures and algorithms used separately by seismologists. However, different modifications, integration and optimization of the routines have become necessary in order to enhance and conform the

122

original algorithms to our purpose. The main feature in ASDP is represented by a modular multi-algorithm detection approach, which allows to optimize the several analysis procedures both for signals derived from one-component and three-component stations. Resulting parameters are used in a multi-station analysis algorithm, MSA, for the event identification and location. Tests on local earthquakes suggest that it is convenient to choose some selection algorithms in series, to be able to distinguish seismic events from noise disturbances instead of using one sophisticated selection algorithm. The control routines implemented in the ASDP module are able to provide the necessary information for the database SNM module for monitoring tile network status. During the operative mode, all the processes can also be controlled by an operator and the parameters modified without stopping the program, through a graphic interface that automatically allows the display and interpretation of processed earthquakes and provides the outputs. The most important advantage of the ASDP program architecture is that it facilities fllture software development, since the individual processes are modnlar and nearly independent. The application of the ASDP module to two data sets recorded at Mt. Etna volcano have provided the opportunity to examine several design featttres implemented in this software. In this Chapter we compare the results obtained by Patan~ et al. (1999), which used a set of 330 local microearthquakes recorded during 1997 at Mt. Etna volcano, with the preliminary results obtained by the on-line application of ASDP to another data set recorded by INGV-CT network in the period 12-18 July, 2001. The comparison of ASDP automatic phase picking with manual ones indicates that for almost the totality of the events the multi-algorithm approach, in the automatic earthquakes detection, optimises the picking estimate and is better than a data analysis performed using a single algorithm (e.g. XRTP-IASPEI). Moreover, our results indicate that both ASDP automatic welllocated events and the related manual hypocenter locations arc comparable within the estimated errors. Therefore, the ASDP module can be useful for automatic detection and monitoring of local earthquakes at a single-station and/or at a seismic array, and it does so with a high degree of reliability. Future tests and optimisations will regard cases of sustained or frequently recurring signals, such as those produced by intense seismic swarms or by volcanic tremor. In this regard, in this paper we tested for the first time the applicability of two new modules for the on-line polarization and spectral analysis of continuous signals, such as the volcanic tremor recorded before and during the July, 2001 Mt. Etna eruption. We foresee that ASDP v-ill be modified and subsequently integrated with soft'are modules for the analysis of regional and teleseismic earthquakes. At present, the software project is almost complete and many of the proposed objectives have been achieved even though further developments in the ASDP module are still in progress (i.e. the application of Artificial Neural Detectors for events identification and classification).

Acknowledgments The present work was ~a'itten trader the permission of Elsevier Science, using parts of previously published papers (D. Patan6 and F. Ferrari, ASDP: a PC-based program using a multi-algorithm approach for automatic detection and location of local earthqtmkes, pp. 57-74, Copyright 1999; D. Patan~, F. Ferrari and F. Ferrucci, First application of ASDP software: a case study at Mt. Etna volcano and in the Acri region (Southern Italy), pp. 7588, Copyright 1999), printed by the Journal "Physics of the Earth and Planetary

123

Interiors", Volume 113 Nos. 1-4, in the Special Issue: Recent Advances in Earthquake Monitoring and Seismic Network Operations. We wish to express our thanks to the Elsevier Science for allowing its publication.

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Fletcher, J.B., Baker, L.M., Spudich, P., Goldestein, P., Sims, J.D. and Hellweg, M., 1992, The USGS Parkfield, California, dense seismograph array:UPSAR. Bull. Seism Soc. Am., 85, 1518-1522. Flinn, E.A., 1965, Signal analysis using rectitinearity and direction of particle motion: Proc.IEEE, 53, 1874-1876. Haikin, L.M., Kushnir, A.F. and Dainty, A.M., 1998, Combined automated and off-line computer processing system for seismic monitoring with small aperture arrays. Seism. Res. Lett., 69, 235-247. Harris, M. and Young, C., 1997. Matseis: a seismic GUI and tool-box for MATLAB. Seism. Res. Lett., 68, 26%269. Him, A., Nercessian, A., Sapin, M., Fen'noel, F. and Wittlinger, G., 1991, Seismic heterogeneity of Mt. Etna: structttre and activity. Geophys. J. Int., 105, 139-153. Hole, J. A., 1992, Nonlinear high-resolution three-dimensional seismic travel time tomogaphy. Joum. Geophys. Res.,97, 6553-6562. Joswig, M., 1990, Pattern recognition for earthquakes detection. Bull. Seism Soc. Am., 80, 170-186. Jurkevics, A., 1988, Polarization analysis of three-component array data: Bull. Seism. Soc. Am., 78, 17251743. Kedrov, O. K. And Ovtchinnikov, V.M., 1990, An on-line analysis system for three-component seismic data: method and preliminary results, Bull. Seism.. Soc. Am., 80, 2053-2071. Kim, W.Y, Aharonian, V., Lemer-Lam, A.L. and Richards, P.G., 1997, Discrimination of earthquakes and explosions in southern Russia using regional high-fi'equency three-component data from the IRIS/JSP Caucasus network. Bull. Seism. Soc. Am., 87, 569-588. Klumpen, E. and Joswig, M., 1993, Automated revaluation of local earthquake data by application of generic polarization pattern for P- and S- onsets. Computer & Geosciences, 19, 223-23 I. Laigle, M., Hint, A., Sapin, M., Lepine, J.C., Diaz, J., Gallart, J. and Nicolich, R., 2000, Mount Ema dense array local earthquake P and S tomography and implications for volcanic plumbing, J. Geophys. Res., ID5, B9, 21,633-21,646. Lee, W. H. K., and Lahr, J.C., 1975, HYPO71 (revised): a computer program for determining hypocenter, magnitude and ftrst motion pattern of local earthquakes, U.S. Geol. Surv. Open-File Rept., 75-311,144. Lee, W.H.K. and Valdes, C.M., 1985, HYPO71PC: A personal computer version of the HYPO71 earthquake location program. U.S. Geol. Surv. Open-File Report, 85~749, 43 pp. Marquardt, D.W., 1963, An algorithm for least-squares estimation of nonlinear parameters, J. SIAM, tune, 431-441. Miuakami, T., 1974, Seismolog;r of volcanoes in Japan. In Physical Volcanology, L. Civetta, P. Gasparini, G. Luongo, and A. Rapolla (Editors), Elsevier, Amsterdam, 1-27. Montalbetti, J.F. and Kanasewich, E.R., 1970, Enhancement of teleseismic body waves with a polarization filter: Geophys. J.R. Astr. Soc., 21,119-129. Mueller, R.J., Johnston, M.J.S., Borcherdt, R.D., Glassmoyer, G. and Silverman, S., 1995, Near real-time monitoring of seismic events and status of portable digital recorders using satellite telemetry, Bull. Seism. Soc. Am., 84, 640-645. Poland, D. and Ferrari F., 1997, SeismPol A Visual-Basic computer program for interactive and automatic earthquake wavefoma analysis., Computers & Geosciences, 23, 9, 1005-1012. Patan~, D. and Ferrari, F., 1999, ASDP: A PC-based program using a multi-algorithm approach for automatic detection and location of local earthquakes. Physics of the Earth and Planetary Interiors, 113, 57-74. Patan~, D., Ferrucci, F. and Gresta, S., 1994,. Spectral features of microearthquakes in volcanic areas: attenuation in the crust and amplitude response of the site at Mt. Etna, Italy, Bull. Seism. Soc. Am., 84, 1842-1860. Patan~, D., Ferrucci, F., Giampiccolo, E. and Scaramuzzino, L., 1997, Source scaling of microearthquakes at Mr. Etna volcano and in the Calabrian Arc (southern Italy). Geophys. Res. Lett., 24, 1879-1882. Patan~, D., Ferrari, F. and Ferrucci, F., 1999,. First application of ASDP software: a case study at Mr. Etna volcano and in the Aeri region (Southern Italy). Physics of the Earth and Planetary Interiors, 113, 75-88. Patane, D., Chiarabba, C., Cocina, O., De Gori, P., Moretti, M. and Boschi, E., 2001, Tomographic images and 3D earthquake locations of the seismic swarm preceding the 2001 Mt. Etna eruption: Evidence for a dyke intrusion, Geophys. Res. Let., submitted. Roberts, R.G. and Christofferson, 1991, Seismic signal detection - a better mouse trap? Bull. Seism. Soc. Am., 81,2511-2515. Rogers, J.A. and Stephens, C.D., 1995, SSAM: real-time seismic spectral amplitue measurement o n a PC and its application to volcano monitoring. Bull. Seism Soc. Am., 85,632-639.

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A

Appendix: Short-Term Average (STA) and Long-Term Average (LTA) and Characteristic Function (CF)

Signals in time domain (such as seismic events) can be examined by comparing a limited set o f values around a single sample (Short-Term Average) and a set o f values in a wider range (Long-Term Average). This method is used when significant variations in the characteristic parameters o f the seismic trace occur. The two sets o f values stated above can be examined in two different ways, by: 9 linear mobile average 9 exponential smoothing

126

In the "lhnear mobile averaoe , if we indicate with x~the value of the function that we want to examine at the sample i and with X,. the value of the mobile average at the same sample i, we have: n-I

Z X{i-J) Xi _

J=O

O)

/'/

where n is the whole set of considered values. Equation (1) can also be expressed as a function of the average obtained at the previous point:

Xi + E Xo--O -- XO-n) Xt

_

J=I n

X~ = Xu_ 8 +

X/ -- X(,_n) 12

(2)

Equation (2) is easier to use, since the number of operations im, olved is smaller than in equation (1). In both eases it is important to store the previous n-1 values of the function. It is worth stressing that, in the case of mobile average, the n values of the function are all involved with the same wei~l~t ha the computation of the average. Whereas, for the short-term average, it is better to have a different weight for each value, giving higher weights to the values closer to that examined. This is what is considered m the exponential smoothing, through the relation: X, -- Xc,.,?- C(x, - Xo-,)

(3)

where C is the smoothing coefficient ranging between 0 and 1. With respect to equation (2), equation (3) does not require any rotating vector since any new sample renews the value of the computed average in the previous step. In this way, the history of the average is considered in the computation. Therefore, the function representing the trend of the influence of the previous samples on the average at sample i, shows a decreasing exponential form. However, it is better to describe the character of a seismic trace by a specific function, named Characteristic Function (CF), which takes into account the amplitude of the trace and its derivative. In fact, if the trace is represented by a time series f(t) and its derivative isf'(O, the characteristic function is defined as:

E(t) =f(t)2 + Cz + f'(t)2

(4)

where C2 is a constant. This value has an important role in varying the relative weight assigned to the amplitude and to its derivative, as a function of the sampling rate of the si~ml and of the characteristic of the noise at each seismic station. Therefore, the parameters of a seismic trace considered are: 9 the value of the sample i under examination: f(i) 9 the variation of the value of the examined sample with respect to the previous value:

f'(i)

These two factors are variable among the samples, especially when the seismic wave reaches the sensor. It is worth stressing that, by the constant C2, the variation is weighted

127

taking into account the characteristics of the station. This function has been chosen because it integrates both the amplitude values and those of its derivative contained in the seismic trace and varies with these two parameters. Moreover it is always positive and is easily determined. As stated above, the value of C2 has an important role as a function of the noise at the recording site. In fact, if the noise amplitude is comparable with that of the ea~hquake, the earthquake is less identifiable. The higher the noise, the lesser the meaning of the control of the derivative of the seismic trace in defining the exact starting and ending instants of the event. Conversely, if the noise level is very low or the signal to noise ratio is high, due to the high energy content of the recorded earthquake, the control by the derivative is important. In order to define the starting time of the seismic wave it is important to determine when the pattern of the characteristic function E(t) abruptly changes. This means observing the STAILTA variation in time. What is above reported is referred to in the paper by Allen (1978). As stated in the ASDP module description, Allen's algorithm has been slightly modified for our purposes.

B

Appendix: Covarianee Matrix Decomposition Method (CMD)

Polarization fiker in time domain based on the Covariance Matrix Decomposition is generally applied to the seismograms in order to investigate the possibility of automatically computing the direction of polarization for P- and S-waves and of translating the concept of quality of polarization into a numerical form. In the past, polarization filters have been tuned to enhance arrivals from a particular direction, especially in teleseismic and regional earthquakes. The CMD filter was adapted to determine the azimuth, 0, and apparent angle of incidence, i'. Attention was focussed on the first few cycles of the first arrivals which are considered to be the most linear polarization section of the record and are expected to approximate to pure P motion. Their polarization direction will be that of the azimuth, and the largest eigenvalues of the covariance matrix, kl, wil! thus have this direction. The behavior of the filter is monitored by the function of rectilinearity and by the coherence function, both of which should be close to unity if the seismic signal is truly P. To compute the covariance matrix, a similar approach to that of Montalbetti and Kanasewich (1970) and Jurkevics (1988) is used. Montalbetti and Kanasewich's method (1970) has been extended to enable the azimuth and angle of incidence of events to be determined from their first arrival at a single recording station. Jurkevics (1988) suggested that covariance averaging is strictly dependent on the choice of the frequency interval of analysis. The choice of window length and bandwidth are subject to the usual trade-off between resolution and estimation variance and only the use of longer windows and wider frequency bands yields more stable and reliable estimates. The main difference, with respect to the polarization filter of Jurkevics (1988), is that the mean for each component of the matrix (over the time window considered) is not equal to zero (Benham et al., 1988). Let us consider a time window of N samples, each sample defined by three coordinates x, y and z. The mean value for each coordinate, over the [7"1, T2] time window, can be defined as: m ~ = - ~1~-~, z..,. `

,

my=--

1~

y

and

m~=

--.

with (N). - N~) r = T2 - T1, where z is the sample rate and N = N2 - Nt + 1.

128

~..,-i

(5)

Then the covariance matrix can be written as:

(x - ~ ) ( y - m.)

1( ~-~(x-m<)~v c = - N l Z ( y - m y ) ( X - m,)

LZ(~-,,,..)(~<-,,,~)

~(x- m.)(z- m~)/

Z ( y - ~.,)~-

(6)

~-'~(z-m:) 2

~"~(z-m:)(y-my)

)

N2

where ~

is replaced by ~

.

i~N1

After a computation of the matrix, we get three eigenvalues 3.1, 22 and 23 and three eigenvectors V1, ~ and V3 (each one is defined by its three direction cosines: v~, v{ and vT). Therefore, under the considerations that x is the East component (E), y the North component (N) and z the vertical component (V) of the ground motion in the seismic signal, if the eigenvector of the largest principal axis is V= (VE, V,v, Vz), then:

O= tan-l(VE/Vu)

and

i'=cos-l(I ~5"[)

(7)

The computation is applied over a window of length N beginning at sample r and runs using a moving window. Each window fields Or, i" of azimuth and apparent angle of incidence. The output values, averaged over n windows, are: t7

= (1 / n ) y ' or

i = sin-t [(V, t V. )sin(i'/2)]

and

(8)

r=l tl

i'=(1/n)~"i,

where

r=l

Confidence limits at 95% on O, i' are calculated by Fisher statistics (Fisher, 1953). Values of O, i' are rejected for any window over which the solution for the covariance matrix has rectilinearity RL < 0.85. Rectilinearity is computed by:

RL

=..i',i

!i

(

2,

~ _ .~_] z ./'1+ ;~

(9)

;~)

This coefficient always lies between zero and 1. It is equal to zero when polarization is null (e.g. a sphere in space) and close to 1 when polarization approaches rectilinear beha~'ior. The coherence function (Sax and Mims, 1965) between E and N component of ground motion is defined by:

Cov[ ,Jv] &'~

-J(V~r[El*Wr[N])

(lO)

The present definition preserves the distinction between pure P motion (for which

Ben .= I) and pure S motion (Ben = -1). BE~-= 0 for elliptically polarized phases.

129

The SIL Seismological Data Acquisition System - A s Operated in Iceland and in Sweden-

R e y n i r B56varsson a n d BjSrn L u n d

Uppsala University, Dept. of Eartia Sciences, S-75236 Uppsala, Sweden. [email protected]

Abstract. The SIL (South Iceland Lowland) seismological data acquisition system is operated in Iceland with 43 digital short- and broad-band seismic stations and in Sweden with 38 digital broad-band seismic stations. The system is mainly designed for automatic evaluation of microearthquakes with minimum operational cost and has shown the capability of automatic evaluation of more then 1500 earthquakes per day or episodically several earthquakes per minute. The automatic, on-line, earthquake analysis performed by the SIL network can be divided into four categories: Singlestation analysis performed at the site stations includes a phase detector, which sends short messages with the characteristics of each detected phase to the centre, and a contimmus ground motion monitor. Multi-station analysis performed at the centre using the phase reports from all detecting stations and producing information about all possible events including estimates of location, magnitudc and fault plane solutions. Alert reporting is used in Iceland to notify the operators of the network in cases of a priori defined changes in parameters derived from the single- and multi-station analysis, with the aim of providing information for the authorities, media and public in case of large earthquakes or volcanic eruptions. Teleseismic data acquisition is performed based on electronic email messages from global seismological networks, no attempt is made to detect and locate teleseismic events locally. After the automatic analysis, further refinement is obtained through multi-event analysis, performed on groups of events within a limited hypocentral distance. This includes relative location of groups of similar events, seismicity pattern analysis using Spectral Amplitude Grouping (SAG) and stress tensor inversion of earthquake focal mechanisms. Analysis of earthquakes with similar waveforms, using correlation techniques, reveals that a substantial fraction of events occurring in a given area belongs to families of events with similar waveforms. Based on this a new approach is being taken regarding the automatic operation of the network. A geographically indexed data base will be created where different classes of earthquakes are stored. As new earthquakes are recorded by the network the system automatically looks for similar waveforms in this data base and, if found, takes the onset and first motion direction picks from the data base.

1

Introduction

Based on an E u r o p e a n initiative, the Nordic countries in 1988 s t a r t e d a project on earthquake prediction research in southern Iceland called the SIL (South I c e l a n d Lowland) project (Stef~nsson et al., 1993). T h e m a i n achievement of the S I L - p r o j e c t was to establish a n a u t o m a t i c earthquake d a t a acquisition a n d e v a l u a t i o n system, the SIL-system. T h e i m p o r t a n c e of microearthquakes in earthquake p r e d i c t i o n research a n d their significance for the u n d e r s t a n d i n g of the physical processes leading to earthquakes significantly influenced the desig-n of the SIL-system. It was recognized t h a t the

131

recording of earthquakes down to mag-aitude ~/[L ----- 0 and retrieval of source information from these events would require a new seismic network design. The rapid evolution in computer and communication technology and the introduction of inexpensive but powerful personal computers has allowed for such a design of the SIL network. The first eight stations of the new seismological network were installed in the South Iceland seismic zone in 1990. Since then, 17 stations have been added in South Iceland, 14 stations in North Iceland and additionally 4 in the central part of Iceland, making a total of 43 stations (Fig. 1). More than 200,000 microearthquakes have been recorded and analysed by the network in Iceland during the operational period 1990 through October 2001. In Sweden, 12 closely spaced d i s t a l broad-band seismic 335"

345"

70" 5"

I0"

15"

20"

25" 70 ~

g

9

65"

9

65"

55"

335"

340 ~

345"

55"

~ 'h-5 5"

1O"

15"

20"

25"

Fig. 1 The networks in Iceland and Swedenthat uses SIL technology. The station spacing in Iceland is, in the dense areas, about 30 km and in Sweden about 90 km. stations with distance between stations less than 100 km were put into operation October 1, 2000 (Fig. 1). This waz an addition to the existing 6 broad-band digital stations located at much larger inter-station distances. As recently as November, 2001, additional 20 broad-band stations are being installed in southern Sweden, also with a station spacing of less 100 kin, making the total number of stations 38. The main purpose of the network in Sweden is to gather information from microearthquakes in order to gain information for a better understanding of the ongoing deformation processes in the intraplate, glacially rebounding, shield area (B55varsson, 1999b). The results from Iceland (Stef~nsson et al., 1993) and previous operation of temporal networks in Sweden (Slunga et al., 1984) have shown the usefulness of the very small microearthquakes as information carriers related to ongoing deformation. The major goals for the design of the system were to minimize the investment and operational cost of the system while retaining full detection capabilities and the highest possible data quality (Stef~nsson et al., 1986; B55varsson, 1987). To achieve this, the system operation is highly automated in order to minimize the analyst's workload and utilizes intelligent site stations to minimize data transmission cost. A detailed description of the SIL system is given by B55varsson et al. (1996, 1999a). The

132

system has been further developed within the project Earthquake Prediction Research in a Natural Laboratory (PRENLAB), supported by the European Union ~dthin the 4th and 5th framework programme Environment and Climate. In this chapter we give an overview of the present version of the data acquisition system and describe some of the enhancements currently being worked on. New features of the system include a geographically indexed database, seismicity patterns through grouping of events with similar focal mechanisms, stress tensor inversion software and the continuous ground motion monitoring software. Some of these concepts have been implemented while others are under development. Most of the discussion in this article refers to the results from the network operation in Iceland and if referring to Swedish operation this will be specified in the text.

2

Automatic Operation of the SIL System

In Iceland, the X.25 service provided by the local telephone company is used to connect the remote stations in the SIL network to the centre in Reykjavik. The fast response of the X.25 telephone service is required since the SIL network is providing a service to the community with fast production of information regarding local earthquakes. In Sweden we use regular telephone lines with dial-up modems for the connection to the remote sites. In contrast to Iceland, no alert function is needed in Sweden due to the low probability of damaging earthquakes. Each remote station is equipped with a three-component seismometer, a GPS synchronized digitizer and a 32 bit computer running the UNIX (mostly Linux) operating system. In Iceland, most of the sensors are 5 second instruments (there are a few 1 second and a few 30 second instruments). The 16-bit gain-ranging digitizers originally used in Iceland are gradually beeing replaced by 24--bit digitizers. In Sweden all instruments are broad-band 30 second to 50 Hz instruments with a 24-bit digitizer. The automatic analysis performed by the SIL system can be divided into four different types of analyses: single-station analysis, multi-station analysis, alert-analysis and the teleseismic-analysis. In addition, multi-event analysis is performed, currently only off-line. In the Swedish operation there is less need for the alert analysis, but some of the functions are used for network operational purposes. Single-station analysis is performed at each site on data recorded by that station. Multi-station and multi-event analyses are performed at the centre where data from more than one station is available. The alert monitoring is also done at the centre, using parameters derived from the single-- and multi-station analyses. A schematic description of the data flow in the SIL system is given in Fig. 2.

2.1

Remote Site Single-Station Analysis

Two types of processes are operated at the remote site and these are called utility processes and application processes respectively. The utility processes are general data management processes, designed for flexibility and valid for any type of data acquisition. The application processes are application specific and they operate by reading a channel of data as if it was an endless file. Channels are opened as regular files would be, by a call to the specific function in the utility library. The most recent part of the data are kept in shared memory for fastest possible access. This allows for

133

SITE

CENTRE

PROCESSES

FILES

FILES

PROCESSES

DETECI'OR

LOGS

PHASELOGS ~ m FROMEACH STATION

MERGER

PHASE

pHASELOGS FROMALL STATIONS (

~

FETCH REQUEST

SELECTOR SOFTWARE

I=:o:

t

[

LOCATED EVENTS

I

DATA

+

[ SoUR Pf~AMETFAtS

..l ALERT DETECTOR

~

ALERT LOGS

&LERT LOGS ALERT DATA

SOFTWARE I ]q

Fig. 2 Flow chart of SIL processing. The phase detector at the site produces phase logs which are trarmferred to the centre. At the centre, a programme merges phases from all s~ations to one file which is input to the "selector' software. The selector software defines possible events through a phase a~sociation procedure and determines time intervals of waveform data to be retrieved from the site stations. At the stations, the net-saver programme copies the data from the ring buffer system to local files and transfers them to the centre. The alert software works in parallel with the acquisition system using information from the selector software and from the alert detector at each site. From Bh~varsson et al. (1999a). extensive algorithms operating on the incomirtg fast data-flow w i t h o u t accessing the disk. T h e physical way the centre and the site stations c o m m u n i c a t e is not determined by the design of the utility processes. As development of c o m m u n i c a t i o n facilities are m a d e available on the market these can be utilized by the SIL s y s t e m . Dial-up networks, X.25, satellites or any other means of c o m p u t e r c o m m u n i c a t i o n can be used. 2.1.1

Phase

Detection

In contrast to m a n y other networks, the S I L - s y s t e m detect phases at the station rather than events. The main reason for using the s i n g l e - s t a t i o n phase detection and m u l t i - s t a t i o n event selection structure is to m i n i m i z e the transmission cost of data between the centre and the remote stations. The basis of the phase detection concept

134

is to treat all transients detected at the stations as if they were phases associated with real earthquakes. The detector uses a simple comparison of power in two adjacent windows on the seismic trace. This is similar to the STA/LTA approach, but in this case the time windows used are both of the same length. Selected windows around the detected transients are processed in a manner one would process a true seismic phase and the results are stored in a compact structure, called a phase log. Each phase log entry is only 128 bytes long and therefore inexpensive to transmit to the centre. The detection thresholds can thus be set very low, allowing smaller earthquakes to be detected. Phase logs are transmitted to the centre immediately upon phase detection. Each phase log includes onset time, duration, reference to previous and following phases, type of phase (P or S), signal and noise averages, maximum amplitude, P-wave azimuth, inter-component coherency (Roberts et al., 1989) and spectral parameters including DC-level and corner frequency (BhOvarsson et al., 1999a). The distinction between P and S phases is made based on the amplitude ratios between the vertical and horizontal components. This method works well for approximately 60% of the used phases. Artificial neural networks are used to obtain additional information for 1oo-

so

so-

?o

To6O-

~

P phase

S phase,

ga-

40SOfro lo

10-

%~ o;~ o:2 o:~ oi~ o:~ Neural

o:6 o17 o:B

o:~

,

o

output

Fig, 3 The results of an artificial neural network trained to distinguish between P and S phases. A value of the neural output close to 0 indicates a P phase and a value close to 1 indicates an S phase. An intermediate value means that the phase could not be classified as either P or S. The neural network correctly identifies over 95% of the used phases. From B56varsson et al. (1999a). distinguishing between the P and S phases. The learning set for the neural network was taken from the manually checked database at the centre. The inputs to the neural net are the amplitude and frequency information plus the coherency measure from three component analysis, all taken from the phase log. The output is set to 0 for P and 1 for S. The neural network increases the correct identification of phases to over 95% (Fig. 3). This is very important for the phase association procedure in the multi station analysis. A detailed description of the processing at the site stations is given by B55varsson et al. (1996, 1999a).

2.2

Continuous Ground Motion Monitoring

The site station software has been enhanced to enable continuous monitoring of ground velocity (B56varsson et al., 1999a). The signals are filtered through 3 band-pass filters that pass data in the ranges 0.5-1 Hz, 1-2 Hz and 2-4 Hz. The filters are implemented

135

in the time-domain in real-time using the expression: 2

'8

= E

+ E bjy _j

i----0

(1)

j=l

where x~ is the unfiltered signal, Yk is the filtered signal and a~ and bj are coefficients of the filter. Each of the three components is filtered using all three filters and an average value .Y

=o,

I

(~'

i~

!

I I

!

!

!

!

!

!

'

!

!

!

E,

~'

o

4000

2000

0

29

30

1

2

,13

4

5

6

7

8

9

10

11

12

13

14

October 1996

Fig. 4 Tremor in the 0.5-1.0 Hz frequency band recorded on a temporary station at Grfmsi%ll prior to and during the 1996 subglacial eruption in Vatnajhkull. From B56vaxssonet aL (1999a). for the amplitude is computed once a minute for each filter band. The average values are sent to the centre where they are stored. A near real-time plot of this data gives a useful visual indication of the seismic activity and the condition of the network. Individual earthquakes larger than about ML2 are seen on the plots9 This data can be used to estimate local magnitude for such earthquakes (Mendi and Husebye, 1994). The primary reason for developing this software was to enable the monitoring of tremors accompanying volcanic eruptions (Bhbvarsson et al., 1999a). Fig. 4 shows the variation in the tremor parameter prior to and during the 1996 subglacial Vatnaj6kul[ eruption in Iceland.

2.3 2.3.1

SIL C e n t r e M u l t i - S t a t i o n

Analysis

Phase Association and Event Definition

The phase logs from the stations are merged into a single time ordered list at the centre. The phase association and event definition process starts by searching for time intervals which contain two or more phase detections that may ori~nate from the same seismic source9 The phase detections in this time interval are then submitted to the iterative location, phase association and phase truncation procedure outlined in Slunga (1980) and Bhbvarsson et al. (1999a). This procedure results in a location of possible earthquake events. As the event is defined, a request for waveform data, in an appropriate time window, is automatically transmitted to the remote stations.

136

2.3.2

Spectral A m p l i t u d e s and Fault P l a n e Solutions

The main purpose of the SIL network design is to acquire geophysical information carried by the seismic waves from the relatively frequent microearthquakes. Apart from locating the earthquake, the routine analysis performed on every recorded event includes estimating fault plane solutions for the earthquake. The estimation of focal mechanism and source parameters are based on results of the spectral analysis of short data segments containing the direct P and S wave arrivals. The spectral estimation is done at the site stations, using windows around the automatic time picks, and is repeated at the centre after manual refinement of arrival time readings. The low frequency amplitude asymptote, or DC-level, of each phase is determined by fitting a three parameter model to the observed spectra (Boatwright, 1978) f2(f)

~2o

=

1-

(2)

1 + ~io/ ) fl0 is the DC-level, which we will refer to, somewhat informally, as the spectral ampiitude, f~ is the corner frequency and 7 the spectral fall off. The frequency range 2 - 30 Hz is searched in the estimation and for the final estimate frequencies up to 1.5 times the corner frequency are included. The DC-levels are estimated on all three components, after deconvolution of the instrument response and correction for the free surface and anelastic damping, and we obtain five amplitude values for each recording station; vertical and radial P (PZ and PR) and vertical, radial and transverse S (SZ, SR and ST). Below, when referring to amplitudes we will imply spectral amplitudes, unless stated otherwise. To estimate the fault plane solution for the earthquake a systematic search over strike, dip and rake is performed. For each combination of the three source angles, the misfit between observed and predicted spectral amplitudes is calculated. In addition to the single best fitting solution, all solutions that fit the observed polarities and have amplitude misfit less than a predefined threshold value are taken as acceptable (Slunga, 1981; R5gnvaldsson and Slunga, 1993). For all located events, the same analysis procedure is used. However, the fault plane solutions will be better constrained for events recorded at many stations than for small earthquakes recorded only at few stations. For earthquakes within the SISZ the optimal fault plane solution can be expected to be within ~15 ~ of the true source angles for events larger than M L "~ 0.5 (R6gnvaldsson and Slunga, 1993). The corner frequency of the spectra is used to est'.mate the source dimensions (Boatwright, 1980) and, together with the seismic moment, the peak slip at the source (Eshelby, 1957) and the static stress drop (Brune, 1970, 1971).

2.4

The Alert System

The alert system is a collection of routines for monitoring extracted parameters in selected regions and sites. For this purpose, Iceland is currently divided into 29 regions and different alert thresholds assigned to each region. The parameters are extracted from the results of the analysis described above and from dedicated alert detectors at the sites. The alert system is started at regular intervals and for each event defined by the multi-station analysis. At present, five parameters are monitored for each region. These are M, the local magnitude of individual earthquakes, N, the

137

number of earthquakes in a time interval, S, a dimensionless measure of moment release during the same time interval and two time-weighted measures of the number of events and accumulated moment release (BSbvarsson et al., 1999a). The dimensionless moment release parameter is defined as N

N

i:1

i:0

Here M~ is the magnitude of the i-th earthquake and S~ = 1 0 (5+M0 is a dimensionless measure of the seismic moment released. The form of the definition of Si sterns from the relationship between surface wave magnitude, Ms, and seismic moment, i.e. log/140 -- 9.1 + 1.5Ms and hence M0 = 109'l+lSMs (Purcaru and Berckheimer, 1978). A time-weighted function of the moment release, N

& =

(4) i=0

is also monitored. Here w~ = k where k is a constant and ti is the time since the occurrence of event i. Thus recent events are assigned more weight than the "older" ones.

Similarly, a time--weighted function of the number of earthquakes is defined as N

N

i=O

i:O

k

(5)

If any of the parameters M, N, Nw, S or Sw exceeds predefined limits, an alert level is declared. A special detector is operated at the individual stations for the alert system. It monitors two parameters, large ground velocity and increase in background noise during some period of time.

2.5

Teleseismic

Waveform

Data

Acquisition

The SIL seismic data acquisition system was primarily designed for automatic acquisition and evaluation of data from local microearthquakes. No attempt has been made to automatically locate teleseismic events but the acquisition system is also used for collecting teleseismic data. The so-called "E" type messages from USGS and NEIC, containing a single line of hypocenter and magnitude information on recent earthquakes, are received via electronic mail at the centre. A selection p r o ~ a m m e reads the messages and selects events that fulfill certain criteria of magnitude and epicentral distance. The programme uses the IASPEI 91 traveltime tables (Kennett and Engdahl, 1991) to compute the first arrival time at each station. The teleseismic body wave data is retreived with a sampling rate of 20 samples per second and the surface wave data with a sampling rate of 4 samples per second. This extended use of the SIL system provides valuable data for various type of structal studies (Darbyshire et al., 1997; Alien et al., 1999).

138

3

SIL Multi--Event Analysis

The SIL-system's multi-event analysis contains a number of methods and applications for detailed studies of groups of earthquakes. Topics covered by these methods are; relative location of groups of similar events resulting in very accurate hypocenter locations, the study of the similarity of focal mechanisms through correlation of spectral amplitudes, and inversion of fault plane solutions for the crustal state of stress. Much of the research and development of the SIL-system also falls under the multi-event analysis label, an example of which will be discussed at the end of this section. 3.1

Absolute

and relative location

It is well established that accurate measurements of the arrival time difference between similar earthquakes can be used to constrain the relative locations of the events. The arri~-al time differences are measured through cross-correlation of the seismogTams. The most common approach is to select one event from the earthquake cluster as a reference or master event and measure arrival time differences of the other earthquakes relative to the master event (e.g., Deichmann and Garcia-Fernandez, 1992; Ito, 1985; Console and Giovambattista, 1987; Fremont and Malone, 1987). A more complete approach is to measure the arrival time differences between each event and all the others, i.e. every earthquake in the group is used as a "master event" (Slunga et al., 1984, 1995; Got et al., 1994; Shearer, 1997). The timing accuracy achieved by cross--correlation techniques can also be used to improve the absolute locations of groups of earthquakes. The main sources of error when locating with time differences of similar events are the uncertainties in the ray directions in the source volume. The deviations of ray directions from those predicted by the 1D velocity model are partly independent of the integrated travel time error along the path. This means that the absolute location errors from the use of arrival time differences are nearly independent of the single event location errors (Slunga et al., 1995). This method has been used to map active faults in the two transform zones in South and North Iceland, as well as at the divergent plate boundaries in SW Iceland (RSgnvaldsson and Shmga, 1994; Slunga et al., 1995; R5gnvaldsson et al., 1996, 1998). The attitudes of actiw'~ faults at depth generally agree well with observations of surface faults. As more earthquake clusters are analysed in this manner, data on mapped subsurface faults is collected in a database at the SIL centre. This database currently holds the results of analysis of more than 100 swarms. An application of the relative location algorithm to a group of earthquakes in the TjSrnes fracture zone (TFZ; in the north) is shown in Fig. 5. After relocation, the epicenters of the 18 successfully located events lie on an appro..,dmately 1 km long line se~nent. Assuming that all the earthquakes occurred on the same fault, the attitude of the fault can be estimated by fitting a plane through the accurately determined hypoeenters. The strike of the best fitting plane through the gToup is N139~ similar to the strike of the main transform faults of the TFZ. The best fitting plane dips 84~ The mean distance of the 18 earthquakes from the plane is 11 m, comparable to the uncertainty in the relative locations. The normals to all planes which can be

139

, ! ; , , , I

1.2

L

a,, ,.._,1.0 84

I

b

,

N

I

"~,

,--,4.6 E ,,,,, ~'4.8

E 0.8

V O.6 0.4-

,41'

5.0

0.2

0.5

1.0

X [km]

40 30 20 10 0

0.6 ' '018

1.0

X' [km]

Fig. 5 The relative location of a group of 18 earthquakes in the TjSrnes fracture zone. (a) shows a map view of the epicenters after relocation, X is east, Y is north. In (b) the hypocenters are viewed along strike of the best fitting plane through the group. Z is depth and X' is horizontal and orLhogona] to the strike. (c) shows the poles to all planes through the hypocenter group, such that the mean distance of the 18 earthquakes from the plane is less than 50 m, plotted on an equM area projection of the lower hemisphere. From B56varsaon et al. (1999a). fit through the hypocenter cluster with mean distance of the hypocenters from the plane less than 50 m are shown in Fig. 5.c on an equal area projection of the lower hemisphere. Clearly the acceptable (according to our definition) plane orientations are confined to a narrow range (approximately i l 0 ~ in strike and • ~ in dip) around the best fitting orientation. 3.2

Spectral

Amplitude

Correlation

and

Grouping

As referred to above, seismic phase amplitudes are widely utilized in the SIL system. In a recent development, closely located earthquakes with similar focal mechanisms can be identified by correlating one event% spectral amplitude distribution with other events' spectral amplitude distributions, subsequently grouping the events according to how well their spectral amplitude distributions correlate. The technique is referred to as Spectral Amplitude correlation and Grouping, SAG, and is described in detail in Lund and BShvarsson (2001). We will briefly outline the technique here and discuss its application to seismicity monitoring. 3.2.1

The SAG Method

The estimation of spectral amplitudes was described above and we only note again here that the spectral amplitudes are estimated on all three components and we obtain five amplitude values for each recording station; vertical and radial P (PZ and PR) and vertical, radial and transverse S (SZ, SR and ST). We will refer to the five amplitude values as amplitude components. Below, when referring to amplitudes we will imply spectral amplitudes, unless stated otherwise. Since in the SIL system focal mechanisms are estimated using both P wave first motion directions and spectral amplitudes (R6gnvaldsson and Slunga, 1993) we have a firm foundation for associating spectral amplitude distributions with focal mechanisms. Closely located events with similar focal mechanisms can, thus, be identified through their spectral amplitude distributions. We measure the similarity of two

140

events' spectral amplitude distributions using the common linear correlation coefficient at zero lag. Only amplitude components in common for both events are included in the calculation. Since the amplitudes for one event at different stations frequently span three orders of magnitude or more, it is advantageous to use the logarithm of the amplitude components in the correlation. This decreases the importance of the amplitudes at the station closest to the source, i.e. taking the logarithm acts to distribute the amplitudes more evenly, thus stabilizing the correlation. In order not to produce very high correlation coefficients between events with few amplitude components, correlations coefficients are down-weighted if tile events have few, 20-30, common components. The events axe grouped together according to their correlation coefficients. The SAG technique allows for three different modes of grouping: (1) as a preprocessor to stress tensor inversion in order to assess the redundancy of focal mechanism; (2) for grouping events to compute composite focal mechanisms and (3) for monitoring of temporal seismicity patterns. We will here concentrate on the mode pertaining to temporal monitoring of how well earthquakes correlate in a certain area. Starting the grouping with a small initial number of events, usually 20, groups are formed based on the median of the correlation coefficients between events in ~he group. Group formation is controlled by requiring the median to be above some threshold value, usually 0.9, and a certain homogeneity of the correlation coefficients within the group. Once the initial set of events have been grouped, events are analysed one by one in time order from the data set. The new event is correlated with all old events and assigned to the group with which members it has the highest correlation coefficient median, or used to form a new group with old, ungrouped events. If the event cannot obtain a median above the threshold, it is left as ungrouped, or solitary. When analysing a large data set, it is often advantageous not to keep the entire data set as "correlation memor};' for later events but instead traverse the data set in a moving window sense, allowing only a certain number of old events in the correlation memory. An example of this will be discussed below. We note once again that the SAG scheme is able to detect closely located events with similar focal mechanisms. The exact meaning of close will depend on the station geometry relative to the events and their focal mechanisms. The separation issue implies that our correlation scheme will not be able to find all events with similar focal mechanisms in an area if they are sufficiently separated in space.

3.2.2

Seismicity Patterns with SAG

The SAG technique has been applied to one year of seismicity from the Olfus area in southwest Iceland (Lund and B55varsson, 2002). 2943 high quality events were selected between November 1, 1997 and November 13, 1998. On November 13, 1998 a Mw = 5.1 earthquake occurred in the ()lfus area, t h a t event and the first seven hours of aftershocks are included in the data set. The result of the analysis is shown in Fig. 6, where we used a correlation memory of 250 events, a minimum group size of 4 events and a minimum median correlation coefficient for group formation of 0.9. In the Figure we have plotted the number of solitary events and the number of groups at the origin time of each new event. In Fig. 6A we see a steady increase in the number of solitary events until March, when there is a rapid drop. Except for a temporary spur in early June, the number of solitary events stays approximately constant until

141

mid-July when an increase in solitary events start that continues until the occurrence of the magnitude 5.1 event on November 13.

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Fig. 6 Spectral amplitude grouping result for one year of seismicity in the (~lfus area between November 1, 1997 and November 13, 1998. The line marked Eq marks the occurrence of the November 13, 1998 Mw = 5.1 earthquake. A) Ushlg a 250 event moving window as correlation memory. Number of solitary events (solid line) and number of groups (dashed line) versus time. B) Same as ia A but now plotted versus the number of processed events. In B the starts of the months are indiea~d by short, solid lines down from the top of the frames and intersecting the solitary events curves. Figure modified from Ltmd and B55varsson (2002). In Figure 6B we have ploted the same information versus event number in order to avoid the influence of seismicity rate on the Figure. We now see that there is a large number of events in June (these are in fact aftershocks to a magnitude 5.4 event north of the (31fus area), these events do not correlate at first, as shown by the increase in solitary events in early June, but very quickly the seismicity conforms to certain focal mechanisms and more groups of events are formed. Decrease in the number of solitary events is due to a combination of new events correlating well either with a preexisting group of events or with old solitary events in the memory, plus the effect of old solitary events leaving the memory. The late June activity can be seen to correlate very well. In mid July the seismicity changes pattern and by August the change is dramatic, making the number of solitary events rise rapidly and the number of groups decrease. The effect continues over more than two memory lengths and peaks on November 13, right at the time of the large event. The seismicity seems to conform to a steady new pattern after the event and the number of solitary events decreases. Vv'e interpret these changes in seismicity pattern as variations in both locations and focal mechanisms of the microearthquakes. The aftershocks of the June 4 event correlate very well, indicating that many of them occur on the same fault, or on closely located faults with similar strike and dip, slipping in the same direction. From August to November, however, SAG indicates that either the focal mechanisms of closely located events are different, both compared to earlier and to current seismicity, or the locations of the events are different both to earlier and current events. We do not, however, observe a seismicity randomly spread over the study area between August and November. This implies that either slip directions vary on the same fault or, perhaps more likely, the microearthquakes occur on many, differently oriented fault

142

planes. The above example indicates that the number of solitary events as defined by the SAG technique could potentially be valuable as a seismic monitoring parameter. Although this example shows surprising correlation between the SAG result and the magnitude 5.1 earthquake, this behavior is not consistent throughout Iceland. However, since SAG detects changes in source mechanism over time for events in a specific location, the technique does provide specific differential information on current crustal processes affecting the generation of earthquakes. The SAG technique is currently implemented at the SIL centre in Reykjavik and runs after the analyst review of the locations and subsequent estimation of spectral amplitudes. This implies that the SAG results are available up to 24 hours after the occurrence of the events. We noted above that spectral amplitudes were calculated for each phase detected at the remote stations and transmitted to the SIL centre in the phase log. For a more rapid deployment of SAG, the technique could be applied directly to the phase logs as soon as an event has been defined by the phase association software. Such an implementation would be able to trace the development of the number of solitary events with only a few minutes delay time. Such an implementation of SAG is planned for the near future in the SIL system. 3.3

Stress Tensor

Inversion

of Earthquake

Focal Mechanisms

The state of stress in the crust governs earthquake generation, determining not only the source mechanism of the earthquake but also whether or not there is sufficient differential stress to induce slip on the fault. Information from earthquakes alone does not permit determination of the differential stress ma~c~nitude but a relative measure, R, of the magnitude of the intermediate principal stress can be obtained. Principal stress orientations, however, can be inferred from earthquake focal mechanisms. In the SIL system an inversion method has been developed by Lund and Slnnga (1999) for estimating the orientations of the principal stress axes and R based on the robust grid search methodology of Gephart and Forsyth (1984). Added features in the inversion scheme includes accounting for errors in the focal mechanisms through the SIL system notion of acceptable focal mechamsms and selection of the fault plane from the two nodal planes based on a stability criterion. Also, inclusion of "known fault planes, e.g. from relative location, is possible in the inversion. Automatic monitoring of the stress state in an area via earthqnake focal mechanisms is certainly possible but care has to be paid not to produce erroneous results. Primarily, the inversion requires a certain number of non-redundant mechanisms for a stress estimate with low uncertainties. 30 to 40 events is usually sufficient, but 40 events with approximately the same focal mechanisms will not produce a reliable stress estimate. To a~sess the redundancy of the focal mechanisms we use the SAG technique described above. All events in the group intended for inversion are correlated with each other and if groups of events with similar mechanisms are formed, only one representative event is used from each group. All the solitary events are included. This significantly increases the non-redundancy of the data, see Lund and B55varsson (2002), and thus the significance of the stress estimates. Second, data should be collected so that subsequent inversions will involve the same area (Townend and Zoback, 2001), implying that the stress estimates will most probably be very irregularly spaced

143

in time. Finally, procedures to compare the uncertainties of different stress estimates have to be devdoped and automated in order to assess whether observed differences are significant. This point is currently being addressed for the SIL inversion software. Adding to the complications of automated stress tensor determinations is the time consuming inversion algorithm. This issue will, however, become less critical as computers evolve.

3.4

A u t o m a t i c R e a d i n g of Onset a n d First M o t i o n D i r e c t i o n

Based on the positive results of the correlation techniques used in the relative location algorithm described above, a new approach is being taken regarding the automatic operation of the network. Experience shows that a substantial fraction of the events occurring within a given area belongs to a few clusters or families of earthquakes, characterized by highly similar waveforms. The cross correlation of seismograms at individual stations can be used to identify such clusters of similar events (e.g. Aster and Scott, 1993; Maurer and Deichmann, 1995). We are currently working on a method for using cross correlation of neighboring events to automatically determine the onsets of P and S phases with accuracy comparable to, or better than, the accuracy achieved in the interactive analysis. The aims are to reduce the need for manual inspection of seismouams from local and regional earthquakes and to improve the quality of the readings in the microearthquake database. We plan to implement a first version of this software in 2002. The objective is to create a geographically indexed database (GID) where different classes of earthquakes will be stored. The area to be covered by the database is divided into equidimensionat cells, 2 • 2 km ~ laterally but of unconstrained depth. When creating the GID, each event within a given cell is correlated with all other earthquakes in the cell. The results of the correlation are used to group the earthquakes into classes. A few events of each class are stored in the GID. As new earthquakes are recorded by the network, the system automatically looks for similar waveforms in the GID, see flowchart in Fig. 7. The initial location estimate of the event is used when accessing the GID. The selection of waveform windows to be compared to data in the GID is done based on the automatically determined arrival times for stations that detected the phase. At other close stations that did not detect the phase, theoretical arrival times are estimated by ray-tracing through a layered velocity model. The new phase is correlated with all phases of the same type (P or S) in the GID, recorded at the same station originating within the same cell or a neighboring cell. The cross-correlation function (CCF) is resampled before determining the time lag, the correlation coefficient and the sign of the CCF at the peak. The lag gives the absolute arrival time of the phase, assuming the reference pick was "correct". If the polarity of the reference phase is known, the sign of the CCF gives the polarity of the new phase. The normalized correlation coefficient gives a measure of the similarity of the new phase to the reference phase. By resampling the CCF the accuracy of the pick is practically only limited by the timing accuracy of the network clocks. For the timing in the SIL system, this is better than 1 ms. The precise arrival time readings can also be used for determining accurate relative locations of similar earthquakes. When all recorded phases for the new event have been compared to all relevant

144

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/

1 ACIS SOFTWARE

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/

J

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Fig. 7 A simplified flowchart of~he automatic cross-correlation procedure. Programs are surrounded by oval boxes, files by square boxes. ACIS stands for Automatic Correlation of Incoming Signals. See text for ex~planadon. From BS~vaxssonet al. (1999a). phases in the GID, a voting procedure is used to determine whether the event is similar to sufficiently many phases in the database to warrant skipping interactive analysis. If enough phases have been picked by correlation with e~sting phases, the picks are written to a file similar to those created in the interactive time picking procedure and the event is relocated using the correlation picks. Otherwise the new event is analysed interactively by the network operators. Figure 3 gives a schematic overview of data flow in the proposed correlation analysis system.

4

Discussion and Conclusions

More than 200,000 microearthquakes have been recorded during the operational period of the SIL system in Iceland from 1990 to 2001. In this period the system has been developed further and the number of stations has been increased from 8 to 43 with variable station spacing. One of the assumptions governing the design of the SIL system was that microearthquakes down to ML 0 would provide useful information for the study of larger earthquakes. The results of the work on relative locations of microearthquakes recorded by the SIL network validate this assumption. In general faults mapped by accurate

145

relative locations and fault plane solutions for ML 0-2 earthquakes have attitudes similar to those of nearby faults that have ruptured in M&7 earthquakes. Information on the earthquake sources carried by the seismic waves is retrieved and processed automatically by the system. The high degree of automatization achieved in the SIL system makes it a good near real-time monitor of earthquake activity. Estimations of locations and source parameters for earthquakes down to magnitude below zero would be impossible without extensive automatization. More than 1500 earthquakes have been recorded and automatically analysed by the network during one single day. The spectral amplitude correlation and grouping (SAG) technique is a powerfull tool to access the redundancy of information in the focal mechanisms used for stress tensor inversion and for monitoring changes in the seismicity patterns in an area. Using SAG as a preprocessor to the stress tensor inversion will allow automatic monitoring of the stress state using the automatic fault plane solutions produced by the SIL system. The result of the analysis in the 0lfus area using the SAG technique shows that SAG can potentially be valuable as a seismic monitoring parameter that can be related to a following larger event. In the near future we hope to implement the automatic onset and first motion direction estimation through the use of a geographically indexed correlation database. We believe that this will both decrease the workload for the persons responsible of the daily operation of the network and increase the quality of the created database. Acknowledgments Much of this work is based on earlier work by Sigur6ur RSgnvaldsson who left us much too soon. The authors benefited greatly from several discussions with Ragnar Slunga. This research was financed by the European Commission (contracts ENV4-CT96-0242 and EVR1-CT-1999-40002), the Swedish Natural Science Research Council (contract G-GU 0642.5-312) and the Swedish Nuclear Fuel and Waste Management Co. Some figures in this article were generated with software from "v~ssel and Smith (1991).

References Alien, R. M., Nolet, G., Morgan, W. 3, Vogfj6r~, K., Bergsson, B. H., Erlendsson, P., Foulger, G. R., Jakobsd6ttir, S., Julian, B. R., Pritchard, M., Ragnarsson, S. and Stef~msson, R., 1999, Iceland's thin hot plume, Geophys. J. Int., 137, 51-63. Aster, R. C. and Scott, 3., 1993, Comprehcnsive characterization of waveform similarity in microearthquake data sets, Bull. Seism. Soc. Am., 83, 1307-1314. Boatwright, J., 1978, Detailed spectral analysis of two small New York State eax~quakes, Bull. Seism. Soc. Am, 68, 1117-1131. Boatwright, J., 1980, A spectral theory for circular seismic sources; simple estimates of source dimension, dynamic stress drop and radiated seismic energy, Bull. Seism. Soc. Am., 70, 1-27. Brune, J. N., 1970, Tectonic stress and the spectra of seismic shear waves from earthquakes, J. Geophys. Res., 75(26), 4997-5009. Brune, J. N., 1971, Correction. J. Ceophys. Res., 76(20), 5002. B56varsson, R., 1987, Design of the data acquisition system for the South Icelandic Lowland (SIL) project, Technical report, Icelandic Meteorological Office, Reykjavik, Iceland. B55varsson, R., RSgnvaldsson, S. Th., Jakobsd6t~ir, S. S., Slunga, R. and Steffiasson, R., 1996, The SIL data acquisition and monitoring system, Seis. Res. Lett., 67(5), 35-46.

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B56varsson, R., PdSgnvaldsson, S. Th., Slunga., R. and Kjartansson~ E., 1999a, The SIL data acquisition at present and beyond yeas- 2000, Phys. Earth Planet. Inter., 113, 89-101. B68varsson, R., 1999b, The new Swedish seismic network, Orfeus Newsletter, 1(3). Console, R. and Giovambattista, R. D., 1987, Local earthquake relative location by digital records. Phys. Earth Planet. Inter.~ 47, 43--49. Darbyshire, F. A., Priestley~ K. F., White, R. S., GuSmundsson, G., aakobsd6ttir, S. and Stef'gnsson, R., 1997, The crustal structure of Northeastern Iceland: Constraints from broadband teleseismic body waves, Abstracts from the AGU 1997 fall meeting, Eos Transactions American Geophysical Union, 78, p. 500. Deichmann, N. and Garcia-Fernandez, M., 1992, Rupture geometry from high-precision relative hypocentre locations of microearthquake clusters, Geophys. J. Int., 110, 501-517. Eshelhy, J. D., 1957, The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. Roy. Soc. London, 241,276-296. Fremont, M.-J. and Malone, S., 1987, High precision relative locations of earthquakes at Mount St. Helens, Washington, J. Geophys. Res., 92, 10223--10236. Gephart, J. W. and Forsyth, D. W., 1984, An improved method for determining the regional stress tensor using earthquake focal mechanism data: Application to the San Fernando earthquake sequence, J. Geophys. Res., 89, 9305-9320. Got, J.-L., Fr~chet, a. and Klein, F. W., 1994, Deep fault plane geometry inferred from multiplet relative relocation beneath the south flank of Kilanea, a. Geophys. Res., 99, 15375-15386. Ito, A., 1985, High resolution relative hypocenters of similar earthquakes by cross-sprectral analysis method, J. Phys. Earth, 33, 279-294. Kennett, B. L. N. and Engdahl, E. R., 1991, Traveltimes for global earthquake location and phase identification, Geophys. J. Int., 105, 429-465. Lund, B. and Slunga, R., 1999, Stress tensor inversion using detailed microearthquake information and stability constraints: Application to the South Iceland Seismic Zone, J. Geophys. Hes., 104, 14947-14964. Lund, B. and BS~varsson, R., 2002, Correlation of microearthquake body-wave spectral amplitudes, Bull. Seism. Soc. Am., Accepted. Manrer, H. and Deichmann, N., 1995, Microearthquake cluster detection based on waveform similarities, with an application to the western Swiss Alps, Geophys. J. Int., 123, 588-600. Mendi, C. D. and Husebye, E., 1994, Near real time estimation of magnitudes and moments for local seismic events, Annali di Geofisica, xXXVII, 365-382. Purcaru, G. and Berckheimer, H., 1978, A magnitude scale for very large earthquakes, Tectonophysics, 49, 189--198. Roberts, R. O., Christoffersson, A. and Cassidy, F., 1989, Real-time event detection, phase identification and source location estimation using single station three-component seismic data, Geophys. J., 97, 471-480. RSgnvaldsson, S. Th. and Slunga, R., 1993, Routine fault plane solutions for local and regional networks: A test with synthetic data, Bui1. Seism. Soc. Am., 83(4), 1232-1247. RSgn~-aldsson, S. Th. and Slunga, R., 1994, Single and joint fault plane solutions for microearthquakes in South Iceland, Tectonophysics, 273, 73--86. RSgnvaldsson, S. Th.., Gudmundsson, G., Ag~stsson, K., aakobsd6ttir, S. and Stef~nsson, R., 1996, Recent seismicity near the Hengill triple-junction, SW Iceland. B. Thorkelsson, editor, Seismology in Europe. Papers presented at the XXV ESC General Assembly', September 9-14, 1996, Reykjavik, Iceland, ISBN-9979-60-235-X, 461-466. RSgn~-aldsson, S. T., Gudmundsson, A. and Slunga, R., 1998, Seismotectonic analysis of the TjSrnes Fracture Zone, an active transfrom fault in North Iceland, J. Geophys. Res., 103, 30,117-30,129. Shearer, P. M., 1997, Improving local earthquake locations using the L1 norm and waveform cross correlation: Application to the Whittier Narrows, California, aftershock sequence, J. Geophys. Res., 102~ 8269-8283. Slunga, R., 1980, International Seismological Datacenter. An algorithm for associating reported arrivals to a global network into groups defining seismic events, Technical Report C 20386-T1,

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Swedish National Defence Res. Est. Slunga, R., 1981, Earthquake source mechanism determination by use of body-wave amplitudes an application to Swedish earthquakes, Bull. Seism. Soc. Am., 71(1), 25-35. Slunga, R., Norrmann, P. and Glans, A.-C., 1984, Baltic shield seismicity, the results of a regional network, Geophys. Res. Lett., 11(12), 1247-1250. Slunga, R., ltSo~nvaldsson, S. Th. and B55varsson, R., 1995, Absolute and relative location of similar events with application to microearthquakes in southern Iceland, Geophys. J. Int., 123,409-419. Stef~aasson, R., Bungum, H., B58varsson, R., Hjelme, J., Husebye, E., Johansen, H., Korhonen, H. and Slunga, R., 1986, Seismiskt datasamlingssystem f'6r sSdra Islands l~gland. Icelandic Meteorological Office, report, In English mith Icelandic and Swedish summaries. Stef~aasson, R., BS~varsson, R., Slunga, R., Einarsson, P., Jakobsd6ttir, S., Bungum, H., Gregersea, S., Havskov, J., Hjelme, J. and Korhonen, H., 1993, Earthquake Prediction Research in the South Iceland Seismic Zone and the SIL Project, Bull. Seism. Soc. Am., 83(3), 696-716. Townend, J. and Zoback, M., 2001, Implications of earthquake focal mechanisms for the frictional stren~h of the San Andreas fault system. R. Holdsworth, R. Strachan, J. Magloughlin and R. Knipe, editors, The Nature and Tectonic Significance of Fault Zone Wcakning, number 186 in Special Publications, pp. 13-21, Geological Society of London. Wessel, P. and Smith, W. tI. F., 1991, Free software helps map and display data, EOS trans., 72, 441 and 445-446.

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Microearthquake Analysis at Local Seismic Networks in Iceland and Sweden and Earthquake Precursors Ragnar Slunga Uppsala University, S-75236 Uppsala, Sweden, [email protected]

A b s t r a c t . Microcarthquakes represent a flow of information from the seismogenic crust up to the surface if they are detected and recorded. If the detection threshold is lowered two magnitudes the amount of information is increased by a factor of about 40 as all microearthquakes essentially give the same amount of information. This is the basic idea behind the local seismic networks in Iceland and Sweden. The large number of microearthquakes requires automatic routine analysis. For these networks the routine automatic analysis includes phase detection, event detection and location, wave form analysis, fault plane solution, and estimation of fault radius and dynamic source parameters. The Icelandic network has since 1990 detected and recorded over 180,000 microearthquakes which all have been automatically analysed and inverted for source mechanisms. In addition two M s > 6.4 earthquakes occurred in June 2000 within the well covered area in SW Iceland. A number of different precursors have been observed. Foreshocks before all

ML > 4.9 earthquakes within the network are found and their

behaviour is similar to observations from shallow strike slip earthquakes in other parts of the world. Premonitary swarms are also observed at the epicenters for several years. Two new precursors which are related to recent theoretical achievements were also observed. One was the statistical ditribution of the micraearthquake fault radii. They showed in all cases remarkable changes including high values prior to the earthquakes. This is in agreement with the idea of each fracture and loading system to have a minimum fault radius. Changes in loading rate may then influence the fault radii. Another related precursor is the observation of increased percentage of low stress drop events before the earthquakes. This may possibly be related to seismic activity at the edges of larger locked patches (stronger asperities) and/or to increasing loading rate. The combination of the foreshock observations and the fault radius variations together with the old idea of a limited number of mieroearthquakes involved in an asperity breaking gave a promising precursory concept: the domino pattern. The essence of this pattern is to have an increased rate of microearthquakes within a small volume followed by a lower rate (quiescence) and ending with an increasing rate. The number of events in such a pattern was found to be 30 - 60 within a volume of 4 - 6 km diameter. Such pattern could be detected by measuring the fit to the theoretical activity rate for an asperity breaking model. Based on these observations a simple earthquake warning algorithm is described and applied to all Icelandic data for the years 1990 - 2001. If the warning threshold is set to produce warnings 0.25 - 3 days before the six

Mz > 5.0 earthquakes and within 6 km of their epicentres the number of

false alarms was 54 meaning a probability for the warning to be correct of 10%. Most of the false warnings are at correct places but months or years too early. This retrospective study illustrates the high value of the microearthquake information when the detection threshold is about M-L = 0. The Icelandic data will be used for future more detailed studies of the earthquake nucleation processes hopefully leading to high quality earthquake warning algorithms.

149

1 Introduction Tectonic earthquakes are spontanous unstable slip on fractures. Thus each earthquake indicates that instability has occurred and inversion for the source mechanism gives information about the fracture orientation, slip direction and slip size, size of the fault area, and also information about the stress field released by the earthquake rupture. This means that the elastic waves created by the earthquakes carry valuable information about the rock conditions at the earthquake source area up to the surface where they can be recorded by seismometer networks. The amplitudes of far field waves are proportional to the derivative of the slip time function which means that fast source slips (during unstable earthquake slip) can be recorded at several tens of kilometers even for source slips less than 0.01 millimeter. As each earthquake gives essentially the'same amount of information independent of its size the value of recording and analysing even small microearthquakes is obvious as the number of magnitude zero earthquakes is about 40 times the number of magnitude 2 earthquakes. As the zero magnitude earthquakes have source volumes of 100 m diameter the stresses involved show normally very consistent patterns (we are of course only sampling the rock stresses at points where the stability is exceeded). The large number of microearthquakes secures that there will be a more or less continuos flow of information from active seismic parts of the crust. This requires however also that the detection, data aquisition, and source analysis of the microearthquakes is highly automatic. The algorithms for microearthquake analysis described in this chapter have been in use in Sweden 1980 - 1989, in Iceland from 1990, and again in Sweden from 1999. While in Sweden only some 400 - 500 events have been analyzed the number of Icelandic events exceeds 180,000. A lot of experiences about the reliability of the algorithms have accumulated, and, more important, as all events are not only located but also inverted for fault plane solutions and dynamic source parameters, a database of great value is being created. The detection threshold for the network areas in Iceland is around Mz = 0 while it in Sweden is around Mz = 0.5 due to a greater station spacing. In Iceland two Ms > 6.4 events occurred within the network during June 2000. This allows a search for precursors and possible earthquake warning algorithms which also will be illustrated in this lecture.

2 The Routine Analysis The routine analysis is mostly automatic but allows interactive analysis which makes it possible for the seismologist to correct mistakes done by the automatic routines and also means a monitoring of the performance of the automatic detection and location. 2.1 E a r t h q u a k e

Detection and Location

At each seismometer site of the network a phase detector works automaticly and reports all detected phases to the central computer. The processing at the sites and the communication are described by B(Sdvarsson et al. (1996). At the centre a timeordered list of phase detections is compiled. The phase detections contain among other things onset times, azimuth direction, spectral amplitudes, corner frequencies and phase type (based on "artificial neural net, see BOdvarsson et al. (1999)). The multistation analysis at the central computer was developed at the Swedish network 1979 - 1981 and translates the list of phase detections to a list of seismic events (origin time,

150

epicentre, focal depth and magnitude). The most important parameters are onset times, azimuths and phase types. The phase types are either P-wave, S-wave or uncertain (P or S). With three observations of onset times or two onset times and one azimuth one can estimate an epicentre. The algorithm makes a complete search of all such triplets and takes the corresponding epicentre and origin time as a possible seismic event. Iterative association of more phase observations and location will then lead to a possible seismic event. A version of this procedure is described by Slunga (1980). For each seismic event a quality measure is assigned. The most important parameter is the number of kinematic observations (onset times and azimuths) fitting the event hypocenter and origin time. When the number of kinematic observations exceeds 4 their value will quickly increase as the ranges of the observations that fits will strongly decrease. The dynamic parameters (spectral amplitudes) are important to use to be able to find events with few kinematic observations and without introducing a large number of false alarms. Therefore the quality 'also includes the fit of the amplitudes. Lack of detections at stations which should detect will decrease the quality. In the location a one-dimensional velocity model is used with non-zero gradients in all layers to stabilize the depths. The use of constant weights (independent of distance) is another feature of the automatic location which will stabilize the procedure. The output from the multistation analysis is a list of possible events of different qualities. This list is scanned by the data fetcher which decides if sig-nals will be requested from the sites, see B0dvarsson et al. (1996). The multistation analysis also produces for each possible event a unique name string and a file listing all phase detections used in the location of the event. This file communicates the results to the following automatic or interactive analysis. When the location and origin time is known the time windows containing the different waves at the different sites are also known and an automatic signal analysis for the source inversion is straightforward.

2.2 I n t e r a c t i v e A n a l y s i s The output of the automatic analysis is not perfect. An effective interactive procedure is required for checking and possibly changing the observations used for the event location. Also this program was created during 1980 for the Swedish network but the graphics has been changed and a number of features have been added during the implementation in Iceland. The data fetcher creates a list of possible seismic events for which observed wave forms are available at the centre. The seismologist scans this list and checks the onset times and first motion directions of the P- and S-waves. The program is "flat", that means it does not use "pop up" windows, one "click" is normally enough for each wanted change or next step. If the seismol~gist changes or adds or removes any observation the event is automaticly relocated. The analysis of one event requires only a few tens of seconds. All events that are accepted as real events are transferred (by one "click") to the list of final events and a new file is created for that event which contains all observations accepted and/or made by the seismologist. Note that only the first P- and S-arrivals are used in the routine analysis. After the interactive analysis the location and origin time are reliable and from this point on all routine analysis is automatic.

151

2,3 S p e c t r a l A n a l y s i s of W a v e f o r m s The main pro'pose of the spectral analysis is to reach to eslimates of seismic moment, fault plane solution, fault radius and static stress drop for the event. The procedure was developed 1981 for the Swedish network by Slunga (1982). First the inelastic damping (Q-model) was found by analysing some 30 earthquakes in Sweden. The Q-damping resulting in constant low frequecy spectral level below the corner frequency was chosen. It was found that this required a frequency dependent Q-value, Q = Qo 9 fo.s. This is in agreement with Rautian and Khalturin (1978) and Rautian et al (1978). It was also found that P- and S-waves required different Qo-values, again in a~eement with those studies. In Sweden the values used are QofP) = 360, Qo(S) = 480, in Iceland we later on found Qo(P) = 100, Qo(S) = 170. No other frequency dependency is included. The analysis also indicated that the type of spectrum proposed by Boatwright (1978) having 3dB at the corner frequency gave a better fit than the often used 6dB spectral models. The best fitting value of the slope, n, at the high frequencies was mostly -2. The estimate of the corner frequency, f~, and the high frequency slope was achieved by systematic search. The DC-level was for each f~ and slope estimated by fitting the theoretical spectrum to the observed spectrum. The frequency band is adopted (iteratively) to the corner frequency so that the upper limit is about 3fc/2. The lower limit is adopted to the DC-level as it determines at which frequency the low frequency ground noise will dominate. This iterative procedure gave the DC-level and f~ for each phase (P, SV, SH) and component (vertical, radial, (P, SV) and tangential (SH)). The same spectral estimate algorithm is also used at the site computers but there applied to the three components N, E, and Z and working with fixed frequency band 5 - 10 Hz. As for all the other algorithms the output is written to files under the event name.

2.4 F a u l t P l a n e S o l u t i o n s In the years 1976-1979 five microearthquakes were recorded by the four stations of the Hagfors Observatory in western Sweden. The four stations were seperated by some 40 km and the events were located within or very close to the array. Mostly only two clear first motions coutd be read and it was obvious that good fault plane solutions could not be reached by use of only first motions. This lead to the use of the "impulse" (time integral of the displacements) of the observed P- and S-phases (Slunga, 1981). If the source slip is unidirectional (no "overshoot") the displacement "impulses" are proportional to the seismic moment multiplied with the source radiation pattern. The different apparent time histories in different directions will not affect the impulses. Thus the use of the impulses for the observed P- and S-waves only required one extra parameter in the source description. When the digital regional Swedish seismic network started in the end of 1979 the fault plane solution algorithm needed to be automatic and this was easily achieved by computing the "impulses" in the frequency domain. The "impulses" are identical to the DC-level (low frequency asymptote) of the observed spectra. That is why the "impulse" method also often is called the spectral amplitude method (Slunga, 1982). The inversion is made by systematic search over the three angles while the seismic moment is linearly estimated for each set of angles. A description of the method (extended from the original single component (vertical) formulation to three component stations) is given by R6gnvaldsson and Slunga (1993). When three component observations are available each station gives three observations of spectral amplitudes, R SV, and SH. The source description consists of four parameters:

152

the three angIes of the fault plane solution plus the seismic moment. In principle (no noise and perfect knowledge of the crust) oniy two stations are required to get an overdetermined solution. In practice already three stations may sometimes give good fault plane solutions. Already with one first motion direction the fault plane solution is in principle unique. The amplitudes cannot themselves discriminate the P- and T-axes of the fault plane solution. One feature of the original tormulation of the method (Slunga, 1981) was that a realistic covariance matrix was assumed for the amplitude errors at each station. It was early verified that the spectral amplitude method gave the same fault plane solutions as the conventtonaI first motion method gave for the cases when the first motion observations were enough to restrict well the range of acceptable solutions (Slunga, 1982; Stunga et al., 1984a). Both of these methods were also consistent with the planes defined by high accuracy multi event locations of aftershocks (Slunga et at., 1984a). Rhgnvaldsson and Siunga (1993) foand also that when the spectral amplitude method was applied to synthetic full wave signals computed by Kind's reflectivity method (Kind, 1978,1979) the inversion gave the three angles of the fault plane solution typically within 5 - 10 degrees of the true values. A study of full wave form inversion of Icelandic earthquakes by Shomali and Slunga (2000) gave the optimum full wave form fault plane solutions to be within the range of acceptable solutions of the spectral amplitude method. Already from the beginning the output of the spectral amplitude method included the whole range of acceptable fault plane solutions, that means not only the optimum solution. This is of value for rock stress tensor inversions (Lund and Slunga, 1998). In the routine use of the spectral amplitude method both in Iceland and in Sweden a double couple source description is assumed. There is however no such restriction in the formulation, any source moment tensor can be used. Tke restriction to a pure shear slip source is made mainly to stabilize the solutions. The systematic search will of course also be slower if the number of source parameters is increased. A few tests allowing slip vector outside the fault plane (expanding fault) have been made for microearthquakes triggered during hydrofracturing in granite but have-not given significant non double couple components. At least in the first order approximation the shear slips are dominating the amplitudes. Compared to full wave form inversion by computing synthetic seismograms the spectral amplitude method has the restriction that no inversion for the time function of the source moment tensor is included. This is however also an advantage for the spectral amplitude method as the apparent time functions require a much more detailed description of the source and thus add complications. The spectral method just requires monotomc source tensor components and determines the final values of the source moment tensor. The output of the fault plane solutions contains the optimum seismic moment, and the three angles of the fauIt plane solution. All acceptable fault plane solutions are also presented graphically. The output is written to special files under the name of the event. 2.5 E s t i m a t e o f F a u l t R a d i u s a n d R e l a t e d P a r a m e t e r s As mentioned above the corner frequency we use is the 3 dB point (where the spectral level is 3 dB below the DC-level). We are not relying on the high frequency asymptote as this requires a larger dynamic range not always available. The comer frequency will be differen~ in different directions fro~- an extended sou:-ce. Slunga (19.~2) modeled the comer frequency for circular fault areas following Savage (1974), and Boatwright (1980).

153

The most robust way was found to be to base the fault radius estimate on the lowest Swave corner frequency at any of the close stations (where crnstal channel waves are not dominating). This lead to the formula r = 700/fc, where r is the fault radius in meter and fc is the corner frequency in Hz. Note that this is different from the corresponding Brune relation (Brune, 1970) which is based on the corner frequency determined by the crossing of the low frequency asymptote with the high frequency asymptote which we are not trying to estimate. The sizes of the fault radius we got by this procedure have in many cases been in agreement with the locations of main shocks and aflershocks in the sense that the aftershocks are typically clustered just within the edge of the main shock area, see for instance Slunga et al. (1984b). Together with the seismic moment given by the fault plane solution the fault radius allows to estimate the mean source slip and the static stress drop (Brune, 1970). The relation by Eshelby (1957) gives then also the peak source slip (when constant stress drop over the fault area is assumed).

3 Multievent Analysis The information contained by the observations of a microearthquake is redundent and combining observations from several events facilitates the extraction of more information. This has in Iceland been used for improving the crustal velocity model by genetic inversion, for estimating the crustal stresses (Lund and Slunga, 1998), and for improved absolute and relative locations (Slunga et al,. 1995; RtSgnvaldsson et al., 1998)).

3.1 M u l t i e v e n t H i g h A c c u r a c y L o c a t i o n s Within the Swedish network we got a small shallow rmcroearthquake swarrn ( J a n , 3 0 Mar.15 1981) of 12 events with similar waveforms. It became obvious that high accuracy timing of the onset time differences could be achieved by simply correlating the signals of different events at the same station. In the first test with these 12 events it was found that all events became located to a plane area of 300 times 300 square meters with a maximum distance from a plane of 3 m. Similar results were achieved by locating the 4 aftershocks to a Swedish ML = 3.2 earthquake 1981, Slunga et al. (1984a, 1984b). These applications of the correlation technique were used only for relative locations. During hydrofracturing in granitic rock in western Sweden Sere were great problems to get reliable depths for the detected microearthquakes. This made it necessary to extend the correlation technique to include also absolute locations as the conventional location algorithms did not solve t the problem. The absolute locations based on high accuracy relative tinting reduced the uncertainty from 200m to 20m, Eliasson et al. (1988). A description of this method is found in Slunga et al. (1995). One valuable aspect of the multievent location technique is that it gives unique estimate of the fault planes in cases when several events are on the same fault. This allows testing of the fault plane solution algorithm. A nice example is given in figure 1 where the fault plane solutions and the multievent locations are both confirmed by the consistency.

154

QUAKE-LOOK C e n t r e : 66.25E, N - 1 8 . 4 4 7 E

127 events.

]

Acce~labie F:PS, b ~

f ~ i n ~ p l a n e s 0..~0 ~_00

_ - 97 08 09 22 25 59.

J

~

t

t S4U~

q

J

~

I

.....

;

......

Fig. 1. The figure shows the multievent locations of 127 microearthquakes at N Iceland in ,~ map (left)and in a depth sec~don (right)looking along the fault. Each earthquake is represented by a disk

with a the estimated fault radius, the orientation of the disk is defined by the best fitting possible fault plane chosen from the range of acceptable fault planes given by the spectral amplitude method. The closest s;ation is about 25 km from the group. The line in the map (left) marks the intersection of the faMt with the surface. 4 The

Icelandic

Experience

1990

- 2001

Since 1990 the new Icelandic seismic network (Stefansson et al. 1993) has grown from 9 stations covering Southern Iceland Seismic Zone (SISZ) to 42 stations covering also the Tj6rnes Fracture Zone (TFZ) in northern Iceland and the Reykjanes area. The number of microearthquakes so far analyzed exceeds 180,000 and includes 6 earthquakes with ML > 5.0 within the SISZ, see table 1 where the earthquake locations are the nucleation points. There were three more ML > 5 earthquakes in SISZ during the first 4 minutes after the large June 17, 2000 earthquake which were probably triggered by the large earthquake. They are not included in this set. In the following some precursors to these earthquakes wilt be presented and combined in an earthquake warning algorithm. I want to emphasize that the work with this large data base has just started and what here is presented reflects only some of the aspects that have turned out to be promising by the preliminary investigations. There are plans for a much more complete and detailed investigation.

4.1 F o r e s h o c k A c t i v i t y Foreshock observation is one of the precursory patterns that has been widely accepted, Wyss and Booth, 1997. The time windows noticed in these studies (Jones and Molnar, 1979; Jones, 1984) vary from about I00 days down to 1 day or less. Most of the foreshocks observed before shallow strike slip earthquakes in Califomia came within 5 km of the main

155

Event

1997~Aug~24 A 1998/&m/04 1998/Nov/13 1998/Nov/14 2000/Jun/17 2000/Jun/21

B C D E F

Table 1: The large earthquakes within SISZ GMT La~. Long. Depth Mz 030511.2 64.035N 21.269W 4 km 5.1 213653.8 64.036N 21.290W 4 km 5.9 103834.4 63.954N 21.346W 5 km 5.6 142406.9 63.958N 21.237W 3 km 5.2 154040.9 63.975N 20.369W 6 km 6.5 005147.0 63.974N 20.706W 4 km 6.5

Ms 5.8

6.6 6.4

Area Hengill Hen~ll Hengill Hengill SIL SIL

shock and during the last day before the main shock. These observations are confirmed by the Icelandic data as such foreshock activity is observed before all our six earthquakes. This is of course expected as the threshold is around ML zero while Jones (1984) used a threshold of ML = 2. Table 2 shows the statistics of the observed activity prior to the six events. Note that the observation of Jones (1984) of having at least one ML > 2 foreshock before 44% of the strike-slip earthquakes means that the number of ML > 0 will be at least 18 - 44 for a b-value of 0.8 - 1.0. Although the number of foreshocks varies strongly the total picture fits well to the results by Jones (1984). Table 2: The seismic activity prior to the large earthquakes compared to the mean daily activity -

A

Number of events within 24h,6km Mean number 24h,6km Largest foreshock 24h,6km

489 13.0 2.1

B

C

786 73 13.8 4.6 4.4 3.1

D

E

F

695 4.1 4.1

5 0.8 0.9

36 1.2 2.1

Note that the lowest increase in activity is found for the first June 2000 earthquake which still have a five times increase in activity compared to the mean value. Figs. 2 - 3 show the time histories of the increased activity before two of the em-thquakes. 4.2 F a u l t R a d i u s V m ' i a t i o n s Dieterich (1972 - 1992) gave a new paradigm by introducing the rate- and statedependent friction model. He also noted that for each fault system there exists a minimum fault radius (Dieterich, 1986). This aspect was later discussed and investigated by Boatwright and Cocco (1996). They presented a model where changes in loading is expected to cause changes in the observed fault radii by activating different fracthres within the crust. The dependence on loading rate was shown by Cao and Aki (1986) and Gu and Wong (1991) although the modelling still contains uncertainties. This was the starting point for my investigations of the variations of the microearthquake fault radii in space and time (Slunga, 2001). I there defined a modified median of the fault radius, MMFR, which was taken as the mean of the 25 %, 50 %, and 75 % quartiles of the distribution of the fault radius for events within a space and time window. These ,~[MiFR were computed for the epicenter and origin time of each microearthquake based on events within a circle of radius 18 k_rn and for the preceeding 60 events.

156

QUAKE-LOOK

Ill

Seismicity rate, <6km, <24hours. ,r~lTflili l t l l l l l l l i l l l l ! l l l l l ! l [ ; l l l l i i i i l l i [ l l l l l i {lillllllllllllFllllllllt~lllllliIItlllli'.i Main event: 000617 5.26 (388.) 63.97-20.37 R= 6 km 000430 - 000804

t 14nn ~90 ~

~_80.

L7o.

h

L~o.

9

I~.o.

i

5. 4.

3.

Fig. 2. Observed number of events within 6 km and 24 hours. This number is computed for the place and time of each microearthquake. All such observations within a circle of 6 kra of the largc June 17, 2000 earthquake are shown. The time window is Apr.30 - Aug.8, 2000~ days are marked at the top and the earthquake is marked at the bottom. TEe scale is marked to the right. Note that there is not only an increase the last day but there is also an increased activity a few days before. qUAKE-LOOK

111

Seismicity rate, <6km, <24hours. I I I - V I I I I - 1 I I I t I-I t I t t I i I q - T 7 Tr-M ~ L , E r q - - F - r - F J q - - F T T q--TT ~_500. Main event: 980604 5 . 5 0 ( 74 .) 6 4 . 0 4 - 2 1 . 2 9 R = 6 k m I 980514 - 980629 I

~

~

I~~

I~

_3o0. 2o0.

b,

Boo. 5. 4. 3.

Fig. 3. Similar to Fig. 2 but showing the activity rate observations around the largest of the Hen~lt area earthquake. The time window is May 14, 1998 - June 29, 1998. Days are marked at the top. Note that the numbers are much higher here than in Fig. 2. Note also that this earthquake is preceeded by strong foreshocks marked at the bottom.

Several interesting aspects were found including remarkable changes prior to all the 6 large earthquakes, see Figs. 4 - 5. The results are summarized in Table 3. For each large earthquake the time of crossing a threshold value for ~s prior to the earthquake and within 6 km of the epicenter is determined (the delay time) and the number of events within 6 km is computed from that time to the time of the event. The threshold value is taken as

157

140 m in the Hengiil area and 120 m in the SIL area. It was found that if one took the number of microearthquakes instead of time the "delay" between changes in M M F R and the main event were much more constant. One should note that the event D (Nov. 14, 1998) was preceeded by event C by less than 28 hours and about 8 km away. The high number of events is due to the aftershocks to the event C. Table 3: The delay and number of events after M M F E exceedance

Delay time, days Number of events

A 0.2 87

B 0.i 103

C 4.4 178

D 3.8 1094

E 80.0 84

F 1.9 69

I want also to point out that the variation of the fault radius is not explained by just variation in the modified median of the event magnitudes although there is a positive correlation. In many cases we get increased fault radii even when the magnitudes get smaller. There are also striking similarities in the variation of the i~MFR from different areas so distant that they are based totally on different events. One possible interpretation is that the variations of the stresses or loading rates are really seen in the B,EV[FR, possibly by affecting the activity rate at different fracture systems in agreement with the theory. This is also supported by the fact that the great eruption at Vatnaj6kull Oct. 30, 1996 (the centre of the Icelandic hot spot) was associated with an increased lVh-MFR in the whole western part of SISZ.

Modified median of fault radius, M M F R , [

I

~

I

Main event: 9 7 0 8 2 4 9 7 0 8 1 6 - 970901

I

1

I

J

1

--7--

4.95 ( 64. 6 4 . 0 3 - 2 1 . 2 7

I

1

;

R= 6 km

] ....

]

l 89

'[

~1~

...

"

]~40.

5.

I I,' L_

i

43.

Fig. 4. The variation of MMFR during Aug 16 - Sap l 1997 within a circle of 6 krn around the Aug 24 1997 earthquake is shown. The scale to the right shows meters. The marks at the top are days. At the bottom the earthquakes within the circle are marked with their magnitudes. All MMFR are based on microearthquakes prior to the time of the value. Note the dramatic increase during the last day.

158

QUAKE-LOOK Ill Modified

11li7 ~I

median

of fault radius,

Ill t II!!iiltli!lrN,ITF~NTiTrlTITllm~l;il',llll

Main event: 000017 900601 - 010221

5.26 (308.)

63.07

MMFR,

illllliii!ll; IIIIql]Tr171T -20.37

R=

6 km

l]7~r~j8o. ~6o. I I I ~ i -120"

~_~o. i

A__4o. 5.

4.

,1

3.

Fig. 5. Similar to Fig. 2 but now the timeperiod is Jun. 1, 1990 - Feb. 21, 2001 and the MMFI-{ observations within 6 km of the epicenter of the large June 17, 2000 earthquake are shown. The marks at the top are now months. Notice the dramatic increase some 3 months before the earthquake marked at the bin;ram. This peak coincides with the vuteanic elnaption at Hekla supporting the view that changes in crustal loading are involved. 4.3 A s p e r i t y B r e a k i n g a n d D o m i n o P a t t e r n Jones and Molnar (1979) proposed a model for asperity breaking where a limited number of successive breakings (foreshocks) redistribute the stress forces to the successively fewer remaining points to be broken. The increased stress at the last points causes an increased seismicity rate for the last events. Under reasonable conditions the model also gives a high activity rate in the beginning due to the large number of subasperities to break. If the total stress on the asperity group is increasing in time the activity at the end of the breaking time will further increase. This model of a restricted number of events in the pattern is slightly supported by the constant number of events during the delay time between MMFR change and the main event (Table 3). This was investigated by making a systematic search over the 180,000 microearthquakes for spheres of radii 1 - 4 krn containing 20 - 90 microearthquakes within a time window of maximum 90 days and following a time history which could be well fitted to the model of the type proposed by Jones and Molnar (1979) but allowing an excess of late events due to increased tectonic stress or due to an immediate start of a new close asperity breaking. The best fitting groups contained typicaUy 30-60 events within spheres of diameters 4 - 6 kin. By favouring slowly developing groups (making the quality of the group also proportional to the time window) the result was that nice asperity breaking patterns were found typically a few to 20 days before larger earthquakes and within a distance of 5 km from the hypocentre. A typical character of these groups is that they contain a quiescence in the second half of their time evolution. This quiescence is important for the quality of the group. The systematic search is made in such a way that for each microearthquake the radius is varied between 1 - 4 km and the number of preceeding earthquakes is sucessively increased from 20 to 90 (or less if the upper time window is exceeded) and the quality of each group is computed. The group of highest quality is taken as the domino pattern observation at the

159

time and place of the microearthquake. Note that it is possible that an asperity breaking which quickly will be followed by an adjacent asperity breaking is more valuable for the earthquake warning algorithm. For this reason the quality is not reduced by a worse fit at the end of the group due to excess activity. This motivates the use of the term domino pattern. Figs. 6 - 7 give examples of the domino patterns at two of the earthquake epicenters. QL~.A,..KE-LO O K tH

Domino Patterns igNTi],'TITr~ITF~]TNTITTITIT1Tt-ilTITiTii ITi ~FITflTff, fflTTN i-I~IT~TTTIT,.rrr Main event: 000617 5.26 (388.) 63.97 -20.37 R= 6 km 920920 - 010221

, t ....tlJlL J

LI t5o

4.

3.

Fig. 6. Sinfilar to Fig. 2 but now showing the qualities of the domino patterns. The time window is Sep. 20, 1992 - Feb. 21, 2001 and ai1 observations within a distance of 6 km from the epicentre of the June 17, 2000 earthquake are shown. High quality domino patterns are observed a few days before the earthquake marked at the bottom. The top marks are months.

4.4 S w a r m s Observations of swarms for years before large earthquakes at their epicenters are well known precursors (Evison, 1977). We are observing exactly the same thing on Iceland with a number of swarmlike activity periods at the sites at the six largest SISZ earthquakes during the last 6 years before the events. So far no large earthquake has occurred (within the network) without observed previous swarms. 4.5 L o w S t r e s s D r o p E v e n t s I have also found that the percentage of events having low static stress drop (after correcting for the magnitude) shows a precursory increase before all the six large events, Figs. 8 - 9. This was given an interesting interpretation in a recent paper by Sammis and Rice (2001). Although they discuss "repeating earthquakes" their discussion leads to lower stress drops for microearthquakes at boundaries of large asperities compared to microearthquakes at boundaries of smaller locked patches. The statistically significant increase of the ratio of low stress drop events before the larger earthquakes thus gets an additional possible physical interpretation. Stick slip experiments with rock samples have also shown a decrease in

160

O~UAKE-L.QOK III

Patterns

Domino

----I

r

T-

i

i

Main event: 981113 980411 - 990617

,l

.I .I

~ ---q

r

5.14 (273,)

,.

T--B

63.95-21.35

,

,

~.... R=

i 6 km

II, t

5.

4. 3.

Fig. 7. Similar to Fig. 6 but now showing a close up around the Nov. 13, 1998 ear&quake. The time period is Apr. l l , 1998 - June. 17, 1999. The time marks at the top are months. Again a high quality observation preceeds the earthquake marked at the bo,:tom. Note that a smaller earthquake in the beginning also is preceeded by an increased domino pa~tern quality. This is quite common. stress drop w h e n the loading rate (load point velocity) is increased (Wong and Zhao, 1990). T h e static stress drop is of course related to the fault radius and there is a n e e d for further and m o r e detailed studies to clarify the picture.

Q U A K E - L O O K HI

Percentage low stress drop events. - ~ j - ~ tq-j--F]-~7 I ! 1 I I I I I T ~ T T T ~ Ii I I Main event: 000617 5.26 (388.) 63.97 -20.37 R= 970913 - 010221

i~llll

km

_70. ._60. ~50. _40.

._30.

I

__20. --10. 5. 4. 3.

Fig. 8. Observed percentages of low stress drop events within a distance of 6 kin from the epicentre of the June 17, 2000 earthquake. The time period is Sep. 13, 1997 - Feb. 21, 2001, months are marked at the top. The earthquake is marked at the bottom. Note the pronounced high percentage during mos; of the four months before the ear&quake.

161

QUAKE-LOOK

Percentage

low

stress

Ill

drop

events.

VrT]T[-~-TUT,!I:II]!IIII!~ l l l l l ! f l r l l l l l l l l - - l ! l l l l , ' l ] l l t ;lllii~l[~llll;lllltl[ i Main

event:

981113

5.14(273.)63.95-

.

=

6km

O. O. i

5.

3. Fig. 9, Similar "co Fig. 8 but showing the observations around the Nov. 13, 1998 earthquake. The time period is Sep. 26:1998 - Dec. 13, 1998. The days are marked at the top. We see here ax~ increase during the !ast weeks before the earthquake marked at the bottom.

5 A simple Earthquake Warning Algorithm, EQWA As seen from Table 2 it is obvious that most of the larger earthquakes are preceeded by a very increased microearthquake activity during the last days. The earthquakes are normally not coming as surprises. In fact the second of the two large June 2000 earthquakes coming 4 days after the first one was predicted less than 12 hours before when the civil defence authorities were informed that a large earthquake was probably coming at one of two possible places (Stefansson et al., 2001). This earthquake warning was based on the microearthquake activity interpreted in connection with wide experience of previous SISZ earthquake sequences. I will here present a simple earthquake warning algorithm which is intended to illustrate the possible value of formalizing the use of the different precursors discussed above. When it has been formalized the programming of an automatic algorithm is straightforward. An early version of what will be discussed here is already implemented within the Icelandic network. The EQWA I present here is based only on information extracted from the observat.ions of microearthquakes. No additional information is used. If other types of precursor observations are available one can expect further improvements in reducing false alarms. No effort is made to estimate the size of the coming earthquake. Instead the warning threshold is put so we will have warnings before the six large earthquakes within the SISZ area and check then the number of false alarms. The idea is to identify the crustal conditions that are needed for a large earthquake to OCCUr.

5.1 Input

Parameters

The parameters used arc all computed only at times and places of detected microearthquakes. Thus an implicit requirement is that at least one microearthquake is observed before the

162

earthquake. The rate of the foreshock activity is covered by a number of parameters. One is the number of events within 6 km and 24 hours. Another parameter is the increase of this parameter. A third parameter divides the close activity with the activity at a distance 6 - 12 kin. The modified median of the fault radius is also a key parameter. I also use the change of fault radius within 150 close events. Thus in an area of low seismic activity the time window will be longer than in a very active area. I also use the modified median of the magnitudes. This is motivated for instance by the extensively used power law model leading to the mainshock, see for instance Quillon and Sornette (2000). Another key parameter is the quality of the domino patterns. A high quality is assumed to indicate ongoing tectonic activity. The percentage of low stress drop events (the threshold is taken so typical percentages are in the range 5 - 20 %) is one of the parameters and may possibly indicate breaking of larger locked patches and/or increased crustal loading rate. The sandwich pattern, the ratio of the seismic activity (number of events) within a slab divided by the activity within the surrounding slabs (Slunga, 2001), is another parameter which has increased values prior to large earthquakes.

5.2 A d a p t l v i t y The seismic activity shows large variations between different areas of SW Iceland. We want to use the same automatic EQWA for whole Iceland and this requires that some adaptivity to the local conditions is used. I therefore defined a grid (3 km times 3 kin) covering whole Iceland. After each whole year the statistical distribution of all variables was estimated for each grid point based on the observations within 6 km and for the whole preceeding period (after 1990). This statistical information was stored in files and was taken as reference when deciding the significance of each observation for the following year.

5.3 E a r t h q u a k e W a r n i n g P a r a m e t e r ,

EQWP

For each new microearthquake all parameters were computed based on the previous microearthquakes. All of these parameter observations were then compared to the parameter's statistical distribution at the corresponding grid point. If the observation exceeded the 75 % quartile it was given a value 3, if it also exceeded the 87.5 % quartile it was given a value 9, if it exceeded 93.75 % it was given a value 27, and if it exceeds the largest previously observed value it was given a value 81. For each parameter it got such a value ranging from 1 to 81 (if it was less than the 75 % quartile the value was taken as 1). All these values were then multiplied to a total product. It is obvious that this is not enough to avoid a large number of high values in any areas where the activity is higher than before. One has to introduce also some requirements on the absolute levels, For all parameters a minimum value Was introduced and if the observed value was less than this minimum value the product was multiplied with the ratio of the observed value to the required minimum value. This reduces the possibility that small bursts of activity in normally quiet areas will lead to alarms.

163

One additional requirement was based on the type of observations m a d e by Evison (1977) about swarm activity as a long term precursor. Similar observations were made on Iceland not only for swarms but also for fault radius (MMFR), d o m i n o patterns, low stress drop events and also other parameters. Thus minimum values were also introduced concerning the m a x i m u m previous observations at the grid. If the m a x i m u m observation was less than required then again the product was multiplied by the ratio of the m a x i m u m observation divided by the required value. This gave a final product value. The natural logarithm of the final product was taken as the earthquake warning parameter. The threshold value which was exceeded before all six earthquakes in Table 1 is 30. The four largest earthquakes actually have E Q W P that exceeds 35 within a few days and within 6 km of their epicentres. The results are displayed in figures l 0 - 16 for the SISZ area. There is of course a starting up problem in all adaptive processes which start from scratch. I went around this by using the grid statistics from the years 1990 - 1994 for the years 1990 - 1995 and 'after that updated the statistics at every new year.

QU AKE-_~OOK III

Earthquake

warnings,

EQWP

> threshold

Alarm

level 30.0

-9-6-(E8-~4X )-(~0-O-- - 9~7D-8-ff4-( T3-O-O---9-70-s ~-4--02I-0~ ). . . . . .

Co4N

r

~W Iceland 22W

21W

20W

Fig. 10. This is a map over SW Iceland for the time window Aug. 24, 1996 - Aug. 24, 1997. The eaxthquake Aug. 24, 1997 is marked with a grey and a black circle. The radius of the bIack thin circle is 8 kin. The polygons mark the places of alarms (EQWP > 30.). The diameters of the polygons scales with time, the smNlest are early in the time window while the largest axe the latest. The squares show that they occur more than 24 days before the earthquake. Grey hexagons axe during the last day. Pentagons and/or hexagons with their centre within the 8 km circle are judged as correct alarms, all squares axe incorrect alarms but possibly at the correct place. There are 9 false alarms of which 2 are at the correct place. This earthquake has correct alarms, one during the last day. Within 5 minutes of the June 17, 2000 earthquake we got three earthquakes with magnitudes of about 5, the analysis of these earthquakes is complicated due to interference. They were most likely triggered by the large earthquake and were all within the S I S Z west of the main event. Two of these came in the Reykjanes area, one where there were several false warnings shown in Fig. 14.

164

Q U A K E - L O O K III

Earthquake Warnings, E 7D-8-23;-02E 7 0 ~

EQWP > threshold Alarm level 30.0 b ~0-4--23-3-0--9-8-0-6 ~ - ~ .......

64N

; 22W

21W

20W

Fig. 11. The same as Fig. 10 but now for the following period up to the next large earthquake, Aug. 24, 1997 - June 4, 1998. Again we see a correct alarm but therc are also 8 false alarms of which one is at the correct place. Q U A K E - L O O K III

Alarm level 30.0 Earthquake Warnings, EQWP > threshold 9-8~f60-4~2-2W0~- ~8-i - ~F~./-I-0~---~8-I ITW-f~-O~

i 64N

~ 22W

Iceland 21W

20W

Fig. 12. The same as before but now for the following period up to the two earthquakes Nov. 13, and 14, 1998. We see here correct alarms before tke first earthquake which also is larger. We have one false alarm during these five months. Note that the false alaxms axe often at the places of coming earthquakes. 5.4 False Alarm

Rate

As I put the threshold so all the six large earthquakes of Table 1 get correct warnings the significance o f this earthquake warning e x a m p l e depends on the false alarm rate.

165

QUAKE-LOOK

III

Earthquake Warnings, EQWP > threshold, Alarm level 30.0 9 8 ] 1 1 4 1-Sb-b~s ~-f7 1 5 3 0 O00-6~f 7 - 1 - 6 - 0 - 0 - -

o

64N

I S Z ISW I c e l a n d

' 22W

21W

20W

Fig. 13. Period is Nov. 14, 1998 - June 17, 2000. During this period there are 8 false alaxms of which 2 are at the correct place, ht addition we have correcs alarms. Note that most of the false alarms are at places of coming earthquakes.

QUAKE-LOOK

Earthquake

Warnings,

9~4-

Ill

EQWP > threshold

Alarm level 30.0

-fS-O-O--q:TO-O5"-17-iq3-3-0--0-0-0~ i 7 - T 6 0 ~ - - - -

64N

i\

i

22W

Iceland 21W

20W

Fig. 14. This figure is the same as Fig. 13 but now the positions of two quic~y following earthquakes of magnitude 4.5 are also shown. Note that many of the previous false alarms are at the place of the western earthquake. For the period 1996 Aug. 24 (one year before the first of the earthquakes in Table 1) to 10 Feb, 2001 (the end of the data base I had at this time and about 8 months after the last large earthquake) and within the SISZ area (the area of the figures) there were 32 alarms of which 6 are correct alarms. With correct alarm is here meant an alarm that is within

166

QUAKE-LOOK

Ill

Earthquake Warnings, EQWP > threshold, Alarm level 30.0 -0(EqY6"97-T600- ---O~)-0 ~ U 00- --073D-6l~-I--0-f0-0- - - -

@~ , 22W

64N

~

Iceland

21W

20W

Fig. 15. A short period, June 17, 2000 - June 21, 2000. False warning at the place of the previous earthquake and correct warnings.

QUAKE-LOOK

III

Earthquake Warnings, EQWP > threshold Alarm level 30.0 ~ 3-01 b~-l--O~l-O-O '~ -0~02 ~ _ - I - ~ E O ~ f i

64N

I 22W

c

e

l 21W

a

n

d 20W

Fig. 16. For completeness, the period covers June 21, 2000 - Feb. 10, 2001. Two false warnings, one early at the place of the June 17, 2000 earthquake and one at the top of the figure. 8 km of the epicentre and less than 24 days prior to the earthquake. For this period the probability to have an earthquake with magnitude larger than 5.0 within 8 km and within 9 days (the largest lead time of the correct alarms) is 19 % (about 5 times more alarms than earthquakes). Note that many of the false alarms were at "correct" places (places of later earthquakes) but earlier than 24 days. As we also had 19 false alarms for the period July 1 1990 - Aug 24 1996 which contained no earthquake with ML greater than 5.0 the total

167

probability after an alarm is lowered to 12 %. Most of these early false alarms came after 1993 during a period of increasing activity.

6 Discussion One must note that the example of an EQWA given here is not meant as a proof that this EQWA is really working in the sense that future earthquakes within SISZ will be anticipated. This is a retrospective study and nothing else. It is shown as an example of parameters that may be of value in the continued efforts to achieve a reliable EQWA. There are however some circumstances that give some credit a priori to the use of these parameters for earthquake warning purposes. All parameters have either been observed earlier as precursors (foreshocks, increased activity (power law), swarms) or are implicitly given by theoretical studies (the fault radius variations and the low stress drop events). If we raise the threshold from 30 to 35 we still get correct warnings before the 4 largest earthquakes while the number of alarms will drop from 51 to 30 within the SISZ area for the period 1990-Feb 2001. It is promising that the larger events give higher EQWP values and it indicates a robustness in the behaviour. It is also positive that the "hit" percentage rises slightly. As mentioned before, the same EQWA was applied to whole Iceland. Almost all the warnings outside SISZ are located to the TFZ in northern Iceland, Fig. 17. This is good as this is also an area where large earthquakes occur. The number of false warnings in northern Iceland is totally 10 for the years Aug. 24, 1996 to Feb. I0, 2001.

QUAKE-LOOK

I11

Earthquake Warnings, EQWP > threshold, Alarm level 30.0

.

~ 22"vV 2 1 W

~

20W

.

/

.

.

.

,

~ 18W

. . . . . .

. . N

Iceland 17W

16W

Fig. 17. All earthquake warnings for the whole period Jan. 1, 1990 - Feb. 10, 2001. All earthquakes

having magnitudes above 4.5 are marked. Notice that the network has bad coverage in central Iceland where the earthquakes of the hot spot area pass unwarned. Of the earthquakes in N Iceland only one of the two largest was anticipated, Fig. 18.

168

QUAKE-LOOK

III

E a r t h q u a k e Warnings, E Q W P > threshold, A l a r m level 30.0 ,r---9-6-0 T(5;I-15b-0-0~-9" ~i3-9~2-o-X~)-o~9"Tug-2,-r ~ r o - o - ~ - - - - - ] l o

66N

TFZ, N Iceland N

21W

20W

1~8W

17W - -

6W

Fig. 18, This s shows the warnings in N Iceland before the Sep. 20, 1997 earthquake. The period starts Jan. 1, 1996 when the Ilorthern network came into operation. There are four false alarms plus one alarm at the correct place bat 17 days before the earthquake. A slight support for the possibility that the algorithm may be of value also in northern Iceland is given by the fact that one of the two largest earthquakes in the area of this period, the Mc = 5.2 Sep. 20, 1997 earthquake, is preceeded by one of the alarms (at correct place and 17 days before the earthquake), Fig. 18. The northern network at that time had larger station spacing than in the south giving higher detection threshold. The median value of the detected microearthquakes is about 0.3 units larger than in SISZ. Before the first of the two large earthquakes in TFZ, July 22, 1997, the detection difference was even larger. That event was not preceeded by correct warnings even if the EQWP had its locally highest value for several years I4 days before that event. If both SISZ and TF-Z are included there is totally 60 "alarms of which 6 are con'ect, a "hit" percentage of 10% during the whole period July 1990 - February 2001. I also checked the robustness by using the total observations (the whole period) when computing the statistical distributions at the grid points. As expected it lowered a little the EQWP values, instead of 30 a value of 29 was required to get warnings before all the six SISZ emXhquakes. It did however also reduce the false alarms before 1997 from 19 to 1 t which increased the overall "hit" percentage to 11%. Thus the correct alarms are not due to previous lack of activity in the epicentral areas of the earthquakes as the high activity observed after the earthquakes did not prohibit high values for the EQWR I have not discussed the effects of variations in the detection capacity of the network. The natural variations in the activity at all places spans over about two orders of magnitudes, a factor 100. With a b-value of 0.8 (which is observed for the 180,000 earthquakes) and with a variation of the general high frequency noise level of a factor 3 corresponding to a magnitude difference of 0.5 the variation of the number of events is only 2.4 which is much less than the variations we are looking for. In addition such large general noise variations at the high frequencies are not common. An interesting aspect is the lead times reported for precursors. Jones and Molnar (1979)

169

found an increased activity 5 - l0 days before the main shocks which culminated during the last day with possibly a decrease during the last 6 hours. Note that five of our earthquakes (the Nov. 14, 1998 excluded as it was preceeded by a close earthquake 27 hours before) have alarms starting 9-0.2 days (median value 3.8 days) and the last alarm comes 1.4-0.02 days before with a median value of 0.25 days or 6 hours. Jones and Molnar (1979) also observed in many i cases lead times of about 90 days and also an increased activity about 20 days before the main shocks. The lead times of the domino patterns for all the six events of table 1 plus the large earthquake in the north are all in the range 19 - 3 days with a median value of 15 days. Geodetic measurements in California have given lead times for premonitory movements of 20 - 22 days and 112 days (Shifflett and Witbaard, 1996). There are striking similarities although they are based on different types of data. As the whole idea of this work aiming at an earthquake warning algorithm is to find parameters responding to changes in the crustal conditions or processes required for a large earthquake such similarities are positive indications.

7 Conclusions The foreshock observations by Jones (1984) about shallow strike slip earthquakes are in agreement with what is observed in Iceland. The expected increase in number of foreshocks by going down to even negative magnitudes is verified. The increase of the microearthquake activity before the six largest earthquakes is statistically significant. The statistical distribution of the microearthquake fault radius shows shifts to larger values prior to the large earthquakes. This shift may be due to changes in the minimum fault radii as given by the rate- and statedependent friction which states that the minimum radius is determined by the fracture system and the loading velocity. The time variation of the modified median of the fault radius shows high similarity at places far away (50 - 100 k m ) from each other. They show also remarkable changes at the times of volcanic eruptions at Vatnaj6kul and Hekla. This is an indicator that changes in the crustal loading affect the variations. The time interval between the large values of the modified median of the fault radius and the earthquake varies between less than one day up to 120 days. It was found that the number of microearthquakes close to the epicentre of the coming earthquake for the time interval from the latest fast change in Nk'VIFR to the time of the earthquake was much more constant than the size of the time interval and typically about 90 with a detection threshold around ME = 0. The possibility that changes in the crustal loading rate is causing the MMFR variations leads together with the idea that asperity breaking is associated with a ~ o u p of close earthquakes of limited number to the definition of a domino pattern which is of the same form as the asperity breaking model proposed by Jones and Molnar (1979). The differencies are that I use a much smaller lifetime of the subasperities (typically about 80 days) and 'also allow for a linear increase inthe total loading of the asperity. This pattern turns out to show up as a precursor to all our six em'thquakes. The reported increase of low stress drop events before earthquakes is also verified. It remains to make a closer study of the variations of MMt"R and the stress drop as ~ e y may be strongly related.

170

An automatic earthquake warning algorithm based on the precursors o b s e r v e d in Iceland can be o f value, one reason is that it can be w o r k i n g continously 24 hours per day. A n u m b e r o f indications about precursors of possible value are a c h i e v e d for the future w o r k and the value o f small microearthquakes is proved.

References Boatwright, J., 1978, Detailed spectral analysis of two small New York state earthquakes, Bull. Seism. Soc. Am., 68, 1117-1130. Boatwright, J., 1980, A spectral theory for circular seismic sources; simple estimates of source dimension, dynamic stress drop and radiated seismic energy, Bull. Seism. Soc. Am., 70, 1-27. Boatwffght, J., and M. Cocco, 1996, Frictional constraints on crustal faulting, J. Geophys. Res., 101, 13895-13909. Brune, J.N., 1970, Tectonic stress and the spectra of seismic shear waves from earthquakes, J. Geophys. Res., 75, 4997-5009. B6dvarsson R., S.T. R6gnvaldsson, S.S. Jakobsdottir, R. Shmga, and R. Stefansson, 1996, The SIL data acquisition and monitoring system, Seism. Res. Letters, 67, 35-46. B6dvarsson, R., S.Th. R6gnvaldsson, R. Slunga, and E. Kjartansson, 1999, The SLL data aquisition system - at present and beyond year 2000, Phys. Earth Plan. Int., 113, 89-101. Cao, T., and K. Aki, 1986, Effect of slip rate on stress drop, Pure Appl. Geophys., 124, 515-530. Dieterich J.H., 1972, Time dependent friction as a possible mechanism for aftershocks, L Geophys. Res., 77, 3771-3781. Dieterich, J.H., 1974, Earthquake mechanisms and modeling, Ann. Rev, Earth Plane. Sci.,2, 275301. Dieterich J.H., 1978, Time dependent friction and the mechanics of stick slip, Pure Appl. Geophys., 116, 790-806. Dieterich J.H., 1979a, Modeling of rock friction 1, Experimental results and constitutive equations, J. Geophys. Res., 84, 2161-2168. Dieterich J.H., 1979b, Modeling of rock friction 2, Simulation of preseismic slip, J. Geophys. Res., 84, 2169-2175. Dieterich J.IL, 1986, A model for the nucleation of earthquake slip, Earthquake Source Mechanics, Geophys. Monogr. Ser. vol. 24, edited by Dos, Boatwright, and Scholz, 37-49, AGU, Washington D.C. Dieterich, J.H., 1992, Earthquake nucleation on faults with rate and state-dependent strength, Tectonophysics, 211, 115-134. Eliasson, T., U. Lindblom, R. Slunga, U. Sundquist, and 3'. Wailroth, 1988, The Swedish hot-dryrock project - some preliminary achievemnts, in Deep Drilling in Crystalline Bedrock, edit.: Boden, A. and K.G. Eriksson, Springer-Verlag, Berlin. Eshelby, J.D., 1958, The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. Roy. Soc. London, 241,276-296. Evison, EE, 1977, The precursory earthquake swarm, Phys. Earth and Plan. Int., 15, 19-23. Gu, Y., and T.E Wong, 1991, Effects of loading velocity, stiffness, and inertia on the dynamics of a single degree of freedom spring-slider system, J. Geophys. Res., 96, 21677-21691. Jones, L.M., and E Molnar, 1979, Some characteristics of foreshochs and their possible relationship to earthquake prediction and premonitory slip on faults, J. Geophys. Res., 84, 3596-3608. Jones, L.M., 1984, Foreshocks (1966-1980) in the San Andreas System, California, Bull. Seism. Soc. Am., 74, 1361-1380. Kind R., 1978, The reflectivity method for a buffed source, J. Geophys., 44, 603-612. Kind R., 1979, Extensions of the reflectivity method, J. Geophys., 45,373-380. Lund, B., and R. Slunga 1998, Stress tensor inversion using detailed microearthquake information and stability constraints; application to Olfus in southwest Iceland, J. Geophys. Res., 104, 1494714964. Quillon, G., and D. Sornette, 2000, The concept of "critical earthquakes" applied to mine rockbursts with time-to-failure analysis, Geophys. J. Int., 143,454-468. Rautian, T.G., and V.I. Khalturin, 1978, The use of coda for determination of the earthquake source

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spectrum, Bull. Seism. Soc. Am., 68,923-948. Rautian, T.G., V.I. Khalturin, V.G. Mariner, and P. Molnar, 1978, Pre!eiminary analysis of the spectral content of P and S waves from local earthquakes in the Garm, Tadjikistan region, Bull. Seism. Soc. Am., 68,949-971. R6gnv,'fldsson, S.Th., and Slunga, R.S., 1993, Routine fault plane solutions for local networks, A test with synthetic data, Bull. Seism. Soc. Am., 1 l, 1232-1247. ROgnvaldsson, S.T., A. Gudmundsson, and R. Slunga, 1998, Seismotectonic nalysis of the TjOrnes Fracture Zone, an active transform fault in north Iceland, J. Geophys. Res., 103, 30,117-30,129. Sammis, C.G., and J.R. Rice, 2001, Repeating earthquakes as low-stress-drop events at a border between locked and creeping fault patches, Bull. Seism. Soc. Am., 91,532-537. Savage, J.C., 1974, Relation between P- and S-wave corner frequencies in the seismic spectrum, Bull. Seism. Soc. Am., 64, 1621-1627. Shifflett, H., and R. Witbaard 1996, Multiple Precursors to the Landers Earthquake, Bull. Seism. Soc. Am., 86, 113-121. Shomali, Z. H., and R. Slunga, 2000, Body wave moment tensor inversion of local earthquakes; an application to the South Iceland seismic zone, Geophys. J. Int., 140, 63-70. Slunga, R., 1980, International Seismological Datacenter. An algorithm for associating reported arrivals to a global network into groups defining seismic events, FOA ReportC 20386-T1, Swedish National Defence Res. Est., S- 17290 Stockholm, Sweden. Slunga, R.S., 1981, Earthquake source mechanism determination by use of body wave amplitudes an application to Swedish earthquakes, Bull. Seism. Soc. Am., 7 I, 25-35. Slunga, R.S., 1982, Research on Swedish earthquakes t980-1981, Swedish National Defence Res. Est., FOA Report C-20477-T 1, S-17290 Stockholm, Sweden. Slunga R., P. Norrman, and A-C Glans, 1984a, Seismicity of southern Sweden, FOA Report C 20543T1 July 1984, National Swedish Defence Res. Est., S- 17290 Stockholm, Sweden. Slunga R., R Norrman, and A-C Glans, 1984b, Baltic shield seismicity, the results of a regional network, Geophys. Res. Letters, 11, 1247-1250. Sluuga r., S.T. Ri~gnvaldsson, and R. BOdvarsson, 1995. Absolute and relative locations of similar events with application to microearthquakes in southern Iceland, Gecphys. J. Int., 123,409-419. Slunga, R., 2001, Foreshock activity, fault radius, and silence - earthquake warnings based on microearthquakes, Rit Vedurstofu Islands. Research report, Icelandic Meteorological Office, Reykjavik, Iceland. Reykjavik, Iceland, February 2001. Stefansson, R., BOdvarsson, R., Slunga, R., Einarsson, R, Jakobsdottir, S., Bungum, H., Gregersen, S., Havskov, J., Hjelme, J., & Korhonen, tI., 1993, Earthquake prediction research in the south Iceland seismic zone and the SIL project, Ball. Seism. Soc. Am., 83,696-716. Stefansson, R., Th. Anladottir, G.B. Oudmundsson, R Halldorsson, and G. Bj6rnsson, 2001, Two recent M=6.6 earthquakes in the South Iceland seismic zone. A challenge for earthquake prediction research. Rit Vedurstofu Islands VI-R01013I-JA01. Research report, Icelandic Meteorological Office, Reykjavik, Iceland. Shifflett, H., and R. Witbaard, 1996, Multiple Precursors to the Landers Earthquake, Bull. Seism. Soc. Am., 86, 113-121. Wong, T.F., and Y. Zhao, 1990, Effects of load point velocity on frictional instability behaviour, Tectonophysics, I75, 177-195. Wyss, M., and D.C. Booth, 1997, The IASPEI procedure for the evaluation of earthqu~e precursors, Geophys. J. Int., 131,434-424.

172

Single Station Real-Time P and S Phase Pickers for Seismic Observatories

Reinoud Sleeman and Torild van Eck Royal Netherlands Meteorological Institute (KNMI) P.O. Box 201, 3730 AE De Bilt, Netherlands i [email protected]

A b s t r a c t . An automatic phase picker is required for real-time procedures to locate seismic events. We preseut a successful implementation at the Royal Netherlands Meteorological Institute (KNMI) of an accurate P picker, based on a dual autoregressive modeling of the seismogram around the P phase. The method only requires a detection of the P phase, wtfich in our implementation is provided by a simple STA/LTA ratio. In the second part of this chapter we describe a fast algorithm to identify and pick S wave energy. This approach combines classical polaxiza~ion analysis and the discrete wavelet transform. Polarization analysis of the P wave arrival is used for initial rotation of the raw data into the radial and transverse components. The wavelet decomposition of the radial and transverse components are filtered with an adaptive noise reducing filter to select scales (frequency bands) containing the S wave energy. This step reveals the type of seismic signal: local, regional or teleseismic. To identify and pick the S wave onset a time-varying characteristic function, defining the degree and direction of polarization and the amount of transverse energy, is applied on the selected scales.

1

Introduction

T h e increase of the number of seismic stations and the advance in real-time seismic d a t a exchange, both on local, regional and global scale, require progressive improvement in automatic processing and analysis.of seismic data. Essential in the automatic analysis of a large number of seismic recordings are accurate procedures to detect, pick, identify and associate the various seismic phases in these recordings. The development of real-time d a t a exchange between seismological observatories and data centers towards real-time seismic monitoring and warning systems requires efficient and accurate real-time phase picking algorithms. This chapter addresses the theory and philosophy behind automatic pickers, demonstrates a robust P picker used in routine operations, and presents an experimental S wave identifier and picker. The seismogram reading of phases may be considered as a process divided into three steps: the detection, the picking and the identification. First, the onset of a phase should be detected. Many successful and robust variants of the simple S T A / L T A (ratio of a Short Time Average and a Long Term Average) detection algorithm are presently available (Berger and Sax, 1980; Murdock and Hurt, 1983; Earle and Shearer, 1994; Withers et al., 1998). Once a phase arrival has been detected it should be both identified as a known seismic phase and picked accurately. Jepsen and Kennett (1990), for example, classify the dominant wave type in regional seismograms based on polarization and particle motion analysis. Another m e t h o d for phase identification

173

is by Bai and Kennett (2000) in which energy, distribution, frequency content, waveform correlation and polarization features are combined. While detection can be an independent _1:_rocess, the picking and identification are not necessarily independent as is demonstrated with the S wave picker presented in this chapter. The P wave picker is the simplest picker. A variety of automatic P picker procedures has been proposed and successfully implemented during the last decades (Allen, 1978, 1982; Baer and Kradolfer, 1987; Ruud and Husebye, 1992; Sleeman and van Eck, 1999; Leonard and Kennett, 1999; Fedorenko and Husebye, 1999). Ahnost all of these procedures are based on amplitude variations, frequency variations, particle motion analysis, or a combination of these. Many of these techniques are designed for single station seismic recordings. The automatic picking (and identification) of later seismic phases in a single, threecomponent, seismic station remains an important and practical problem for seismological observatories. Recently, different approaches have been suggested. Takanami and Kitagawa (1991) developed a procedure to detect P and S phases: based on multi autoregressive modeling of the seismic signal. Differences in polarization properties between P and S were used by Cichowicz (1993) to construct a S picker for seismograms of local earthquakes. Tong (1995) and Tong and Kennett (1995) describe an automatic analyzer to separate P and S arrivals, based on the ~se of pattern recognition techniques and the energy distribution over time. Another approach, by Anant and Dowla (1997), uses the wavelet decomposition to construct characteristic Nnctions across different scales (frequency bands) on which P and S detectors are constructed using polarization and energy information. Gendron etal. (2000) and Ebel et al. (1996) use the discrete wavelet transform to detect and classify seismic events. A neural network approach by Wang and Tong (1997) applies several signal attributes in the decision process to declare the presence of the S phase. The system is trained using data from local earthquakes. In the first part of this chapter we describe the automatic P wave picker presently used on a routine basis at the KNMI. It is based on an autoregressive (AR) modeling technique proposed by Morita and Hamaguchi (1984), Pisarenko et al. (1987) and Takanami and Kitagawa (1988, 1991). The technique is implemented at our observatory as to provide automatic P phase onset times to the seismic warning system at the European Medkerranean Seismological Center (EMSC) (Sleeman and van Eck, 1999). In the second part of this chapter we describe an efficient technique (a) to classify the type of earthquake signal (local, regional or teleseismic) recorded by a single, three-component broadband station, and (b) to estimate the S phase onset time. Our goal here is to provide automatic S wave arrivals for fast epicenter determinations of local earthquakes. Our approach combines the power of the wavelet transform with classical polarization analysis. The motivation for using the wavelet transform lies in the muttiresolution concept which is inherent in wavelet analysis. In this concept the signal is separated into different scales of constant normalized frequency bandwidth, which are studied with a resolution that is matched to the scale. This wavelet decomposition is implemented in a very efficient way and is the first step in our approach. Next, we select those scales that contain most of the S phase energy. Finally, a classical polarization analysis is applied on these selected scales to identify and pick the S phase onset time. This technique is independent of the selected scales.

174

The advantage of this approach is that the second step reveals the ~ype of data we are dealing with: lower scales for recordings from local earthquakes, intermediate and higher scales for data from regional and teleseismic events. Results of both algorithms are shown, using local, regional and teleseismic earthquakes which were recorded by seismic station HGN in "the Netherlands.

2

P Wave

Picker

The P wave picker is based on a simple model in which both the noise before the onset and the signal after the onset are modeled as stationary autoregressive (AR) processes (Morita and Hamaguchi, 1984; Takanami and Kitagawa, 1988). In this model the onset time is the time for which an optimum fit of both models simultaneously can be found. Obviously, such a model fitting around a specific time requires an indication of this time. This indication is provided by the detection algorithm, which is in our case a simple, but robust STA/LTA ratio detector operating on a suitable bandpass filtered signal. Below we describe the dual AR model approach and the specific implementation at the KNMI. 2.1

Dual Autoregressive Model Approach

We assume a time-series xn = { X l , ..., XN} that includes the estimated onset of a seismic signal. In other words we assume the time-series to consist of two segments: one (i -- 1) before the onset with seismic background noise only, and one (i = 2) after the onset with seismic b a c k ~ o u n d noise plus a seismic signal. We also assume that the time series z,~ includes a sufficiently long segment before and after the real onset time to mz&e aa~ effective AR model fit for each segment separately. In both intervals i = 1, 2 we fit the data to an autoregressive model of the same fixed order M, but independent coefficients a{~ (m = 1,..., M): M

at =-: Z

i

,.

-1-

i

(2.1)

amlt--m ' et

~ri=l

with t = 1, ..., M for interval i =: 1 and t = N -- M + 1, .., N for interval i = 2. Vv% assume that we can model both intervals as stationary processes with uneorrelated Gaussian noise e~, mean E { e ~ } = 0 and variance E{(e~) e} = a~. The AR coefficients a m~ in (2.1) are used to model the data simultaneously in intervals [M + 1, Ki~ and [K + 1, N - M ] , with K the division point between the two intervals. The approximate likelihood function s for this modeling procedure is:

2(

1 )~

aj Z ama_m

where e i = e ( a [ , ..., ak~, a~) represents the model parameters for interval i, and p~ = M + I, P2 = K + I,

ql = K ,

q~ = N - M ,

nl = K -

M,

n2 = N -

The m a x i m u m in the logarithm of the likelihood function is found at Ologs

175

M-

K. = O,

which has the solution:

(Y~,rr'azx

---=- - 72i J = P i

Xj --

(2.3)

amXj-m m=- i

Using (2.3) the maximum value of the logarithmic likelihood function for the two models as function of K becomes:

log(Z( ; K, M,

e._,)) =

- 89

- M) log (2.4)

- } ( N - M - K ) log

+ C

where C is a constant. By maximizing the joint likelihood function (2.4) as a function of K we find the best possible estimate of K separating the two different AR processes. We interpret x~ as the optimal P phase onset. Equation (2.4) is the first term in Akaike's Information Criterion (AIC), defined as: AIC = - 2 log ( ma~ximized likelihood function) 4- 2 M. The first term quantifies the misfit of the model and the second term the unreliability of the fit (Akaike, 1974). In our application we fix the order M, consequently only the joint likelihood function (2.4) is a variable in the AIC equation and we refer to the above described optimization technique as AR-AIC. The picker using this technique has therefore been called the AR-AIC picker. Kvaerna (1994), Leonard and Kennett (1999) and Leonard (2000) present some more variations of this picker. 2.2

P Phase Picker Implementation

After extensive experimenting with different parameter settings for she detector and the picker (Sleeman and van Eck, 1999), we found an optimal procedure which is implemented as follows. First, detections are produced by applying a bandpass filter (0.6 - 6.0 Hz) on the vertical component data, followed by a simple and robust STA/LTA detector (STA = 1 sec, LTA = 30 sec, threshold 8). Second, the AR-AIC picker is applied on a different bandpass filtered signal (2.0 - 10 Hz) on a portion of the signal around the detection. The optimum phase onset is searched using (2.4) within the interval 8 seconds before the detection and 4 seconds after the detection. Fig. 2.1 provides an illustration of this implementation for one event. The performance has been tested on a large dataset: comparing the manual picks by the analysts with the automatic picks following the above described procedure. In a dataset of more than 1000 P phase onsets, with signal to noise ratio SNR > 1: more than 70% of the manual picks were automatically estimated within a 90% confidence interval of ].6 sec and a mean of about 0.1 sec (as compared to the manual picks) as is shown in Fig. 2.2. 3

S Wave

Picker

A S wave picker is more complicated as it requires not only a detection but implicitly also an identification. A number of approaches have been proposed (Roberts et al., 1989; Cichowicz, 1993; Tong and Kennett, 1995; Earle and Shearer, 1994; Bai and

176

-T-

T

I

/ 0

--5~ 36

J

I

I

I 37

J

I 38

I

I

I 39

40

I

I

41

42

43

Seconds

Fig. 2.1. Upper trace: vertical component of a seisnfic broadband recording, sampled with 20 samples per second. Lower trace: likelihood function (2.4) around the onset. The time of the ma~xS_mumin the likelihood function corresponds within one sample with the manual onset estimate. Kennett, 2000), mostly differing on the a priori information used. Ia~ our case we are interested in a single station procedure operating in a near real-time environment to facilitate rapid earthquake location procedures. Consequently, the a priori available information is then restricted to the information in the P wave train that precedes the S wave arrival. Therefore, our approach is mainly based on creating a new time function that characterizes the properties of the signal as a function of time, starting from the P wave onset which is assumed to have been picked and identified. Such a function is often called a characteristic function and may have different forms (Baer and Kradolfer, 1987; Magotra et al., 1987; Wang and Teng, 1997; Tosi et al., 1999; Der and Shumway, 1999). We are looking for a characteristic function that emphasizes the specific S phase characteristics, such as polarization and linearity, and reduces those characteristics not typical for S waves. The S wave is picked and identified when this characteristic function reaches a certain threshold. We have chosen for a characteristic function based on the wavelet decomposition of the signal, enabling us to apply effective denoising using different, selected scales (Oonincx, 1999). Below we present the relevant aspects that compose the characteristic function we used. First, we give an introduction of the wavelet transform and some of its relevant properties. Subsequently, we describe the different typical characteristics of the S wave such as polarization and linearity, and finally the characteristic function.

177

40 mean: 0.130 sec 90 % : 1.27 sec A

~

30

Ill "o

o

e.

2O tr Z

(D

~

10

| .....

-5

-4

-3

-2

-1

.~G

0

1

0

0

2

3

4

5

Offset (seconds)

Fig. 2.2. P phase onset time differences between automatic and manual picks, as function of the signal to noise ratio (SNR). The thick fine is the 90% confidence interval. More than 700 detections were used from local, regional and teleseismic events. (A_fter Steeman and van Eck, 1999).

3.1

Wavelet Transform

The Fourier transform is a powerful routine tool for seismic data analysis, transforming time information into frequency information. The essential assumption, that the signal analyzed is composed of infinite sinusoids, is however not always appropriate. The wavelet transform is a more generalized transform that allows the signal to be decomposed into wavelets of different scales (Rioul and Vetterli, 1991). This has a number of advantages which we try to use. In signal processing a wavelet can be viewed as a bandpass filter. In this view the wavelet decomposition is comparable with decomposing a signal into the frequencytime domain by using a set of bandpass filters. However, the discrete wavelet transform has some advantages. Firstly, it is more efficient in terms of number of calculations, as compared to the discrete Fourier transform. The number of operations in the Fourier and wavelet transforms are in the order of N log N and N respectively (Wickerhauser, 1994), where N denotes the number of samples. This becomes significant for a real-time S phase picker, particularly when dealing with broadbafid seismic recordings from teleseismic earthquakes. Secondly, the Fourier transform filters are selected on the basis of the spectral content, whereas in the wavelet transform wavelets can be selected based on particular time domain features. This seems more appropriate for picking seismic transient phases. Thirdly, the wavelet transform decomposes in a set of orthogonal functions. This feature, not realized with a bandpass filter bench using the Fourier transform, has some useful applications. Suppressing noise adaptively in different "frequency" bands is implemented in our S picker to enhance the signal. This

178

feature will also be used to reveal the type of data we are dealing with. A wavelet is a waveform in the time-domain with limited duration and an average value of zero, which ensures that the wavelet has a wiggle shape. It is well localized both in time and frequency domain. Dilated and time-shifted wavelets are the basis functions of the continuous wavelet transform (Daubechies, 1992) of time-series x(t), which is defined as:

where r is the wavelet, * denotes the complex conjugate, a is the scale factor representing dilation or contraction, and b is a translation in time. A large a represents a wavelet of low frequency, whereas a small a corresponds with a high frequency wavelet. The time shift b determines which :local' part, in the time-series is analyzed. The parameters for scale and translation enable signal analysis at specific time locations with the ability both to look at 'global' and 'local ' behavior, thus extracting information at different 'levels of resolution' or 'scales'. Higher scales use dilated wavelets and show rough appro:dmations of the signal, i.e. low frequency features, while lower scales use compressed wavelets and reveal higher frequency features or details. This concept of multiresolution analysis (Kumar and Foufoula-Georgiou, 1997) is the essence of the wavelet transform and enables us to ':see the wood and the trees" (Vetterli and Herley, 1992). In order to implement the wavelet transform on discrete signals, both the scale and location parameters must be discretized. Appropriate choices of wavelets and discretization schemes lead to a relatively easy implementation, called the discrete wavelet transform (DWT) (Mallat, 1989; Strung and Nguyen, 1997). The implementation uses operators which convolve the input signal with a filter and decimate the output by downsampling (Fig. 3.1). Such operators are not invertible, as they lose information during the decimation step. However, it is possible to find two complementary filters - one highpass and one lowpass filter - with each one preserving the information lost by the other after decimation. Certain conditions are required to find inverse operators, sometimes called synthesis filters, which can assemble the decomposed output of the complementary- operators to reconstruct the original signal as shown in Fig. 3.1. The inverse operators upsample their input signal and convolve the output with a filter. Such a set of complementary and inverse filters which decomposes and reconstructs the original signal is called a set Of perfect reconstruction filters. One condition that leads to perfect reconstruction filters is the symmetry ('mirror') of the amplitude of the Fourier transform of each complementary filter around f:Cuq~,~st/2, the quadrature frequency. This symmetry condition removes the aliasing introduced by the decimation (Jackson, 1995). The set of complementary filters is called a quadrature mirror filter (QMF). Other types of filter banks with the property of perfect reconstruction are described in Strung and Nguyen (1997). The perfect reconstruction filter approach can be iterated as in Fig. 3.2, to form a sequence of filters of constant normalized bandvddth. Each step shifts the bandwidth by one octave. During each iteration step (i) the lowpass filter with corner frequency we is divided into a lowpass and a highpa.ss filter, each with corner frequency c~r and (ii) the filter output signals are decimated with a factor of 2. After k iterations the filters have corner frequencies w/2 ~ and the signal is decimated by

179

,__ AJ

Aj+l

---!

Decomposition

oJ+,

J Fig. 3.1. Schematic representation of tile discrete wavelet analysis: decomposition and reconstruction. The decomposition convolvesthe input AJ with both a highpass (H) and a Iowpass (L) fiker, followed by downsampling with factor 2 (J,2). AJ represents ~he appro:dmation at scale j, IN the details (see te~). The reconstruction step involves upsampling (]'2) of the approximation and detail coefficients at scale j + 1, followed by convolution with the inverse filters/~ and L. The summation yields the approximation coefficients (AQ at scale j.

the factor 2k. Normally, the maximum number of iterations L is determined by the low frequency resolution that is desired. Each step in the iteration corresponds to a change of scale in the wavelet transform. Let | be the operator which convolves two time-series, Ji~ and g~, and downsamples the output with factor 2:

(3.2) in which n and m are sample indices. Then we can write one step in the discrete wavelet transform, called decomposition, as:

,4~+l = ( L O A i ) ~

(3.3)

where j indicates the scale number of decomposition (j > 0) , tt,~ are the highpass filter coefficients and L,~ the lowpass filter coefficients. D j-~ are the wavelet coefficients at scale j + 1 which describe high-frequency features or 'details' at scale j + 1, and A~+I are the low-frequency components or 'approximations' at that scale. Note that for j = 0 the input for the decomposition step is the discrete time-series z,~. The inverse operators of the perfect reconstruction filters reconstruct the wavelet coefficients D J at scale j into time-series d j. This concept makes it possible to compare localized features at different scales. The reconstruction scheme for Fig. 3.2 can be written as:

180

/

r--1,'-~ { } D - D'

x

-1

~,r-a2D---,-q~.,-- ~ ~4~-)_~

.3

Fig. 3.2. Muttiscale decomposition of input time-series x.

z

=[-IcD~,s163163 = d I + ae + d 3 +

a3

(3.4)

z = Ed

j +a J

j=i

with J the number of decomposed scales, d j the reconstructed time-series at scale 3 and a J the error time-series of the reconstruction. @ is the operator that upsamples and convolves:

( / 9 .q), = Z h,_,~g~

(3.a)

f/2

with h~ =

fk 0

forn=2k for n = 2k + 1

where n, m and k are sample indices. Fig. 3.3 shows an example of a broadband seismogram of a local event, sampled with 40 samples per second~ and the reconstructed time-series dj at scales 1 to 8 using the Daubechies 4 filter bank. Lower scales show the higher frequency features in the original seismogram, and lower frequencies are observed at higher scales. The wavelet transform treats frequency in a logarithmic way, unlike the (shorttime) Fourier transform. This corresponds to a constant normalized bandwidth as is illustrated by Fig. 3.4. The f i ~ r e shows the frequency passband of the wavelet reconstruction process, as function of level J. The steepness of the response slope depends on the order of the wavelet, as is illustrated in Fig. 3.5. The wavelet decomposition is used to select scales which contain significant S energy, as is described in section 3.3. The characteristic function uses a multiscale polarization analysis applied on the selected scales to detect the onset of S energy.

181

.:

_ g_._.'

7-

.

.

.

.

.

.

.

.

.

.

7

.

.

.

-P-~.~

.

.

.

.

.

_ '

.

.

"

.

'

.

-r-~

.

.

"

.

'

~.

a

Seconds

Fig. 3.3. Example of reconstructed time-series using the wavelet transform. From top to bottom are displayed: the raw data x, the reconstructed time-series dJ from scales j = 1 to 8, the sum of these reconstructed signals ( i = y~?~dJ), and the error time-series or approximation a s = x - i. Scales 1-3 clearly show the P and S phase, while scales 6-8 contain energy from microseisms. All traces have the same amplitude scale factor.

a.2

Polarization Analysis and Characteristic Function

W h i l e the faster P waves oscillate in the direction of p r o p a g a t i o n , S waves are typically oscillating p e r p e n d i c u l a r to the wave p r o p a g a t i o n direction, i.e. P wave oscillation direction. Therefore, the essential element for identifying t h e presence of S wave energy is the p o l a r i z a t i o n analysis of the t h r e e - c o m p o n e n t seismic r e c o r d i n g (Jurkevics, 1988; Cichowicz, 1993). This is described below. T h e c h a r a c t e r i s t i c f u n c t i o n for t h e S wave is based on different p r o p e r t i e s o b t a i n e d from this t h r e e - c o m p o n e n t p o l a r i z a t i o n analysis. We a n a l y s e t h e p a r t i c l e m o t i o n in a t h r e e - c o m p o n e n t seismic r e c o r d i n g a = (n, e, z) which can be described q u a n t i t a t i v e l y using the t h r e e - c o m p o n e n t p r i n c i p a l c o m p o nents m e t h o d (Flinn, 1965; M o n t a l b e t t i a n d Kanasewich, 1970; P a r k et al., 1987). T h e covariance m a t r i x Coy of recording a is c a l c u l a t e d in a time window of length of N samples:

COb" :

Gnn O'ne (Tnz ) O'en Gee O-ez O-zn O-ze Gzz

(3.6)

where crij represents the zero lag cross power between c o m p o n e n t s si a n d sj: N

1 a~j= ~Esi,k k=l

182

sj,k

(3.7)

,

,

,--l"-:"r

m

" V - " r

r'---'r'--

'

'

I

-"r"

'----

'

'

'

'

'

'

I

q

I0 Q i0 -1 !0-2

E

/

10-3 10-4~--

I0-5E_ E 10-6f 2

4

5

8

2

10 -1

4

6

8

2

100

4

S

8

101

Frequency in Hz

Fig. 3.4. Frequency passbartd of the wavelet reconstruction process, as function of decomposition level J, using the Daubechies 10 wavelet. Each curve represents the amplitude response of the sum of reconstructed time-series ~jJ-=t dJ, with J = 1,5.

,o-2p

~

/

/

I

.~E !0 -3

lO_,F J-

jo,o

:o-~. E

lo-6L

10_i

,

2

__.#__

.

,

4

./

X

5

/'~176

/// . . . .

3

// /

_L

/ .

6 7 8 90 s

2

Frequency

;rl

.

] .

.

3

.

.

4

.

5

.

.

I

6 7 8 gO 1

.....

d

2

Hz

Fig. 3.5. Amplitude response of the first level of decomposition (J = 1), using Daubechies 4, 10 and 20 wavelets. The higher order wavelets show a steeper response slope than the lower order.

183

where indices i andj denote components n,e, z, and k is the sample index. Tile covariance matrix is decomposed into eigenvectors e~, e2 and ~ with corresponding eigenvalues A1, A2 and An, with AI > A~ > An. The direction of the largest eigenvector (g~) is a measure for the direction of polarization in the correlation window, whereas the relative sizes of the eigenvalues are indicative for the degree of (linear) polarization (Samson and Olson, 1980). [n our application this decomposition is applied in a time window around the P phase onset ~-p to produce eigenvectors e-T(~-p),g~(~-p) and N(~-p) of the initial compressional particle motion. Components (n, e, z) are rotated into motion along the lon~tudinal direction ~(7-p) and the transverse directions N(7-p) and N(~-p). The rotated components are denoted as (l, q, t). Next, a moving time window is applied on (I, q, t) to calculate eigenvectors and eigenvalues as functions of time. From these fnnctions a number of polarization parameters can be extracted to characterize the type of seismic phase. An overview of such parameters is given by Wang and Teng (1997). In our approach we extract the attributes described by Cichowicz (1993) as functions of time: deflection angle (F1), degree of polarization (F2) and ratio of power in the (q, @plane to total power (F3).

Deflection angle The deflection angle F1 at rime r is the angle between the largest eigenvector at time ~- and the largest eigenvector at time 7-p: = I

(3.8)

As the S phase particle motion is perpendicular to the P phase, F1 will attain its maximum at the S phase onset.

Degree of polarization The degree of polarization F2 is a function of eigenvalues of the covariance matrix at time r:

F2(r) =

(a~ - A2)2 + (a, - ~3) 2 + (A2 - ~a)~ 2(A~ + 32 + a3) ~

(3.9)

This function can be used to identify both P and S type phases as they show a high degree of polarization.

Ratio transverse and total chewy F3 is the ratio of transversal ener~" in the (q, t)-plane to tile total energy in the (l, q, t) system N

Fa(r) =

.~. i=1

(3.10) +

+

i=1

which will have a maximum at the S phase onset; i is the sample index. All three attribute functions, F1, F2 and F3, are normalized and have values ranging between 0 and 1, where values close to 1 indicate the presence of S wave

184

energy. The characteristic function (SDF) for the S wave picker is then defined as the squared product of these attribute functions: SDF(T) = [FI(T). F2(r). F3(r)] ~"

(3.11)

SDF enhances values related to the S energy, but reduces values related to other features in the signal.

3.3

D e n o i s i n g and Scale Selection

The energy distribution over different scales provides important information on the characteristics of the signal (local, regional or teleseismic) and thus also the S wave properties. Essentially both the P wave energy" and S wave energy can be found in increasing scales with increasing epicentral distances. This is comparable to the lower frequency content for more distant events as compared to local ones in conventional Fourier spectral analysis. However, for such an analysis so be effective, one should be able to remove most of the background noise. The wavelet transform allows for such an effective denoising. Our aim is to remove the noise, characterized by the signal immediately preceding the P wave onset, from the signal. In this process we assume that the noise remains stationary during the whole signal including the P wave and S wave arrivals and a large part of the S wave coda. Once the noise has been removed from the raw data the signal energy distribution over the different scales is used to characterize the event as a local, regional or teleseismic event. The scales with the largest signal energy proportion are also used for applying the characteristic function.

Denoising In our application the components (k = I, q, t) are decomposed into its wavelet coefficients through iterative use of (3.3). For each component k the noise level at scale ~ , in a time window of 20 j is estimated by the the maximum wavelet coefficient D ,k.j see starting 30 see before the P onset (rp). The noise is subtracted from the seismic signal by using a wavelet soft-thresholding method Donoho, 1992; Abramovich and Benjamini, I996):

if (D~ ~ <

0 =

- am~

if ID~'J>

kj (3.12)

D~,J q-- Dma ~J • where i is the coefficient index in time-window [rp, rp + 12.5] sec. With this thresholding technique we remove the noise from the seismic signal at each scale. This is possible, because the wavelet coefficients Dc~+~,_u(a, b) of the linear combination of two signals ci. z(t) + c2. y(t) are equal to the linear combination of their wavelet coefficients q 9 D~(a, b) + c2. D,a(a, b). After applying the above described noise reduction we can better estimate the signal energy distribution over the different scales by defining for each scale j the

185

I

70

I

I

i

I

~

i

]

7Q

60

o~- 60 -

50

50 -

~4o ,~ ao

30-

20 r ix. 10

10-

!

I

i

40 -

0

0

1

2 3 4

5 6 7

8

i

i

1

~

i

i

i

1

2

3

4

5

6

7

Scale

Scale

(~)

(b)

Fig. 3.6. Energy distribution over 8 scales of decomposition using the radial and transversal component data in Fig. 3.3, (a) before and (b) after noise reduction by applying a soft-threshold on the wavelet coefficients. The energy is calculated in a time window of 12.5 see after the P or,set, and given as percentage of the total energy in that window before and after noise reduction. ratio

E]: -, \-~ (/:?k,j~2 E j _ )-~i z--k~'~i J E{ E k ( D ~ " ) 2

(3.13)

defining the energy at scale j as a fraction of the total energy. Fig. 3.6 compares the energy distribution before and after denoising over the different scales for raw d a t a as shown m Fig. 3.3. After denoising the energy in the higher scales disappears and a clear domi.uant energy contribution appears in scales 2 and 3 denoting a typical energy distribution for a local event. The energy at higher scales, typically microseisms, has been removed. Our experiments show a distribution of energy- over scales 1-3 for local events and higher scales for regional and teleseismic events.

Scale selection After denoising and characterizing the energy distribution over the scales for the P wave part of the signal, the scale with the m a x i m u m energy, i.e. scale jp, is chosen to represent the bulk of the P wave energy. Due to its property the S wave energy should therefore be distributed in die same or a higher scale. We select scales jp and jp + 1 to detect S wave energy. T h r o u g h significant experimenting we obtained the following optimal procedure. Scales jp and jp + 1 are reconstructed through (3.4) using the original wavelet coefficients with noise. For the two bandpass filtered time-series thus obtained, we construct two characteristics functions (3.11). Subsequently, to enhance features across scales related to tile S wave energy, both detector functions are multiplied.

186

Table 3.1. Percentage of automatic S picks in tile time intervals [-0.5, +0.5] sec and [-1.5, +1.5] see around the manual S pick. Filter/Wavelet

3.4

Threshold

[-0.5, +0.5] sec

[-1.5, +1.5] see

Bandpass filter (0.6 - 6.0 Hz)

0.4

38.3

52.2

Daubechies 4

0.2

46.6

68

Daubechies 10

0.1

45.1

66.1

Daubechies 20

0.1

46

68.1

Beylkin 18

0.1

44.1

68.9

Coiflet 6

0.2

45.1

65.5

Coiflet 30

0.1

47.9

68

S Phase Picker Implementation

First the signal is rotated to a radial and two transverse directions using a covariante matrix decomposition (3.6). The covariance matrix is determined from a 2 seconds window starting at the initial P wave arrival in a bandpass (0.6 - 6.0 Hz) three-component filtered signal. Then the raw data are rotated into longitudinal and transverse components (l, q, t). Second, the denoising procedure is applied to the rotated raw data in order to determine the scales with the most significant P wave signal energy and classify the event either as local, regional or teleseismic. The S wave energy is assumed to be in the same or one scale higher, i.e. with slightly lower frequency content. We therefore select two scales, the one with the m a ~ m u m P wave energy and the scale above (i.e. lower frequency), as basis for defining the characteristic functions (3.11). Finally, we run a search window over the normalised combined SDF functions (3.11) for the two selected scales and assign the S wave onset when this combined SDF reaches a threshold value. Lower scales require relative short search windows, whereas higher scales use relative longer time windows. The search starts at the P wave onset time and ends there where the envelope function of the transverse component q(t) reaches its maximum.

Performance test for local events To test the performance of the S phase picker, we used a set of 313 local events, within a large range of different SNR values. The reference picks consist of the first S phase as picked by the analyst. For this performance test we looked only at local events, therefore we restricted the multiscale analysis for this data set to scales 1 to 5, which roughly covers a frequency range between 0.6 and 10 Hz. Our m a x i m u m search window is limited to [~-p,Tp + 30] sec, and we varied the S wave picking threshold level from 0.1, 0.2,....,0.9. To investigate the influence of the type of wavelet on the accuracy of the S pick, we tested the algorithm using different wavelet types and orders (Table 3.1) For comparison we also derived a characteristic function (3.11) from simple bandpass (0.6 - 6.0 Hz) filtered traces of (/, q, t) as used in many standard procedures.

187

x

c=, x

x

Seconds

Fig. &.7. Example of an automatic S pick using a local earthquake recording. From top to bottom are displayed the east-west, north-south and vertical component, the S detector function based on the bandpass filtered data (0.6-6.0 Hz) and the S detector function based on reconstructed scales 2 and 3.

Table 3.1 shows the number of automatic S picks in time intervals of [-0.5, 0.5] sec and [-1.5, 1.5] sec around the manual picks, as well as the optimum threshold level. This level results in the highest number of picks between [-0.5, +0.5] sec. The use of wavelets in the algorithm significantly increases the number of S picks in both intervals. Obviously, the type and order of wavelet do not significantly influence the overall result. The optimum threshold level of 0.1 - 0.2 using wavelets as compared to the optiminum level of 0.4 using a single bandpass filter indicates that features in the SDF function which do not correspond to $ energy are effectively suppressed using wavelets. Fig. 3.7 displays an example of this observation, using data from a Mrl.9 earthquake at 120 km fi'om the station. The SDF function which is constructed using the bandpass filter has a peak just prior to the S phase onset but is contaminated between the P and S phase. The SDF function which is constructed using scales 2 and 3 clearly identifies the S onset. In this example the difference between the automatic S pick and the manual pick is 0.18 sec, using wavelet Daubechies 4 and threshold 0.2. The order of the Daubechies wavelet does not significantly influence the result of this test. Although it is expected that shorter wavelets would resolve features in the time domain more accurately, this is not evident from our test. Olmo and Lo Presti (1994) even report better results using high order wavelets on sig~nals with first order discontinuities. Higher order wavelets approximate the ideal highpass filter better than lower order wavelets (Fig. 3.5), and hence separate the transient behavior of the seismic phase better from the stationary behavior of the signM. Also this is not evident from the experiment.

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4

Discussion

Automatic procedures to detect and pick phase arrivals, in particular the first P wave, are successfully applied on a routine basis in many obse]watories. The accurate P wave picker presented in this chapter, has proven to bc valuable in aiding rapid earthquake locating procedures and in facilitating the routine seismic data analysis at the KNMI.

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(Johnson et al., 1995), Seisan (Ilavskov and OttelnSller, 1999) and SIL (BSdvarsson et al., 1999). The usual application is for rapid (automatic) determination of earthquake locations and for this purpose the pickers seem to provide adequate results. Consequently, automatic detectors and pickers have been strongly integrated in the routine analysis procedures at seismic observatories. However, a note of caution is relevant for using these automatic picks in tomographic analysis. The possibly biased arrival time picks may introduce unwanted effects. It is presently unclear how much of the automatic picks are reviewed by an analyst, or how they influence the manual onset picking, as little research has been done yet on possible deviations or inconsistencies (Aster and Rowe, 2000) in systematic picking techniques. Although we have tested the P wave picker on a magnitude larger dataset than many others, we have not made a systematic study yet as R6hm et al. (1999), who found even systematic picking variations due to specific station procedures. Picking later phases require more sophisticated methods in order to identify the pick as well. For single station approaches the S wave pickers belong to the simplest in this category, as this wave is distinctly different from the P wave. Different a priori information may be used depending on its availability. A priori information becomes available as one gathers a large data base of events from the same station and similar regions. This reflects the experience of a well trained analyst, and neural techniques (Wang and Teng, 1997; Zhao and Takano, 1999; Dai, H. and MacBeth, C., 1995, 1997; Mousset et al., 1996) and pattern recognition techniques could be applied (Joswig.. 1990). Even more a priori information becomes available as data from other

191

s t a t i o n s can be c o m b i n e d in real time. In these cases also t h e e a r t h q u a k e location, using a u t o m a t i c P picks and s t a n d a r d t r a v e l - t i m e tables, can be used ( W i t h e r s et al., 1998; Tong, 1995; Tong and K e n n e t t , 1995).

Acknowledgements We t h a n k B e r n a r d Dost for his initiative to s t a r t a n d s u p p o r t this research. P a t r i c k O o n i n c x from t h e Center of M a t h e m a t i c s a n d I n f o r m a t i c s is t h a n k e d for his coopera t i o n a n d useful ideas in the field of wavelets d u r i n g this research.

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Gendron, P., Ebel, J.E. and Manolakis: D., 2000, Rapid joint detection and classification with wavelet bases via Bayes Theorem, Bull. Seism. Soc. Am., 90, 764-774. Harvey, D.J., Vernon, F.L., Pavlis, G.L., Hansen, R., Lindquist, K., Quinlan, D. and Harkins, M., 1998, Real-time integration of seismic data from the IRIS-PASSCAL broadband array, regional seismic networks and the Global Seismic Network, EOS Trans. AGU, 79, 567. Havskov, J. and OttemSller, L., 1999, SeisAn Earthquake Analysis Software, Seismol. Res. Lett., 70, 5,532-534. Jackson, L.B., 1996, Digital filters and sigzlal processing, Kluwer Academic Publishers. Jepsen, D.C. and Kennett, B.L.N., 1990, Three-component analysis of regional seismograms, Bull. Seism. Soc. Am., 80, 2032-2052. Johnson, C.E., A. Bittenbinder, B. Bogaert, L. Dietz and Kohler, W., 1995, Earthworm: a flexible approach to seismic network processing, II~IS Newsletter, 14, 2, 1-4. Joswdg, M., 1990, Pattern recognition for earthquake detection, Bull. Seism. Soc. Am., 80, 170-186. Jurkevics, A., 1988, Polarization analysis of three-component array data, Bull. Seism. Soc. Am., 78, 1725-1743. Kumar, P. and Foufoula-Georgiou, E.: 1997, Wavelet analysis for geophysical applications, Rev. of Geoph., 35, 4, 385-412. Kvaerna, T., 1994, Accurate determination of phase arrival times using autoreg-ressive likelihood estimation, Annall di Geofisica, 37, 28%300. Leonaxd, M. 2000, Comparison of manual and automatic onset time picking~ Bull. Seism. Soc. Am., 90, 1384-1390. Leonard, M. and Kennett, B.L.N., 1999: Multi-component autoregressive techniques for the analysis of seism_ograms, Phys. Earth and Planet. Interiors 113, 247-263. Magotra, N., Ahmed, N. and Chael, E., 1987, Seismic even~ detection and source location using single station (three-component) data, Bull. 8eism. Soc. Am., 77, 958-971. Mallat, S.G., 1989, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans. Pattn. Anal. Much. Intell., 11, 674-693. Montalbetti, J.F. and Kanasewich, E.R, 1970, Enhancement of teleseismic body phases with a polarization filter, Geophys. J. R. Astr. Sou., 21, 119-129. Morita, Y. and Hamaguchi, H., 1984, Automatic detection of onset time of seismic waves a~ld its confidence inter~zl using the autoregressive model fitting, Zisin 37:281-293 (in Japanese with English abstract). Mousset, E.~ Cansi, Y., Crusem, R. and Souchet, Y., 1996, A co,mectionist approach for automatic labeling of regional seismic phases using a single vertical component seismogram: Geophys. Res. Lett., 23, 681-684. Murdock, J.N. and Hutt~ C.R., 1983, A new event detector designed for the seismic research observatories, USGS Open-File Report 83-785. Olmo, G. and Lo Presti, L , 1994, Application of wavele~ transibrm for seismic activity monitoring, Wavelets: Theory., algorithms and applications. Academic Press, London. Oonincx, P.J., 1999, A wavele~ metimd for detecting S waves in seismic data, Computational Geosciences, 3, 111-134. Park, J , Vernon IlI, F.L. and Lindberg, C.R., 1987, Frequency dependent polarization analysis of high-frequency seismograms, J. Geophys. Res., 92, B12, 12664-12674. Pisarenko, V.F., Kushnir, A.F. and Savin, I.V., 1987, Statistical adaptive algorithms for estimation of onset moments of seismic phases, Phys. Earth and Planet. Interiors, 47, 4-10. Rioul, O. and Vetterli, M., 1991, Wavelets and signal processing, IEEE Sio~nal Proc. Magazine, October 1991, 14-38. Roberts, R.G., Christoffersson, A. and Cassidy, F., 1989, Real-time event detection, phase identification and source location estimation using single station three-component seismic data, Geophys. J. R. astr. Sou., 97, 471-480. R5hm, A.H.E., Trampert, J., Paulssen, H. and Snieder, R.K., 1999, Bias in reported seismic arrival times deduced from the ISC bulletin, Geophys. J. Int. 137, 163-174. Ruud, B.O. and Husebye, E.S., 1992, A new three-component detector and automatic single station bulletin production, Bull. Seism. Soc. Am., 82, 22]-237.

193

Sarason, J.C. and Olson, J.V., 1980, Some comments on the descriptions of polarization states of waves, Geophys. J. R. Astr. Soc., 61, 115-129. Sleeman, R. and van Eck, T., 1999, Robust automatic P phase picking: an on-line implementationin the analysis of broadband seismogram recordings, Phys. Earth and Planet. Interiors 11a, 26,5-275. Strang, G. and Ng-uyen, T., 1997, Wavelets and filter banks, Wellesley-Cambridge Press. Takanami, T. and Kitagawa, G., 1988, A new efficient procedure for the estimation of onset times of seismic waves, J. Phys. Earth, 36, 267-290. Takamami, T. and Kitagawa, G., 1991, Estimation of she arrival times of seismic waves hy multivariate time series model, Ann. Inst. Statist. Math., 43, 407-433. Tong, C., 1995, Characterization of seismic phases - an automatic analyser for seismograras, Geophys. J. Int. 123, 937-947. Tong, C. and Kennett, B.L.N., 1995, Towards the identification of later seismic phases, Geophys. J. Int. I23,948-958. Tosi, P., Barba, S., De Rubeis, V. and Di Luccio, F., 1999, Seismic si~ml de~ection by fractal dimension analysis, Bull. Seism. Soc. Am., 89, 970-977. Vetterli, lVI. and Herley, C., 1992, Wavelets and filter banks: theory and design, IEEE Trans. Signal processing, Vol. 40, No, 9, 2207-2232. Wang, J. and Teng, T., 1997, Identification and picking of S phase using an artificial neural network. Bull. Seism. Soc. Am., 87, 1140-1149. Wiekerhauser, M. V., 1994, Adapted wavelet analysis from theory to software: IE]~E Press. Withers, M., Aster, R., Young, C., Beiriger, J., Harris, M., Moore, S. and Truji!o, J., 1998, A comparison of select trigger algorithms for automated global seismic phase and event detection, Bail. Seism. Soc. Am., 88, 95-106. Zhao, Y. and Takano, K., 1999, An artificial neural network approach for broadband seismic phase picking, Bail. Seism. Soc. Am., 89,670-680.

194

Recognizing Explosion Sites Using Self-organizing Properties of Their Temporal and Spatial Shooting Practice Matti Tarvainent t Institute of Seismology, PO BOX 26, 000 I4 Universityof Helsinki, Finland

Abstract. In this report efforts to automate locationand classificationof seismic recording, stemming from local and regional mining and other explosions,are reported. The first step here is that of establishinga knowledge base on mining activities such as their waveform envelopes, temporal behaviour of individual mines or waveform attributes in a given mining area. Using eventsof the comprehensiveHelsinki Bulletin for 2000 and waveforms connected those analysed events, the mentioned attributes have been extracted for some mines in Finland and Sweden. Consistent diurnal, weekly and spatial patterns are typical for most of the seismic events included in the bulletin. Then self-organizingmaps trained with these attributes are used to identify newly detected unidentified mining explosionsin different environmentsin the area. The main advantage of the method is its ability to aummaticaliyfmd a suitable network structure and naturally correctly identify explosions as such. The explosion site recognition was done using extracted waveform attributesof various kind event records from the Finnish seismograph stations. The parametrization leads to correct mining district identification where more detailed tuningwas performedusing differentphase amplitudeand signal-to-noiseattributes. The benefit of the method is that the variousparameter dusters are characterized in terms of shared attributes, thus making it easy to explore the contents of an unknown event atu-ibutes. The method can be extended to the global monitoringof active explosion or seismic zones, in general. 1

Introduction

The monitoring issue of the comprehensive test ban treaty (CTBT) is to detect, locate and identify type of seismic events globally down to magnitude 4.0 which is equivalent to an explosion yield of 1 kT in a well-coupled medium. Further, the CTBT assumes that events are located within an area of t,000 k m 2, and that the largest error ellipse axis is less than 50 kilometres. Otherwise on site inspections (OSI) to examine possible treat? violations would not be very meaningful. In the beginning of the monitoring regime, the focus was on events at teleseismic distances, while today the main interest is on events at local and regional distances (e.g. up to 2,000 kilometres). At these distances using differential P- and S-arrival times the epicentral distances can be estimated precisely. Also, the depth of earthquakes can be used to form some indication of constrains on events (Thurber et al., 1989). Accordingly, the following guideIines may be used to improve the locating performance in traditional methods: 9

Mid-crust focus is used. For events at deep focus areas, secondary phases (e.g. pP, sP, PcP), if reliably identified, can be used to estimate the depth. The usefulness of Moho bouncing phases such as PmP and SmS to the identification of local events has been studied recently.

Reprinted from Physics of the Earth and Planetary Interiors, Vol. 113 (1-4), Matfi Tarvainen, Recognizing explosion sites with a self-organizing network for unsupervised learning, 143-154, Copyright (1999), with permission from Elsevier Science B.V. 195

-

Normal depths (e.g. 33 kin), seemingly fixed to indicate the Moho depth in Jeffreys-Bullen travel time tables.

9

Zero depths for presumed explosions.

9

If the Rg-phase is recorded for local events, the depth is assumed to be less than 4 km.

Event locations at distances around 1,500-2,000 kilometres are also problematic owing to weak velocity gradients in the upper mantle and the travel time curve triplication associated with 400 and 670 km discontinuities (Kennett and Engdahl, 1991). Some illustrative events have taken place in the past which have caused turmoil, not only in the scientific, but also in the political world. A good example is the earthquake near Novaya Zemlya on August 16, 1997. The event was located approximately 130 kilometres east of the Novaya Zemlya test site, and its error ellipse showed values which left the potential search area in Kara Sea (Richards and Kim, 1997; Macllwain, 1997). The many recordings stemming from well-known sites, such as: quarries, mines and other types of man-made explosions are a nuisance in seismograph network operations as their analyses add considerably to the daily analysts~< workload. This problem is rather acute in Fennoscandia where well over 90% of local events stem from man-made explosions (Tarvainen and Husebye, 1993). Still, in the CTBT context seismic event classification is a very important task and it is not always simple to distinguish between earthquakes and explosions. In recent years considerable progress has taken place in this field. That is source classification at local distance ranges (Blandford 1996). Schemes based on artificial neural network techniques have proven to be effective and useful (Dowla et al., 1990; Dowla, 1996; Pulli, 1996; Tiira, 1996; Fedorenko et al., 1998). Cross-correlation approaches based on digital recordings have been used to improve relative locations of seismic events clued to some specific sites (Harris, 1991; Schulte-Theis and Joswig, 1993; Shearer, 1997). However, if mines are only a few kilometres apart, it is possible to connect registrations to two or more mines, when only seismic locations are taken into account. Figure 1 shows records of 6 explosions from identified mines and quarries forming three pairs of closely spaced mines. The phase arrival times are similar between these pairs~ but signal attributes differ siguifically from each other. Tarvainen (1999) tried to separate those closely spaced mines in Russia and Estonia with the help of unsupervised learning algorithm. This study presents the mine or explosion site recognition tied to self-organizing maps (SOM). Results and their discussions are in the context of network operations. In this work we formed a set of 168 explosions in identified mines or quarries and which were found in the HelsinkT bulletins in 2000 (Uski et al., 2000; Uski et al., 2001) to train the computer to recognize events stemming from recent explosions in Finland, and Sweden. The main point of this paper is to present the visualization method of self-organizing maps and thus bring forth their power. The self-organizing maps combines vector quantization and projection which together provide a map of the data giving a visual influence to the properties of the data. Comparing new data with the map helps in classifying the data and gives an indication of whether the new set belongs to the same data distribution as the map was trained with. In general framework of knowledge mining, the methods discussed here are especially useful in the everyday analysis of seismological tasks.

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2 Testing SOM with Real Data For this work two, well-defined mining areas in Finland, and Sweden were selected. The mining areas or individual mines were selected from an obsolete template of 39 known mines coded in 1960s at the Institute of Seismology to ease the analysts workload simply relying on the visual waveform recognition of explosion records (Table 1). There are several ways to display data histograms. The annual distribution of detections in northern Sweden in Kiruna-Malmberget area is show~a in Fig. 2. The main part of the detections are concentrated on two mining areas, but there are several detections which did not fit any of these sites. If the locations obtained via seismological methods (mainly with a derivative of least squares approximations) are not well constrained the locations may spread over a wide area. TABLE I: Mining sites used in the work Latitude

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Longitude (OE)

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197

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Fig. 2. Seismic events detected and located in northern Sweden, Malmberget-Kimna area. Even though epieentres concentrate around mines, there are many events which can be tied to any of these mines. This, in ~rrt may lead to wrong source association. T a r v a i n e n and H u s e b y e (1993) s h o w e d clear diurnal and w e e k l y distribution in the explosion activity in Fennoscandian mining. Fig. 3 shows the diurnal distribution o f seismic detections connected to events in northern Sweden.

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198

The self-organizing mapping was based on seven real valued attributes calculated from seismic signals records. These attributes were selected owing to their distinct site characteristics to describe multi-dimensional data into a two-dimensional grid. Consequently, it is a similar as described by Ritter and Kohonen (1989). A set of fuzzy numbers is described to evaluate the weight for the attributes used in the training phase of SOM. These triangular fuzzy numbers /~ can be expressed as: O, x_
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The a~ and a 3 are the extremes of the mapping district. In this work the self-organizing maps were tested on seismic events in 2001 which occurred in Fennoscandia near some well defined mining sites. In the analysis a matching attribute from an event generates a cell reaction while non-matching attributes do not cause any reaction. At the end of the self-organization process it was tested where each of the input vectors was located on this map, a two-dimensional network embedding was constructed and meaningful partitions of the test event population were obtained. The test results show clearly that using only a few pre-defined signal attributes it is possible to connect seismic signals to correct mines or mining zones with an acceptable reliability, when all the attributes of the training set match with the incoming signal attributes. The number of matching attributes plays a significant role in the identification. The SOM locations were achieved by mapping the attributes and finding the best matching unit between input and learning documents. Figs. 4 and 5 show best-matching-unit (BMU) behaviour at two different mining areas in Sweden and Finland. The same ordered display can be used for illustrating the clustering density in different regions of the data space. The density of the reference vectors of an organized map will reflect the density of the input samples. SOM associations are based on signal attributes only, which in turn are tied to specific mines while Helsinki bulletin locations are based on conventional location schemes, such as least squares method for minimizing P-S-phase travel time residuals. This means that the SOM provide correct mine locations as compared with conventional locating schemes. Of particular importance is that signal attributes are connected well with ground-truth data from known mines. Fig. 6 shows how the attributes activate this ground-truth at a well-defines area, in this case near Siilinj ~'vi mine area in central Finland.

199

1 Fig. 4. An example of good response surfaces around Kiruna mining area in northern Sweden. The best matching unit (BMU) attributes cause two clear clusters near the mines.

NN -.

. ~

I Fig. 5. A poorer response surfaces around Siilinj~r'vi area, Finland. Even though Siilinj~rvi mine has a well-identified mining practice with high yield explosions, the mine locates in an area where several mines or construction sites locate9 Consequently, relying only on traditional locating schemes may tie waveforrns in wrong source. In the figure BMUs form several tuplets, but the two strongest tuplets are from Sitli@irvi and Nilsiti mines, only 20 kilometres apart, from each other.

200

Fig. 6. Quantization activation plot obtained from readings of Siilinjgrvi area. The colour of grid cell marker is inversely proportional to the accuracy of the match (the lighter the better). In the figure one can identify well the south-western trend of matching, which may be caused by the improvement works done on the intra-nafional highway #5 nearby.

3 Discussion The seismicity in Fennoscandia is very' Iow with up to 10 earthquakes per annum equivalent to less than one percents of the explosion data base for 2000 and 2001. Even though telcseismic events are taken into account, the dominance of local explosions prevails contributing over 80 per cent of the total event recording population at every station in this r e , o n . If all event recordings are subject to the same careful screening this would in practice mean that at least 90 per cent of the analyst workload is tied to local explosion recordings of no scientific value. Such work allocations are not feasible over extended periods of times at most seismological observatories. For example, in Sweden the local explosion recordings are not processed regularly while as mentioned in Finland explosion recordings are carefully analysed. The major outcome of this study is that mining explosions waveform can be connected to certain mines by the SOM method which extracts only a few simple attributes from the incoming seismic signal. Furthermore, the issue of incorporating well-established seismicity information and signal attributes is of particular importance for automatic seismic network operations. The reason is that the observational data at hand are often less voluminous and less reliable than those extracted through analyst inspections of station records (Ruud et al., 1993). As repeatedly demonstrated, formal epicentre solutions could be unreliable when they are based on P- and S-arrival times only due to odd network configaxrations. The kind of seismicity information to be incorporated will naturally be spatial and temporal characteristics of mining operations. For example, being confident that given event recordings stem from a specific mine, the coordinates of that mine should replace the formal, seismic epicentre solution. This is the essence of this study. Another seismicity parameter o f interest is station detectability, that is which stations are most likely to record explosions from a specific mine. This was not studied here because only high signal-to-noise recordings

201

at one station were utilized. This kind of information would be useful for detecting phase association errors. Moreover, most of the Fennoscandian mining explosions are events of small magnitude (ML<2) and as such very seldom recorded beyond distances of 500 km (Ruud and Husebye, 1992). To use signal attributes in automatic seismic network operations require wave form stationarity for a given station for a specific mine. This appears to be the case (see also Rivi~re-Barbier, 1993), so the challenge here is to mimic analyst template and experience operation numerically. The mentioned elaborated IMS-system (Bache et al., 1990; Bratt et al., 1990) has provisions for implementing such features and also, learning abilities. Anyway, basic requirements here are compilation of representative reference events and their training attribute sets for every station in the network, and that the initial guess of epicentre locations are fairly accurate (RJvi&e-Barbier and Grant, 1993). A final remark here is that no network can be operated fully automatic in terms of producing high-quality bulletins simply, because signal attributes for weak events would be unreliable due to noise contamination. However, a robust first hand outcome from this kind of data analyser will ease the tedious workload of analysts, instead of reading ali signal parameters and possibly rejecting all those unwanted data.

4 Conclusion In this study the seismic aspects of the mining activities in Finland and surrounding areas were examined. The mines were well identified by clear signal characteristics. There was no effort to try to classify events according to their source type earthquake or explosion, but to recognize locations of mines where signals originate. With digital seismograph networks being deployed in various parts of the world the challenge is to teach our computers to locate reliably, and identify the many thousands of explosions recorded per annum. This wouid require much painstaking work, since surprisingly little detailed information are available on many mining operations. However, it may be plausible, that this kind of problem can be solved using grid search or other robust techniques for incorporating priori seismicity knowledge of the kinds dealt with here. Thedifficult problem is to mimic numerically the analyst s ability to quickly recognize mine specific waveform. Naturally, this implies that signal attributes are spatial stationary, which also have been observationally documented (Rivi~re-Barbier and Grant, 1993). The final remark is that observationally seismology has progressed tremendously over the last decade in terms of station design and deployment, digital recording, satellite communication and advanced data centre facilities in various countries. A paradox in this context is the scant attention paid to the pressing problem of automatic signal analysis and bulletin production. With a few suitable exceptions (e.g. see Bache et al. t990; Bratt et aI. 1990; Fedorenko et al., 1998) far too little efforts are invested in this most essential aspect of network operation and explosion monitoring. As demonstrated in this study, even small efforts in incorporating seismicity information (e.g. mining and quarry activities) can greatly enhance the bulletin quali~ and at the same time reduce significantly the monitoring workload. It was shown that SOM could be used to attain high levels of retrieval effectiveness. Methods to improve the precision, especially when considering subtypes have to be further investigated. This can be done for instance by giving more or less weight to some boxes (or to some regions of the map) when analysing the image icons. The outputs formed by the SOM can be used as such, or as a tool for gaining insight into seismic data. They can also be used to summarize data sets. Further, SOM can be used 202

in facilitating exploration of a data set, searching for known data, filtering of new data, as well as visualization of the results. Acknowledgments

The author wants to thank Prof. Tetsuo Takanami, Institute of Seismology and Vulcanology, University of Hokkaido, for initiating this study. References Bache, T., Bratt, S. T., Wang, J., Fung, R. M., Kobryn, C. and Given, J. W., 1990, The intelligent monitoring system, Bull. Seism. Soc. Am., 80, 1833-1851. Blandford, R., 1996, Regional seismic-event discrimination, Eystein S., Husebye and Anton M. Dainty editors, Monitoring a Comprehensive Test Ban Treaty, NATO ASI Series. Kluwer Academic Publ. Dordrecht, The Netherlands, 689-719. Bratt, S., Swanger, H. I., Stead, R. J., Ryall F. and Bache T. C., 1990, Initial results from the intelligent monitoring system, Bull. Seism. Soc..~m., 80, 1852-1873. Dowla, F. U., Taylor, S. R. and Anderson, R. W., 1990, Seismic discrimination with artificial neural networks, preliminary results with regional spectral dam, Bull. Seism. Soc. Am., 80, 1346-1373. Dowla, F. U. 1996, Neural networks in seismic discrimination: Eystein S., Husebye and Anton M. Dainty editors, Monitoring a Comprehensive Test Ban Treaty, NATO ASI Series. Kluwer Academic Pabl. Dordrecht, The Netherlands, 777-789. Fedorenko, Yu. V., [-Iusebye, E. S. and Ruud, B-O., 1998, Recognizing explosion sites without seismogram readins: neural network analysis of envelope transformed multistation SP recordings 3 - 6 Hz, Geophys. I. Int., 133, F1 - F6. Harris, D. B., 1991, A waveform correlation method for identifying quarry explosions, Bull. Seism. Soc. Am., 8l, 2395-2418. Kennett, B. L. N. and Engdahl, E. R., 1991, Travel times for global earthquake location and phase identification, Geophys. J. Int., 105,429-465. Kohonen, T., 1982, Serf-organized formation of topolo~catly correct feature maps, Biological Cypemetics, 43, 59-69. Kohonen, T., I991, Self-Organizing Map: Optimization approaches, T. Kohonen, K. M~isara, O. Simula and J. Kangas editors, Artificial Neural Networks. Proc. of ICANN 91, International Conference on Artificial Neural Networks, Vol. II, North-Holland, Amsterdam, 981-990. Macltwalu, C., 1997, Seismologist claim quake data being mis-read as bomb test, Nature, 389, 425. PULE, J. l., !996, Extractir~g and processing signal parameters for regional seismic event discrimination, Eystein S. Husebye and Anton M. Dainty editors, Monitoring a Comprehensive Test Ban Treaty', NATO ASI Series. Kluwer Academic Publ. Dordrecht, The Netherlands, 743 - 754. Richards, P. G. and Kim, W-Y., 1997, Testing the nuclear test-ban treaD', Nature, 389, 781-782. Ritter, H. J. and Kohonan, T., 1989, Self-organizing semantic maps, Bilogical cybernetics, 61,241-254. Rivi~re-Barbier, F., 1993, Constructing a reference event list for NORESS. Special technical report C93-06, Science Applications International Corporation (SAIC), Center for Seismic Studies, pp. 81. Rivigre-Barbier, F. and Grant, L. T., 1993, Identification and location of closely spaced mining events, Bull Seism. Soc. Am., 83, 1527-1546. Ruud, B-O, and Husebye E. S., 1992, A new three-component detector and automatic single-station bulletin production, Bull. Seism. Soc. Am., 82, 221-237. Ruud, B. O., Lindholm, C. D. and Husebye, E.S., 1993, An exercise in automating seismic record analysis and network bulletin production, Bull. Seism. Soc. Am., 83,660-679. Shearer, P. M., 1997, Improving local earthquake locations using L I-norm and waveform cross correlation: application to the Whittier Narrows, California, aftershock sequence, J. Geophys. Res., 102, 8269-8284. Schulte-Theis H. and Joswig, M., 1993, Clustering & location of mining induced seismicity in the Ruhr basin by automated master event comparison based on dynamic waveform matching (DWM), Computers and Geosciences 19,233 - 241. Tarvainen, M, and Husebye, E. S., 1993, Spatial and temporal patterns of the Femaoscandian seismicity - an excereise in explosion monitoring, Geophysica, 29, 1-20. Tarvainen, M., 1999, Recognizing explosion sites with a serf-organizing network for unsupervised learning, Phys. Earth Plan. Int., 113, 143-154. Thurber, C. H., Given, H. and Berger, J., 1989, Regional seismic event location with a sparse network: Application to eastern Kazakhstan, USSR, J. Geophys. Res., 94, 17767-17780. Tiira, T., 1996, Discrimination of nuclear explosions and earthquakes from teleseismic distances with a local network of short period seismic stations using artificial neural networks, Phys. Earth Plan. Int., 97,

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247-268. Uski, M., Pelkonen, E., Franssila, M., Karilas, M., Gr6nholm, P. and Vasamies-Leppanen, L., 2000, Seismic events in northern Europe, P. Heikkinen editor, Institute of Seismology, University of Helsinki, Helsinki, Finland. Uski, M., Pelkonen, E., Franssila, M., Karilas, M., Gr/Snholm, P. and Vasamies-Lepp~en, L., 2001, Seismic events in northern Europe, P. Heikkinen editor, Institute of SeismoIogy,University of Helsinki, Hetsinki, Finland.

A Appendix: Self-organiTing Maps The self-organising maps (SOM) also called Kohonen map according to their invertor (Kohonen, 1982) are effectively a vector quantization algorithm which creates reference vectors in a high-dimensional input space and uses them to approximate the input patterns in an image space in an ordered fashion. The basic algorithm is first motivated by the competitive learning. Competitive learning is an adaptive process in which the neurons in a neural network gradually become sensitive to different input categories, sets of samples in a specific domain of the input space. It does this by defining local order relations between the reference vectors so that they are made to depend on each other as though their neighbouring values would lie along a hypothetical surface. Adaptation of the weight vectors of a neuron occurs through a similar process to competitive learning except that subsets of nodes are adapted at each learning step (rather than just a single node) in order to produce topologically ordered maps. This also means that the weight vectors on the neurons adapt so as to become ordered along the axes of the network. The SOM is therefore able to approximate the parameter density function p(x) of a complex high-dimensional input space in two dimensions by preserving its local features. The ability of the SOM to perform exacting statistical analysis on difficult stochastic signals even in noisy environments has meant that most applications using it involve the visualization or monitoring of high-dimensional vectorial input spaces which can only be vector quantized using complex non-linear discrimination borders. One such application is the visualization/monitoring of a complex high-dimensional input space in two dimensions by preserving its local features. The ability of the SOM to perform exacting statistical analysis on difficult stochastic signals even in noisy environments has meant that most applications using it involve the visualization or monitoring of high-dimensional vectorial input spaces which can only be vector quantized using complex non-linear discrimination borders. Basically, a self-organizing map (SOM) is a two-dimensional artificial neural network, that is, an array of interconnected cells. They are used to categorize and classify large multi-dimensional data sets. Each data item has an association with it an vector of elements. These elements are features of the data, and they are achieved by calculating some parameters of the data. The spatial location of a cell in the map corresponds to a specific region of the multidimensional space. The training process of self-organizing maps can be described in terms of input pattern presentation and weight vector adaption. A set of data samples are used to train the map. During training, the map has its cells i, characterized by reference vectors m i that are updated after each input. The learning process is described by

rp~i(t)

.Jm,.(t) + a(t)[x(t)- m,(t)] if

i E X(t). elsewhere

[mi(t )

204

(A1)

In the expression t is the updating time, x(t) is the current input vector and a(t) is called the adaptation gain, and it gets values 0 or 1. The neighbourhood function N(t) determines which cells must be updated for a given input point. Thus, the topological structure of the input space is conserved in the map. As the training phase is completed, the reference vectors are left unchanged. They determine which cell must react to an input point. Since the topology of the input space is conserved by the map, nearby cells react also to nearby input classes. The conservation of the topology allows to visualize a multidimensional space in two dimensions. Therefore, maps can be used to visualize the differences between input points occurring in a data set. During training a series of pattern vectors x are presented to the network. Each node i compares its weight vector with the input vector and the one that is closest wins. The winning node c then aligns its own weight vector with the training input and hence becomes activated to it and will provide maximum response if it is shown to the network again after training. Figure A 1 illustrates how a self-organizing maps works with random sets of parameters Pij. It is first trained to react to the shape of boxes. Then, as shown in the figure, two samples are presented to the trained SOM. A box of a given shape generates a cell reaction at the bottom left of the map. The other box, which has a significantly different shape, generates a cell reaction at the top right. Remarkably, if the shape of two boxes differ only slightly, their corresponding cell reaction are also nearby in the map. The vector-spaces (P~ contains in image icons are used as input data to SOMs. Each box produces a single cell reaction. By summing the cell reactions corresponding to individual boxes, a total map can be associated with a given input. This approach is attractive for the following reasons: Nodes in the neighbourhood set of the winning node must also be modified in a similar way to create regions of nodes which will respond to related values and hence provide an average representation of that class of patterns. The network will then generalise to spatially close vectors that it hasn't previously seen. Nodes outside the neighbourhood set remain unchanged. It has been found experimentally that in order to achieve global ordering of the map the neighbourhood set around the winning node should initially be large to quickly produce a rough mapping, but then be reduced with time (where time means number of passes through the training set data) to force more localised adaptation of the network. This tends to improve spatial resolution without destroying the previously created global ordering. Apart from reducing the neighbourhood, it has also been found that quicker convergence of the algorithm results if the adaptation rate of nodes in the network is reduced over time. Initially the adaptation rate should be high to produce coarse clustering of nodes. Once this coarse representation has been produced, however, the learning rate is reduced so that smaller changes to the weighr vectors are made at each node and regions of the map become fine-tuned to the input training vectors.

Ix(j)- w (J)l =

w,(J)!}.

After this the weights and nodes within neighbourhood are updated.

205

(A2)

/

/,

\p, \

)

\

Y_) ',._j

1

\Y

Fig..41. A simple fi~nctional example of the self-organizing map. Assume that the map is trained to react to Parameter sets" Pr It will organize itself so that different shapes o f parameter sets will make different regions of the map react_ In the example parameter set P~ activates the lower left corner tuplet, while parameter set Pj activates the upper right corner tuplet.

Computation and Selection of the Maps Kohonen (1997) described the guidelines how to compute the maps. In this work the public domain software package SOM_PACK was utilized. The reference vectors are first initialized to lie in an ordered configuration on a plane spanned by the two principal eigenvectors of the data. After that the training is a two-stage process. The learning starts with a wide neighbourhood kernel covering most of the map. During the first stage the kernel quickly converges close to the final width. In the seconds stage the convergence is much slower toward the final width and magnitude. The first stage maps the global ordering of the map and the second stage the final accurate state of the map is formed. Since the training of self-organizing maps is stochastic there wiil be variation in the learning results. Consequently, to guarantee good quality, several maps can be computed and the best map can be chosen according to the cost function (Kohonen, 1991). E = Z Zh<~txk - m, il'[

(A3)

1

The cost-function of the SOM is specific to the size of the map and to the topology lying on the map lattice, which in turn is defined by the neighbourhood kernel. The value of the cost-function will decrease as the map size increases. Further, the value of cost-function increases as the width of the neighbourhood function increases. In measurement data there may exist outliers, data items lying very far from the main body of the data. The oatliers may result, for instance, from measurement errors or interpretation errors made while inserting the statistics into a data base. In such cases it would be desirable that the outIiers would not affect the result of the analysis. This is indeed the case for map displays generated by the SOM algorithm: each outlier affects only one map unit and its neighbourhood, while the rest of the display may still be used for inspecting the rest of the data. Furthermore, the outliers can be easily detected based on the clusterirtg display: the input space is, by definition, very sparsely populated near the outliers. If desired, the

206

outliers can then be discarded and the analysis can be continued with the rest o f the data set. It is also possible that the outliers are not erroneous but that some data items really are strikingly different from the rest. In any case the map display reveals the outliers, whereby they can either be discarded or paid special attention for further examination.

207

Automatic Itypocenter Location at Times of Extremely High Seismic Activity ShigekiHoriuchi National Research Institute for Earth Science ar.d Disaster Prevent,ion, Independent Administrative Institution, Tennodai a-l, Tsukuba, tbaraki 3~5-0G06, Japan, [email protected]

A b s t r a c t . In general, many earthquakes occur after a destructive shallow earthquake or be[ore a volcanic eruption. It is very important to determine accurate hypocenters as first as possible at a time of such a huge seismic activity, since seismicity data are essential for the understanding of the seismic or volcanic activity. We developed an automatic data processing system of seismic waves that can locate accurate hypocenters. It has a swarm mode processing which works even at a huge seismlcity. The main difference between the swarm and ordinary modes is that the former assumes hypocenters for all events to be in a small area. The application of swarm mode to waveform data at a huge seismicity after the 1996 Ouikobe earthquake sequence showed that the new system is very effective and can determine more precise hypocenters rather than manual pickings.

1

Introduction

Seismic observations before 1980 were conducted with using magnetic tapes to record waveform data. It was very difficult even to locate hypocenters, because we must spend much times to re-produce seismograms on chart papers and pick arrivM times of P and S waves manually. Therefore, it took long times to determine large number of hypocenters having a large number of stations. Considering the difficulty to locate hypocenters for a large number of events and the importance of locating hypocenter in a short time, technique to pick arrival times of the P and S waves have been developed by many researchers (e.g., Stewart, 1977; Shirai and Tokuhiro, 1979; Morita and Hamaguchi, 1984; Takanami and Kitagawa, 1988, 1991; Yokota et al., 1981). Horiuchi eL al. (1985,I992) developed an automatic processing system that detects and locates seismic events and record triggered waveforms by the use of personal computers. It had an A / D converter of 128 channels and was used in the actual temporary seismic observation made in 1986 at the aftershock area of the 1984 Western Nagano Prefecture Earthquake. This observation was made very successfully and demonstrated strongly the effectiveness of personal computer not only to locate hypocenters but also to record high quality waveform data. Although the software of automatic processing system has been improved for a long time, it could not locate hypocenters as precise as those by manually picking. It frequently picks noise or remarkable phase for different events as P or S wave arrivals and miss-locate hypocenters. It was also shown that the automatic processing system could not locate precise hypocenters at a time of huge seismicity, such as just after the occurrence of a large earthquake or before a volcanic eruption.

209

The information of seismic activity is most important in such c~es: because it is often a signal of the occurrence of earthquakes or volcanic eruptions. Recently, the number of seismic stations is in':teasing. It becomes more difficult fbr us to locate hypocenter quickly with using manually picked data. Therefore it is very important to develop more reliable automatic system.

Horiuchi et al. (1999) developed an automatic processing system of seismic waves that works at the time of very high seismicity. In the present note, I will show the methods how to detect seismic events, pick arrival times, eliminate wrong readings, locate hypocenters in the automatic processing system with introducing the papers by Horiuchi et al. (1992, 1999).

2 2.1

Method Event Detection

The method of event detection has shown by Horiuchi et al. (1985,1992). In general, there is a large variation in the amplitude of ground noises generated by rainfall, wind blow~ automobiles, etc. The amplitude of long period tremor is very large in winter at stations locating near the Sea of Japan. High frequency noises are predominant at stations with seismometers not in a borehole or tunnel but at the surface. Therefore, it is very important to eliminate ground noises to detect seismic signal for small events. However, we have no information about the fi'equency band of ground noises generated by various phenomena because they change with time. They also change from station to station. We introduce an auto regressive function, 4

E,, : U,, -

c,J/,,_,,k

where U~ and Ck are n-th waveform data, and k-th coefficient of the auto regressive model: respectively. We determine coefficients of the model so that the following equation becomes minimum, M

p = E r:

(2)

where, M is the number of waveform data in a time window" of noise model. The least-square solution give us coefficients in Eq.(1), which make the amplitude of noises to be minimum. Therefore, we can design a band pass filter to eliminate ground noises without knowing their predominant frequency. If these coefficients are calculated every one or two hours, Eq.(1) can cope with changes of the predominant frequency of ground noises against time. The next step of event detection is to set a threshold value of the trigger level for each station. However, it is difficult to know an adequate threshold x,'alue, since the amplitude of ground noises changes with time. The ratio of the short-term to longterm averages (STA/LTA) is used for the event detection. It is independent to the noise level but increases at a time of the arrival of remarkable phases. A recursive digital filter is effective to calculate approximate value of short-term or long-term average. Relative values of short (Q~(n)) and long(Qt(n)) term averages are calculated easily by following two equations, Qs( ) = IF i + (1 - Es)Q,(

21.0

- ])

(3)

Qt(n) = IF~[ + (1 -- ei)Qt(n - 1)

(4)

where, ~, and ct are small constants defining lengths of short and long terms. They are put as e~ --- 1/N, ~ = 1/N , where, N~ and J~ are numbers of sample data for short and long-term averages. Absolute values are put by dividing values of Eqs. (3), (4) by and , respectively. The ratio, S T A / L T A can be put as,

S T A / L T A = {Q,(n)s~}/{@(n)st}.

(5)

In general, appropriate values of the threshold level are ranging from 2.5 to 3.0 in the ease of micro-earthquake detection. Noises caused by cars or construction works are very large. It is difficult to filter out these signals. Since the energy of earthquakes is much larger than that by artificial noises, many stations detect seismic signals, while the former is recorded by only one station. The event detection is made when two or three stations have values of S T A / L T A larger than a threshold level. There are cases that more than two or three stations, which are apart, observe simultaneously a large amplitude noise generated at different places in a case of using many stations distributed in a very wide area. The event detection in this case should be made with using stations located in a narrow region. It is noticed that we must determine not only trigger start times but also duration of trigger, list of stations which detect seismic signals (trigger station) together with de~ected times, and list of stations near trigger stations. These data are used for the picking of P and S waves and hypocenter location.

2.2

A u t o m a t i c P i c k i n g of P a n d S waves

Shirai and Tokuhiro (1979), Yokota et al. (1981), Morita and Hamaguchi (1984): Takanami and Kitagawa (1988, 1991) and other researchers have developed methods of automatic arrival time picking. Some of these are successfully applied to the actual seismic networks in Japan (e.g., Hasegawa et al., 1986; Suzuki e t a l . , 1986; Hori and Matsumura, 1987; Horiuchi et al., 1999). The process of automatic picking is separated in to two parts. The first, is to design filter that eliminates ground noises for P wave picking and eliminates P wave signals in a case of S wave picking. The auto regressive function shown by Eq. (1) is also used as this filter. P wave data are used to calculate coefficients of no~se model in Eq. (2) in a case of S wave picking. The second part is to measure P wave or S wave arrival, time with using filtered data. Seismogram can be considered to be a time series of data. Since the amplitude of seismograms becomes large after P or S wave arrival, P or S wave picking is to divide the time series into two parts according to their amplitude level. ~fokota et al. (1981) demonstrated that Akaike's Information Criteria (AIC), which was proposed by Akaike (1973), is very effective for precise picking of P and S wave arrival times. AIC is defined as k

N

AIC(k)=:-(k-1)log{1/k~F2(i)}+(N--k)log{l/(N-k+l) i=1

~

E2(i)}

(6)

i=k+l

where, N is the number of waveform data. The minimum of Eq. (6) gives, us the onset time of P or S wave arrival. There are several suggestions how to pick P and S wave arrival times. Since P wave amplitude is much smaller than that of S wave,

211

trigger times obtained by Eq. (5) often correspond not to P wave arrivals but to S wave fbr small events or far events. Therefore we must search for P wave arrival from a long time window be{bre trigger times. There are cases that both P and S waves arrive within a same time window, since we must search for a long time widow. If P and S waves are in a same time window, Eq. (6) has two minimums~ which correspond to P and S wave arrivals. It is necessary to check that there is no another minimum before estimated P wave arrival. There is a large variation in S-P times because they depend on hypocentral distance. We must search fbr S wave arrivals with taking a long time window so that S wave arrival is included in it. There are also two minimums in this case. The first corresponds to the onset time of S wave arrival and the second corresponds to the end of seismic signal, since Eq. (6) becomes small even if the amplitude of the earlier part becomes larger than that of the later part. Sometimes, the value of second minimum is smaller than that of the first minimum. We must neglect solutions whose amplitude of the earlier part is larger than that of the later part. There are cases that two events are included in a time window of trigger times. It is necessary to pick arrivals of clear phases more than two to locate all of them.

2.3

Elimination of Wrong Readings

Automatic processing system often reads noises as P or S wave. It also reads onset times of P or S wave for other event. Correct hypocenter locations cannot be obtained without eliminating wrong readings. However, there are many causes of wrong readings, it is very difficult to eliminate all of them. Successful hypocentef locations depend very strongly on the technique of eliminating wrong readings. Even if we locate hypocenters with using arrival times, in which a small number of serious wrong readings are included, a convergent solution is not obtained. We cannot use val.ues of travel time residuals in the non-convergent solution to search for wrong readings. It is very important to remove wrong readings before hypocenter locations. P wave wrong readings are removed as foltows. An arrival time difference for two stations is expressed by the function of the geometry of the two stations and hypocenter locations. However, it should be less than a critical value, which is calculated from a distance of the separation of the two stations and seismic velocity. If an arrival time difference is larger than this value, we can consider that one of readings is wrong, though we cannot know which is wrong. If a station has a wrong P wave reading, most of arrival time differences between this reading and that of the other stations become larger than the critical value. Therefore, this station has many stations whose arrival time is inconsistent with that of this station. Hasegawa et al. (1986) pointed out that wrong readings could be known by comparing the numbers of inconsistent readings. Their method is very effective to remove wrong P wave readings, which differ largely with actual P wave arrival times. As pointed out by Horiuchi et al. (1999), S wave wrong readings can be removed by the use of Wadachi diagram, which is almost independent to the hypocenter location. Since an approximate origin time can be determined from the Wadachi diagram, we can calculate the difference of S wave arrivals from the diagram and can remove wrong readings. If S wave readings are only two and they do not satisfy the Wadachi diagram, we cannot know which is the wrong reading. Both reading are not available in this case. P and S wave amplitude and their predominant frequency decrease with hypocentral distance. Spatial distributions of the amplitude and predominant frequency give us

212

the information about hypocentral distances. However, there is a large heterogeneity in the Q and seismic velocity structures of the mantle above subduction zones. We must take account for the existence of the laterai heterogeneity in a case of using amplitude or predominant frequencie data. It is very difficult to pick S wave arrivals for a large event or very far event, in general. There are cases that a large event has a few to several S wave wrong arrivals, which are not eliminated by the above two procedures. The elimination of these wrong reading is made with locating hypocenter and checking arrival time residuals. However, the existence of a large lateral heterogeneity of earth structure makes difficult to find ~ wrong readings. It is widely known that Pn velocity in the upper mantle is 7.5km/s beneath the land area of Japan and 8.0 km/s beneath the Sea of Japan and Pacific sea (Zhao et al. 1992). Events have large arrival time residuals if they occur beneath the sea far from Japan lands; Let's consider that an event occurs beneath the sea and its hypocenter is calculated with using arrival times including a few incorrect readings. It is often in this case that stations close to the hypoeenter have large arrival time residuals owing to the large heterogeneity and poor station coverage. We must take care not to remove readings for close stations, which have clear onset, correct readings but large travel time residuals. Horiuehi et al. (1999) suggested the method to remove wrong readings with comparing arrival time residuals, S/N values of readings and the order of arrival times. Hypocenter locations can be calculated after removing wrong readings. Obtained solutions give us information about theoretical arrival times of P and S waves for stations without having arrival times. The automatic system re-picks P and S wave arrival times for these stations with setting time windows at their theoretical arrival times. As shown by Horiuchi et al. (1999), the process of re-picking is very e'ffective to measure precise P and S wave arrival thnes. The number of readings becomes about twice by the re-picking. Final hypocenter location is calculated with adding re-picked data. Even though wrong readings are removed very carefully, there are cases that hypocenters are miss-located. Horiuchi et al. (1999) check the number of total reading, number of eliminated stations, geometrical locations of the calculated hypocenter and seismic network, and rate of stations near hypocenter with arrival times and without arrival times, tn a case when the number of eliminated stations is large compared with the total readings, or the rate with and without readings is small, obtained solution is not reliable. They pointed out that obtained solutions should be evaluated by these parameters. 3

Software

The software of the automatic system has many functions, as shown in Fig.l. They are, (1)reading of all waveform data sent from each station (adhp in Fig.l) or a lane cable(read_eisei), (2) detection of seismic events(trigin), (3) location of hypocenters, determination of magnitudes and focal mechanisms (ateq_mem), (4) recording of triggered waveform data (dkwrt_trig), (5) recording of continuous waveform data (dkwrt_cont). The processing time of these jobs depends on the number of stations, size of earthquake, CPU speed, etc. It is important to make software that all jobs work at correct timings. As shown in Fig.l, the shared memory is used to exchange data among jobs. VVaveform data and some parameters about the trigger levels are memorized on the shared memory. The job (I) reads waveform data and writes them on the shared memory. The job (2) reads waveform from the shared memory and writes trigger

213

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86 g2t 213 3~.E2 0.05 35.8271 0.G009 $37.570? 0.0010 2.53 0.17 0.065 23-O.t0 811 82Z 83Z 84Z 85Z 8fiZ B7Z 66z 69g 18Z Ill 12Z 13Z t4Z 15Z 16g I?Z 21Z 22Z 18Z 19Z 28Z 23Z 241 251 26 Z 98T g8T Fig. 2. An example of vertical component seismograms for an Mtershock. Automatically picked P onset times are shown by solid lines with U, D or P, as~d $ onset times by solid line~ with S. The symbols U, D and P indicate polarity of initia~ motions of P wave to be compressional, dilatational and unknown, respectively.

214

flags on the shared memory at a time of event detections. The job (3) waits till job (2) writes trigger flag and locates hypocenters with reading waveform d a t a from the shared memory. The job (4) and job (5) read waveform data from the shared memory and write triggered or continuous waveform data on disk. Since all jobs except (1) wait till values on the shared memory change, it is not necessary to communicate data among jobs. The usage of the shared memory is very important to make simple software. 4

An

Example

of Automatic

Hypocenter

Location

As mentioned by Aoki (1988), 26 stations equipped with three or four channel telemetries were set up in and around the aftershock area of the 1984 Western Nagano Prefecture Earthquake. This observation was made with using magnetic tape recorders. Horiuchi et al. (1992) set a personal computer system, which can detect, locate seismic event and record waveform data. Fig. 2 shows an example of seismograms together with the location of atttomaticalIy picked P and S wave arrival times obtained in this seismic observation. Fig. 3 shows the hypocenter distribution determined automatically during the observation. The total number of located events is 1,264. About 350 hypocenters are determined manually after several months later from the observation. It is shown from the comparison of hypocenter distribution determined by the manually picked data and that by the automatic system that the automatic system can locate very precise hypocenters. 5

Swarm

Mode

Processing

In general, seismic activity is very high just after a large earthquake or at a time of the occurrence of an earthquake swarm associated with a volcanic activity. There are cases that more than 10 events occur per minute. It is very difficult not only for seismologists but also for the automatic system to choose a set of correct P and S wave arrival times correspond to a same event among many candidates. The ordinary automatic systems could not read correct phases correspond to a same event, leading location error in a time of huge seismicity. However, we need precise data of seismic activity in such a case for the understanding of the volcanic eruption or earthquake occurrence, because the data of seismic activity are essential for the understanding of the crustal activity. Horiuchi et al. (1999) developed an automatic system that can locate hypocenter even at such huge seismic activity. Considering that aftershocks or swarm occur only in a narrow area, they proposed swarm mode processing with assuming that all swarm events occur within a swarm area of a certain radius. Firstly, arrival times for all clear phases are picked with using seismograms recorded at stations near the swarm area. Then, their origin times are estimated under an assumption that all of them are P waves. Their estimation errors are also determined with calculating the maximum and minimum values of P wave travel times for ray paths from the swarm area. The detection of event occurrences is made i n a case when there is more than a critical number (three or four) of stations whose calculated origin times coincide each other within the estimation errors. The estimation of origin times make Possible to calculate time ranges of theoretical arrival times of P and S waves for all stations. They demonstrated that P and S wave arrival times for swarm events can be measured very precisely with setting time windows thus estimated. F'ig. 4 shows an example of seismograms just after the occurrence of the main shock of the 1996 Onikobe earthquake. The swarm mode processing locates 5 events

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217

a m o n g 6 events, while the o r d i n a r y m o d e processing locate only one event. This result d e m o n s t r a t e s the effectiveness of the swarm m o d e processing. Fig. 5 shows epicenter d i s t r i b u t i o n s of the 1998 off Ito e a r t h q u a k e swarm. T h i s is the result for 4 days. It is clear t h a t e a r t h q u a k e swarm was s t a r t e d at a n a r r o w region and the area e x t e n d e d t o w a r d east and south. T h e result by a u t o m a t i c s y s t e m showed t h a t focal d e p t h s b e c a m e shallow at the first stage. This figure s t r o n g l y suggests t h a t a u t o m a t i c s y s t e m can locate very precise hypocenters.

6

Future Problems

We presented the method to locate hypocenter automatically. As mentioned in the previous section, the automatic processing system can read very precise arrival times if we can set a correct time window of P or S wave arrival. However, it is very difficult to get approximate P and S wave arrival time automatically owing to many kinds of noises and the large changes in the shape of earthquake waveforms. We showed many small techniques to remove wrong readings. Although the rate of incorrect hypocenter locations was decreased by the development of the software, about 10 % of events are not located or not precisely located. A high gain seismic network (Hi-ne~) was installed in whole Japan with a station density of 20 to 25 km. The total number of stations is about 600. \,Ve can also use another 600 station data installed by JMA and universities. Since the number of stations is increasing, it becomes more difficult to pick all arrival times manually. On the other hand, the automatic system can locate hypocenters more precisely by the increase of available stations, because we can use more information 'co remove wrong readings. It is very important ~o develop complicated software to read precise arrival times, remove and correct wrong readings. References Akaike, H., 1973, Information theory and an extension of the ma~ximum likelihood principle, In B. Petrov and F. Csaki (Eds.), 2nd International Symposium on Information Theory, 267-281, Budapest Akademiai Kiado. Aoki, H., 1988, The 1986 Joint Seismological Research in the Western Nagano Prefecture ? short note for the seismological network-, Gekkan Chikyu (The Earth Monthly), 10, 657-659 (in Japanese). Hasegawa, A., Umino, N., Ya.~namoto, A. and Takagi, A., 1986, Automatic event detection and location system of microearthquake observation network, Zisin (J. Seismol. Soc. Jpn), Ser. II, 39, 381-395 (in Japanese with English abstract). Horiuchi, S., Yamamoto A., Matsuzawa, T., Kono, T., Hasegawa, A., Takagi, A., Ikami, A., Yamada, M. and Aoki, H., 1985, A real-time detection and location of aftershocks of the 1984 Western Nagano Prefecture Earthquake by using personal computer, Zisin (J. Seismol. Soc. Jpn), Ser. II, 33, 529-539 (in Japanese with English abstract). tloriuchi, S., Matsuzawa, T. and Hasegawa, A., 1992, A real-time processing system of seismic wave using personal computers, J.Phys.Earth,40, 395-406 Horiuchi, S., Matsuzawa~ T. and Hasegawa, A., 1999, Automatic data processing system of seismic waves that works.even at times of huge seismic activity, Zisin, 52,241-254 (in Japanese with English abstract). Morita, Y. and Haznaguchi, H., 1984, Automatic detection of onset time of seismic waves and its confidence interval using the autoregressive model fitting, Zisin (J. Seismo. Soc. Jpn.), Ser.II, 37,

218

281-293 (in Japanese with English Abstract). Shire[, K. and Tokuhiro, I., 1979, Detection of seismic wave onsets, Zisin(J. Seismol. Soc. Jpn): Set. If, 32, 141-147 (in Japanese with Engl!sh abstract). Snewart, S.\u 19"/7, Real-time detection and location of local seismic events in central California, Bull. Seism. Soc. Amer., 67, 433-452. Suzuki, S.: Takana~!i, T., Motoya, Y., Kasahara, M. and Nal~aisl".i,I., 1986, Automatic processing system for micro-earthquake network of Hokkaido University, Program. Abst. Seismol. $oc. 3pn, 287 (in Japanese) Takanami, T. and Kit~gawa, G., 1988, A new efficientproced~,re for the estimation of onset times of seismic waves: J. Phys. Earth, 36, 267-200. Takanami, T. and Kitagawa, G., 1991, Estimation of the arrival times of seismic waves by multivariate time series models, .inn. Inst. Statist. Math., 43,407-433. Yokc,ta, T., Zhou, S., II.[izoue, M. and Nakamu:a, I., 1981, .in automatic measurement of arrival time of seismic waves and its application to an on-line processing system, BuU. Earthq. Res., Inst., 55, 449-484. Zhao, D.: Horiuchi, S. and Hasegawa A., 1992: Seismic velocity structure of d~,e crust beneath the

Japan Islands, Tectonophys., 21'2, 289-301.

219

Application of Pattern Recognition to Seismic Event Discrimination Shin~ca Tsukada 1 and Kazuo Ohtake ~1Earthquake Disaster Prevention Technology Division, Railway Technical Research Institute, Hikad-cho, 2-8-38, Kokubunji, Tokyo, 185-8540, Japan. [email protected] 2 Seismological and VolcanologicalDepartment, Japan Meteorological Agency, Ote-machi 1-3-4, Chiyoda, Tokyo, 100-8122, Japan. [email protected]

Abstract. The hypocenter determination is one of the most basic analyses in seismology. In recent years, the ability of hypocenter determination has improved rapidly. The more we try to raise the ability of automatic hypocenter determination, the more essential the discrimination of the seismic signal from the background noise becomes. Even if the technique of automatic picking or calculation of hypocenter determination is upgraded in the automatic processing, the reliability of hypocenter determination worsens when there are a lot of misreading of the phase by the noise. We propose a new approach or "a method of seismic event discrimination with pattern recognition" that determines seismic events precisely, which may serve for increasing the reliability of automatic reading of seismogram and hypocenter determination. In the current method of seismic signal discrimination, the information of seismic wave arriving at the station is positively used. However we can not say that we have explicitly used the information that the seismic wave still has not arrived at the station. We try to use this information effectively. Our method wiU be useful for the obse~-ation of the seismic wave-field on a real time.

1 Introduction The hypocenter determination is one of the most basic analyses in seismology. The Japan Meteorological Agency determines the hypocenter of earthquakes which occur in and around Japan day after day as a routine work mainly by hand picking and calculations by a computer. Recently, this has required an enormous amount of work since a high-quality seismic observation network was developed. When computers were introduced into hypocenter determination in the Japan Meteorological Agency in the 1960s, for instance, the number of hypocenters determined for one year was several hundreds, which now reaches 100,000 (Fig.l). It is forecasted that this number will increase further as the seismic observation network and the hypocenter determination ability are improved in the future. The amount of work will reach a limit soon if operators are not increased or an automatic phase reading and hypocenter determination system is not introduced. Under the circumstances, a variety of automatic processing systems for phase reading and hypocenter determination have been developed along with the rapid development of computer hardware (e.g., Yokota et al., 1981; Matsumura, 1989; Urabe and Tsukada, 1992; Horiuchi et al., 1999). Many of these systems are designed according to the following steps: i) detection of ground motion by triggering at a single station; ii) discrimination of seismic event with the use of trigger information at plural stations; iii) automatic phase reading of seismic wave; and iv) hypocenter determination. Among these steps, the steps iii) and iv), in particular, have attained positive development. The step iii) means to implement automatic phase reading at the same accuracy as in manual

221

operation by applying the "Auto Regression model" (e.g., Shirai and Tokuhiro, 1979; Morita and Hamaguchi, 1984; Maeda, 1985; Takanami and Kitagawa, 1988). The step iv) means to get steady solutions of the hypocenter determination (e.g., Hirata and Matsu'ura, 1987).

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However, the reliability of the automatic processing system has not necessarily been improved to a satisfactory level yet. This is because the steps i) and it) are not sufficiently examined. In other words, wrong discrimination of seismic event by the background noise has been allowed in fear of missing real earthquakes. In such a situation, automatic processing might fail because a false hypocenter is determined or the calculation of hypocenter determination becomes unstable. Namely, although the technique of automatic phase reading and hypocenter determination has almost been completed, the reliabilit)" of automatic processing will be mined by improper preprocessing. An automatic processing system should obtain a reliable result anytime even if there is no crosscheck by manual operation. If the reliability of hypocenter determination is 80%, for example, we are required to check all data again. As described later in this chapter, the reliability of automatic phase reading and hypocenter determination will be improved when the accuracy of seismic event discrimination in the steps i) and it) is improved by introducing the idea of the "pattern recognition".

222

2

Pattern Recognition

The conventional technique of trigger detection and seismic event discrimination is called "a group trigger method". It is judged that an earthquake has occurred when the number of triggered stations exceeds the number preset in the relevant region. This technique such as combining the data at plural stations can reduce wrong seismic event

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discrimination caused by regional ground noise even though the processing is performed independently at different stations. Moreover, this method has the merit that the processing time can be saved by a simplicity of data processing algorithm even ff a large

223

load is added to the computer when the trigger detection and the seismic event discrimination are operated for all stations. However, this technique occasionally causes wrong seismic event discrimination due to the noise which appears at ~ ' o or more stations almost at the same time. To avoid such a mistake, we calculate the apparent velocity of the seismic wave at the triggered station. We have to exclude the combination of the stations if an impossible apparent velocity is obtained. However, the algorithm becomes complex since it requires the evaluation of distance from one station to another station and the judgement of validity of the apparent velocity. So, we deal with the problem how to prevent such wrong seismic event discrimination. We occasionally use a multi-channel pen recorder in seismic observation. At a glance, we can immediately judge the properties such as, the magnitude, signal or noise and location, from such a record section shown in Fig. 2. Because the pattern image of arrangement of their records makes us understand whether they are seismograms or not. This is an example of the most basic pattern recognition. In this chapter, we try to discriminate a seismic event by using the idea of this pattern recognition. First, we make a theoretical pattern of P wave arrangement from the travel times of P waves at stations by using a hypocenter assumed. We call it the model pattern. Secondary, it is compared with the actual arrangement of the observed P waves. By this comparison, irregular ground noise can easily be removed.

3

Making Pattern and Calculation

There are some methods devised to make a binary digit from the seismic wave, such as using the value of the amplitude or the ratio of the amplitude of horizontal motion to that of the vertical motion. In this chapter, we consider that the pattern of bit image is set at "1" when the average amplitude of continuous data exceeds a certain threshold every second, and "0" otherwise (Fig.3). In general, the threshold should be set at a certain value depending on the magnitude of earthquake. However, the discrimination between

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224

the ground noise and real seismic event is still difficult. So, the ratio of "short term average (STA)" and "long term average (LTA)" of the time series of amplitude data is referred to as a criterion for discrimination. The threshold is here set at about 2.0 at each station by trial and error. The lower bound of the magnitude of earthquake which can be discriminated may be controlled not only by the threshold of decision of "1" or "0" but also by the station density. We used the seismic stations of the Japan Meteorological Agency set up at intervals of several ten kilometers for the present analysis. In addition, we used a lot of seismic stations of other organizations from where data are collected concentratedly by the Japan Meteorological Agency; such as Earthquake Research Institute (the University of Tokyo), Nagoya University, Disaster Prevention Research Institute (Kyoto University), The National Research Institute for Earth Science and Disaster Prevention, Geological Survey of Japan, Tokyo Metropolitan Government and Kanagawa Prefecture. As a result, we used the data of 248 stations in total. The average interval between the stations is about 20 kilometers. The left-hand side of Fig. 4 is a part of the bit pattern for 32 seconds obtained from actual observation data. The observation pattern drawn from the observed seismic waveform can be written as vector X with only "1" and "0" as its components,

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O~DOOOl3OOOOOO~O~OOnO~OOO'~OOOOOOO OOOOOOO~OOOOOOOOO~OOO~OOOOOllll OOOOOCOO~ODOOOOOOOilllllliilllll OOOOOOOO~OOOOOO~OoOOn~OOO~Ollml :STATI@N~ C o ~ o n o o o ~ O ~ O O O C O O O O O O O O O D O O O O ~ O ~ :~,~rlol n r ~ D o ~ O O ~ O c ~ o r ~ o m O O o O i m l l l l l l l l U l l l l l l n l l l l l l a :S'TATI~ ~ O O ~ O O O O O O ~ O ~ O O O O O O O O O C O O O O O l i I N :STATZ~ la o n o o o o o o m O o n O o O O O o O ~ o m O O O O o ~ n O o o :~'TATION 11 O O O r T r T C O r T O O O C ) O O n o r I D ~ r 7 O O O r 1 ~ O O c ~ [ 3 0 0 .'~AT[~ t 2 0 o o o G c o ~ o o o o c o o ~ c o o o m m n m l l m l l m m u

:~AT[~ Z ' 8 0 ~ ) U n l l l l l l l l l l l l l l l l l l l l l n l i l l i l :b"TATL~~ t 3 0 ~ O O [ 0 0 ~ r ~ ( 3 ~ [ 3 O H l a n n l l l H l l l l l l l l l l :~ATI~ 39 : ~ O O O ~ E ~ l l l l l l l l l l l l l l l l n i l i l :~TATT6N3? O ~ O ~ O O O ~ O E O ~ C O O ~ E O O O O O O O O O ~ O O H i :~'T~TIQ~39 O O D ~ O O O O O ~ O ~ O O O O ~ D O O O O O O ~ O O O O O O O :ST~TI@~~4 m O O O ~ O O O ~ O O O O ~ D O O ~ O O O O O O ~ O O O O O O :~I"ATION~ O O O O ~ O O O ~ O O O O O O O D O O O O O O O ~ o o n o o o O ;~'TATIflN ~S ~ O O ~ O O O O O O O ~ o o r ' o o o o ~ O O O O O O ~ O O O O

m

:~'TAT!.@N~S O ~ D ~ O D ~ O O O O ' ~ O O O O D ~ O O O o o ~ n o o ~ O ~ O :~'[ATIO~ 3~ O o o o r T o t ] O O m O o o o n ~ o O O r ~ o m o ~ O i l l l l i :&'TAT!~ @ O D D ~ O O O O O O O O O O O ~ C U O O O O ~ E O O i l I I :ErAT|~L 41 ~ O ~ O ~ O ~ O O O O D O O O O G G O O O O I I l I i l I I I :~'TATION ~ 3 0 0 D ~ O O O G O O ~ O O ~ O U O O ~ ' ~ O ~ Q O O D O ~ O O

Fig.4. Example of observed bit pattern (left-hand side) and model bit pattern calculated for an assumed hypocenterfor 32sec (right-handside). [] and n denote "0" and "1", respectively.

created by the theoretical travel time assuming a hypocenter. The pattern is assumed to

225

be "0" before P wave arrives and "1" after P wave arrives at the station (right-hand side of Fig.4). Now, assume hypocenters beforehand, then the model pattern for the hypocenter "i'" will be written as

M i = (m,l,m,2,m,~,,m~)

(i = 1,2,3,.-., N).

(2)

Looking for a model pattern most similar to the observation pattern of the seismic waveform among N patterns is the same as calculating the hypocenter determination. We used the technique which is called "the shortest distance method" to compare the resemblance degrees of two or more vectors. This technique calculates the foUowing quantity for two or more Mi patterns, i IIx-Mill

o

k-m,

z

'

(3)

and identifies the pattern with the minimum value. A general explanation for pattern recognition is, for example, given by Funakubo (1991). As mentioned above, these patterns are represented in binary by "1" and "0". Therefore, we do not need the arithmetic operation like (3) because the bit operation among data is easy in the C language. But we have to execute the bit operation in mathematical logic, "CXOR" (Complement of eXclusive OR) shown by the formula (4) every second (Fig. 5)

X *Mi"

(4) DATA (X)

} mmmmmmmmmmmmmmmm mmmmmmmmmmmmmmmm FT~mF7F7FTD[~FT~FTFt~F-1F7

MODEL (M 0

X~M, X e~M, (scoreO)

DATA (X) ~ m m m m u m m n m n n

MODEL (Mi) X ~M,

n n n n u u ~ n ~ s n

X e M , (score8)

Fig.5. An examplecalculationof"exclusiveor (XOR; X ~M,)"-and "exclusiveor complement( X ~ M , ) ". Open squares show 0 (=bit off) and solid squares show 1 (=bit on). This bit operation saves the processing time. Here, the purpose of taking the complement is that the more the observation pattern is similar to the model pattern, the more the value increases. The formula (4) means that when the observation pattern agrees with the model pattern digit "1" is obtained and otherwise digit "0" is obtained. The score of resemblance between two patterns is defined by the total sum of "1" and "0". We identify every second the region where the earthquake has occurred within the targeted time by counting this score. In an actual calculation, the score larger than a normal is given when the observation pattern agrees with the model pattern near the epicenter.

226

The number of assumed hypocenters and the number of stations used are limited by the performance of the computer. The travel time was calculated by setting a virtual hypocenter on lattice point, every 0.25 degrees in latitude and longitude and to two layers (10kin and 60kin) for depth, as shown by solid circles in Fig. 6 with the use of the standard travel time table employed routinely by the Japan Meteorological Agency (Hamada, 1984.) 135 ~

136 ~

Depth

137 ~

= lOkm,

138 ~

139 ~

140 ~

60kin

,

141 ~

142 ~

143'

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39 ~

38 ~

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r

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31" m

Fig.6. V'trtualhypocenters(circles) and the seismicstations(crosses)used in this study.

The total of the model pattern is 1980 pieces. The time window width used for comparing the model pattern and the observation pattern is assumed to be four seconds by trial and error. This duration nearly equals to the F-P time of a magnitude 2.0 earthquake. A high score is obtained for the model pattern that has a virtual hypocenter in the vicinity of actual hypocenter. Virtual hypocenters are arranged in the descending order of scores, and the average and the variance of latitude and longitude are calculated for nine places from high rank. When the average is obtained with the variance of 0.3 or less as the location, we regard that an earthquake has occurred in the region. Fig. 7 is an example of the spatial distribution of the score obtained by this method. The star shows the hypocenter determined by the manual picking. Fig. 8 is an example of change of the

227

score with time at the epicenter. It is understood that both epicenter and origin time are correctly discriminated. 135"

136"

137"

138'

139"

140"

141"

142"

143"

39"

!

oo:48 4~.~.262 ~37.6~ 5.~k~ M2i,

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Fig.7. Spatial distribution snapshot of the score. The star shows the epicenter determined by manual. 35O0

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Time (sec} Fig,& Change of the score with time. Time 0 (dashed line) shows the origin time of the event.

4

Example

of Earthquake

Discrimination

Fig. 9 shows the result by the method described in section 3 for about one month from January 11, 2000 to February 17 (with an interruption of several days according to the switching o f power supply system). The plotted epicenters (a) in the left side o f Fig. 9

228

and (b) in the right side of Fig.9 were determined manually during the same period by the Japan Meteorological Agency. (a) shows the epicenters for which the discrimination succeeded by the present method, and (b) shows the epicenters for which the discrimination failed due to the overlooking of earthquake occurrence or the wrong determination of the epicenter. We compared the result of hypocenter determined by the Japan Meteorological Agency manual picking with the result by the present method. We regard the identification to be successful when the origin time is determined within the difference of +/- 2 minutes, and the epicenter is determined in latitude and longitude within the difference of +/- 2 degrees for coastal zones, and within the difference of +/- 1 degrees for inland areas. Fig.10 shows the number of events discriminated successfully in inland areas (a) and undersea and deep (depth > 100kin) region.s (b). The numbers are summed up for twelve magnitude ranges respectively.

135"

136"

I

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Fig.9. (a) Epicenters of successful discrimination. (b) Epicenters of false discrimination. Asterisk shows an example of failure in the seismic event discrimination for M3.0 earthquake.

A s s h o w n in Fig.9 and Fig.10, earthquakes w h o s e i n a p t i t u d e is larger than 2.5 can m o s t l y be discriminated for inland areas, and those w h o s e m a g n i t u d e is larger than 3.5 can m o s t l y be discriminated for coast regions. H o w e v e r , about 30 % o f inland earthquakes w h o s e m a g n i t u d e is 2.0-2.5 are not d i s c r i m i n a t e d e v e n t h o u g h they are considered as identifiable f r o m the duration t i m e o f s e i s m i c signal. M o s t o f the earthquakes that could not be d i s c r i m i n a t e d are those w h i c h o c c u r r e d at the central K a n t o district. T h e reason is c o n s i d e r e d that the s e i s m i c w a v e s are strongly attenuated in the crust beneath this district (Ide, 2000). T h e amplitude o f s e i s m i c w a v e o b v i o u s l y attenuates through this region. ~ & e n the m a g n i t u d e o f earthquake is small, the pattern o f the o b s e r v e d s e i s m i c w a v e will not be w e l l d e t e r m i n e d and not agree w i t h the theory pattern sufficiently. The s e i s m i c event discrimination by the theory pattern is s i m p l y m a d e f r o m standard

229

travel time table. Thus, when there are media which cause strong attenuation or a large travel time anomaly, it is inevitable that the seismic event discrimination becomes difficult. Moreover, there are regions where seismic event discrimination is essentially difficult. In these regions, the seismic signal is detected at the only single station within the assigned time windows.

450 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(a)

.....................~

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.

/ 251)

J

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. . . . . . . . . . . . .

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~0.4

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1.0~1.4

1 5~1.9

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2.5~2.9

,3.0~3,4

3.5~3.9

4.0~4.4

4.5~4,9

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180

(b)

- -

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140 =

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.................................

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....... \~ ........

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5.0~

Magnitude

Fig.lO. Relationship between the number of events discriminated successfully by the present method and magnitude. (a) events which occurred in inland area, Co) events which occurred in shore area and deep region (>lOOkm).

Asterisk in Fig. 9 (b) shows an example of failure discrimination of an earthquake of M=3.0, which occurred inland area (the western Tochigi Pref.). The time interval of

230

occurrence from a preceding earthquake was only nine seconds and it is too short to discriminate the later earthquake. The smallest earthquake for which the discrimination succeeded has magnitude 0.6 in this analysis. Fig. 11 shows the comparison of the number of earthquakes discriminated by two different methods, one by "the group trigger method" and the other by this analysis. The shaded part in the figure shows that the earthquakes actually exist as the discriminated events. It seems that the number of earthquake discrimination by this analysis decreases. The reason is that the lower bound of the ma~maitude of the earthquakes to be discriminated has raised. If we try to discriminate small earthquakes, the number of cases where "the earthquake does not actually exist though the event is discriminated" increases. This is a relation of trade-off. If we use not only the amplitude but also VPrI ( = amplitude ratio of horizontal component to vertical component), we may discriminate the events with much smaller magnitude.

~000 7N10

. . . . . . . . . . . . . . . . ~2.;;~-~........ i_

E ' i 4000

10o0

Group trigger

Determined in this study

Fig.lL Comparisonbetween the number of seismic events discriminated by "Group trigger" method and the method in this study. [ ] shows the number of discriminated events without corresponding earthquakes. [ ] shows the number of events discriminatedsuccessfully.

Fig.12 shows the number of earthquakes discriminated by the following four methods; manual picking, this analysis, primary automatic operation by the Japan MeteoroloNcal Agency (automatic hypocenter determination only by automatic picking of P phase), and secondary automatic operation (automatic hypocenter determination by automatic picking of P and S phases). The vertically striped area shows "earthquake discrimination or automatic hypocenter determination was not made though the earthquake actually existed". The unshaded area shows "the earthquake actually existed, and seismic event discrimination or an automatic hypocenter determination was made. However, the result is improper''. The shaded area shows "the earthquake actually existed, and seismic event discrimination or automatic hypocenter determination was made and the result are excellent". The obliquely striped area shows "seismic event discrimination or automatic hypocenter determination was made to non-existing earthquake, and the false hypocenter was produced". The number of false earthquakes is shown as a negative number. An "automatic" hypocenter determination means that automatic picking is made from the raw waveform and usual hypocenter determination is made. The judgment on

231

whether the seismic event discrimination or automatic hypocenter determination has succeeded or not is made aceording as the obtained hypocenter agrees with that determined by manual picking. The most important point is a decrease in the number of earthquakes which belong to the following category, "seismic event discrimination or automatic hypocenter determination is made to non-existing earthquake, and the false hypocenter is produced." This fact shows that our algorithm can interrupt the processing when the order of arrival times or the combination of the stations does not meet the condition of apparent velocity after the trigge r has worked. Strictly speaking, two concepts, that is, earthquake discrimination and hypocenter determination are different. If we introduce this technique to the processing for the trigger detection and hypocenter determination, we may decrease the number of false earthquakes.

2o~0 .

Manual determination

Determined in this study

Automatic determination

(using only P phase)

! !

"

Autoi'natio determination

:

P & S phases)

(usin

! i; i~ i I~

i!!:.'i I: L '

I

~,~!

9

!':,L .; : , 9

',;~~'.', ',~' :l""~. ~i~''l~

> ..<:,,:~-'.'~3-

r~..,~;~.,', ',., :,~+.

.~'.~ ;si,. ;

9

-~0o

I i

[ ] Existing EQ- & failed determination

.r':t No EQ. & Wrong d e t e r m i n a t i o n

[

Fig.12. Comparison among the number of hypocentersdetermined manually, by the method in this study, and by two automatic determination methods now in use: one uses only P phase data artd the other uses both P and S phases data picked up automatically.

In this text, we do not refer to the processing speed of the calculation. It takes about one second per station for picking the phases automatically by the technique of the Japan Meteorological Agency. It takes about three minutes of processing time for earthquake of magnitude 5.0 or larger due to a lot of picking stations. However, if the current method is applied to such a large earthquake, the epicenter can be located within several seconds. When the hypocenter information is urgently required like the tsunami forecast, this method can be used as an extremely effective technique. The amount of data processing may increase rapidly as the network is upgraded with the reduction of the price of hardware in the near future. Then, this technique may become a powerful toot for dealing with these large quantity of seismic data and will show great ability for high-speed processing and epicenter discrimination.

232

5

Conclusion and Future Subjects

From the viewpoint of "reliable earthquake discrimination" and "immediate determination of epicenter," our method is thought to provide a simple and effective processing technique. Even by the simple parameter tuning implemented in this study, satisfactory results were obtained for earthquakes at the magnitude of 2.5 or over in inland areas and at the magnitude of 3.5 or over in coastal areas. In the conventional automatic data processing system, efforts have been made to correctly detect the seismic phase and solve the inversion in a stable form. In the future, however, it will be required to combine the algorithm shown in this chapter with the conventional technique, in order to obtain the reliable results without human intervention. Subjects to be addressed in the future are as follows. (1) While the STA/LTA of amplitude is used to create a pattern from the observed waveform at present, parameters that more closely represent the features of seismic wave should be used for the same purpose, by taking note on the changes in AR coefficient over time or VAI of amplitude. (2) Parameter tuning should be performed in detail for earthquakes and area to be discriminated. (3) To create a model pattern, a travel time table should be used to reflect the regional characteristics of three-dimensional crustal structure for travel time and attenuation. (4) The technique should be improved to cope with earthquake swarms and earthquakes that take place at different places almost simultaneously.

Acknowledgements We thank Earthquake Research Institute (the University of Tokyo), Nagoya University, Disaster Prevention Research Institute (Kyoto University), The National Research Institute for Earth Science and Disaster Prevention, Geological Survey of Japan, Tokyo Metropolitan Government and Kanagawa Prefecture for providing real-time waveform data. We also thank Tesuo Takanami, Taku Urabe, Toshiyuki Matsumori, Yasuhiro Yoshida, Shin-ichi Sakai, Yoshio Mural, and Hiroshi Ueno for their useful discussion and comments. Figure 2 was offered by Earthquake Observation Center (Earthquake Research Institute). We used the Generic Mapping Tool (Wessel and Smith 1995) for drawing some of the figures.

References Funakubo, N., 1991, Pattern Recognition (in Japanese), Kyoritsu Shuppan Co. Ltd., 172pp. Hamada, N., 1984, Re-examination of travel time table for local earthquakes, Papers in Meteorology and Geophysics, 35, 3, 109-167. Hirata, N., Matsu'ura, M., 1987, Maximum-likelihood estimation of hypocenter with origin time eliminated using nonlinear inversioin technique, Physics of the Earth and Planetary Interior, 47,50-61. Horiuchi, S., Matsuzawa, T., and Hasegawa, A., 1999, Automatic data processing system of seismic waves that works even at times of huge seismic activity (in Japanese, with English abstract), Zisin (J. Seismol. Soc. Jpn), 52, 241-254. Ide, S., 2000, Estimation of seismic source parameters and structure properties and application to regional swarm and wide area seismicity (in Japanese), Abstr. Seismol. Soc. Jpn., 2, P066. Maeda, N., 1985, A method for reading and checking phase times in auto-processing system of seismic

233

wave data (in Japanese, with English abstract), Zisin (J. Seismol. Soc. Jpn), 38, 365-380. Matsumura, S., 1989, Computer-based systematization of seismic data processing and its progress (in Japanese, with English abstract), Zisin (J. Seismol. Soc. Jpn), 42, 371-390. Morita, Y. and Hamamachi, H., 1984, Automatic detection of onset time of seismic waves and its confidence interval using the auto regressive model fitting (in Japanese, with English abstract), Zisin (J. Seismol. Soc. Jpn), 37, 281-294. Shirai, K. and Tokuhiro, I., 1979, Detection of seismic wave onsets (in Japanese, with English abstract), Zisin (J. Seismol. Soc. Jpn), 32, 141-147. Takanami, T. and Kitagawa G., 1988, A new efficient procedure for the estimation of onset times of seismic waves, J. Phys. Earth, 36, 267-290. Urabe, T. and Tsukada, S., 1992, win - a workstation program for processing waveform data from microearthquake networks (in Japanese), Abstr. Seismol. Soc. Jpn., 2, 331. Yokota, T., Zhou, S., Mizoue, M., and Nakamura, I., 1981, An automatic measurement of arrival time of seismic waves and its application to an on-line processing system (in Japanese, with English abstract), Bull Earthq. Res. Inst. Univ. Tokyo, 55, 449-484.

234

Extraction of Hydrological Anomalies Related to Earthquakes Norio Matsumoto 1 and Genshiro Kitagawa 2 1 Geological Survey of Japan, National Institute of Advanced Industrial Science and Technology, Tsukuba 305-8567, Japan, n. mat sumoto@ai s t . g o . j p The Institute of Statistical Mathematics, Minato-ku, Tokyo 106-8569, Japan, kitagawa@ism, ac. _~p

Abstract. Time series analysis using state space modeling is applied to extract hydrological anomalies related to earthquakes. This method can break down the observed groundwater level and/or groundwater discharge into four components: (1) burometfic response, (2) response to earth fide, (3) observation noise component and (4) 'residual water level', which means gradually' changing trend of the observed data. Groundwater level observed at Haibara observation well Shizuoka Prefecture, central Japan is analyzed by this method. In the groundwater level at the Halbara well, 28 coseismic changes are detected during the period from April 1981 to December 1997. There is threshold in the relationship between magnitude and hypocentral distance of the earthquakes, which affect the coseismie changes in the residual water level. All of the coseisrnic changes of the water level at Halbara are decreasing, however, 33 % of estimated coseismic step of volumetric strain is contraction. qq~s result shows the whole amount of the residual water-level change at the Haibara well is not explained by the hypothesis that the water level of confined wells changes in response to volumetric strain. Four possible pre-earthquake changes are detected in the residual water level at Haibara well. Finally, we show the relationship between this method and the TANK model, one of the conceptual runoff models, in the estimation of the response to precipitation.

1 Introduction Many hydrological anomalies related to earthquakes are reported (Roeloffs, 1988). Most anomalies are coseismic, but some o f them are preseismic (Roeloffs, 1996). In order to know mechanism o f the hydrological anomalies, it is very important to extract exact quantities o f them. Since observed water level includes responses to the barometric pressure, earth tide and rainfall, suitable corrections should be applied to extract anomalous changes from the observed water level. Quilty and Roeloffs (1991) developed a frequency-dependent transfer function method to eliminate frequency-dependent barometric response and regression analysis using two coefficients for each major tidal constituent. Meanwhile, Igarashi and Wakita (1991) and Koizumi (1993) applied the computer program BAYTAP-G (Bayesian Tidal Analysis Program in a Grouping Method) (Akaike et al., 1985; Tamura et al., 1991) for their own groundwater level or discharge to estimate the baromeuic and the tidal responses. This method breaks down the observed water level into barometric and tidal responses, noise component and 'trend component', which gradually changes using Bayesian analysis. Although these two methods are among the best methods to estimate the tidal and barometric responses,

235

these methods are not sufficient if the data changes in response to the precipitation because they cannot estimate the response to precipitation. Kitagawa and Matsumoto (1996) and Matsumoto (1999) proposed a method which break down the observed water level into barometric and tidal responses, response to precipitation, noise component and residual groundwater level using the Kalman filter via state space representation (Kalman, 1960; Kitagawa and Gersch, 1984). In this chapter, we review this method and the application to groundwater level observed at the Haibara observation well, Shizuoka Prefecture, cenlral Japan during the period from April 1981 to December 1997, which Matsumoto et al. (2001) describes in detail.

2 2.1

Analysis Method Modeling of Groundwater Level

The following model for the break down of the observed groundwater level y~ (n = 1 , . . . , N) is considered: Yn = t,, + Pn + En + P~ +r

(1)

Here, tn is the residual water level, Pn is the barometric response, En is the tidal response, / ~ is the response to precipitation and varepsilon,~n is a Gaussian white noise with zero mean and variance ~r2. Both P,~ and E,~ are assumed to be expressed by regression model of observed barometric pressure p,, and theoretical earth tide e,~ of the observation site with a lagged term as follows: l

P'~ = E aip~-i

(2)

i=0

E,~ --- ~

b~e~_~

(3)

i=0

(Matsumoto, 1992). The R~ is assumed to be expressed by the following ARMAX type model (Box and Jenkins, 1970), /e

k-1

i=1

i=0

(4)

using observed precipitation r,~. The residual water level t,~ is assumed to change gradually, and satisfies the following random walk model: t,, = t,,_~ + v~, v,~ ~ N ( 0 , ~-~). (5) Anomalous changes of t~ are compared with the occurrence time of earthquakes whether the anomalies depend on the earthquakes or not.

2.2

State Space Modeling and Kalman Filter

The unknown parameters in the observed water-level model are t,~,/~ (n = 1 . . . . . N), a0, .... at, bo. . . . . bin, cl . . . . . cA, do. . . . . dk-1, ~-2 and if2. The Kalman filter via state space

236

representation (Kalman, 1960; Kitagawa and Gersch, 1984) is applied for the estimation of such huge parameters. The generic state space modeling is x~

=

F~x~-I

y,~

=

Hnx,

+

+

(6)

G,v,

(7)

~,~,

(Kalman, 1960). Specifically, our model for groundwater level y,~ given in (1)-(5) can be expressed as: xn

= . Fxn-1 + Mrn + Gvn

y~

=

(8) (9)

+z~,

H,,x.

where x~ is the state vector defined by x , = ( t,~ , n o , . . . ,

a,, , bo , . . . , b,~ , I ~ A , . . . , R~_k,k ) t.

(10)

F, M, G and H,~ are defined by

!s

I~+1

F =

cl

1

."

(11) ".,

c~_~

1

Ck

G = (1, o, o, o,..., o, o)~', M = (0,...,

O, d o , . . . ,

dk-2, dk-1) T,

H , = (1,p,~,... ,p,~_~, e,,,..., en-.,~, 1, 0 , . . . , 0),

(12) (13) (14)

where Rnz is defined by R~,I = Rn and for j = 2 , . . . , k k-I

k

Rnz = E

ciP~+j-i-1 + ~

i=j

d~r,~+j-,-1.

(15)

i=j 1 -

If matrices F, G, M, H,~, initial state vector x010, its initial variance covariance matrix Voica2 , and the ratio of variances (T2 /o-2 ) are given, x,~ can be easily estimated using the following recursive Kalman filter computation (Kalman, 1960; Kitagawa and Gersch, 1984). In the procedures, the notation x,~l~denotes the estimates of the state at the time n when the observation Yz . . . . . y~ are given in advance. The following procedures are modified from the generic Kalman filter computation since the state vector x , is modified in (6). Furthermore, when ~72 is stationary with time, the ratio 7--~/~2 is the essential parameter, and ~ can be automatically determined (Kitagawa, 1993). ' O n e -step a h e a d p r e d i c t i o n ' Xn!n-1

=

FXn-lln-1 + Mr~

(16)

V.In_ I

=

9 t + T~GGt FI~,~_II~_IF crg.

(17)

237

'Filtering' K,~

=

X~l,~ = ~'~1,~ =

l,~b_iH,,t(H,~V,o,_iH,~ ~ + 1) -a

(18)

x~b_l + K,~(y,~ - H , ~ z n b - i ) (~ - g,,)V,~,,_l.

(19) (20)

When the ratio 7-2/a ~ and elements of F, G, M and H,~ are specified, we can automatically calculate t,~b, P~ (n = 1. . . . . N), ao . . . . . al, bo. . . . . b,~ as a result of the estimation of x,~l,~using this algorithm. Thus, the unknown parameters are reduced to cl . . . . . ck in F, do . . . . . dk--i in M and the ratio ~-2/a2 under the specified orders l, m and k.

2.3

Estimation of Parameters and Orders

The maximum likelihood method is used to estimate unknown parameters of the model with specified orders l, m and k. The log-likelihood of the water level model, L(O), can be calculated by N

L(O) =

-~1 (N log 27r,cr2 +

E

log D,q,~-i + N),

(21)

n=l

where Y,~b-i -Dnl,,-1 =

H,~X,~ln_i H,~b-iH,~

(22) (23)

t+ 1

1 ~r (y,, - y,~l,~_l)2

(24)

(Kitagawa, 1993). For these expressions, we can use the results of the Kalman filter computation. The maximum likelihood estimates Of the parameters are obtained by maximization of (21). The simplex method, one of the non-linear optimization methods (e.g. Kowalik and Osborne, 1968) is used to estimate the 2k + 1 optimal parameters. The best orders l, m, k of the model are determined by Akaike's minimum AIC procedure (Akaike, 1973; 1974). The AIC is defined by AIC = - 2 log(maximized likelihood) + 2 x (number of fitted paxameters).

(25)

In tiffs water level model, AIC is AIC = - 2 x L(O) + 2 x ( l + m + 3

+ 2 • k).

(26)

The best model is determined from the orders with the smallest value of (26).

3

Presentation of Data

The analysis method is applied to the groundwater level data at the Haibara well, Shizuoka Prefecture, central Japan. The observed period is from April 1981 to December 1997. The

238

i

,

9

,

5Okra

,

Oi River

]

,S

["""-~'~

Mr..Furl [

, ~.~

[

k5~I~l

Ka.IIl aa~t

138"

139" E

Fig. 1, The location of the Haibara observation well.

July, 1982 Observed ground water level

3.6

(hPa) l 1010'

(ram) 40

60

Observed barometric pressure ,~a.

V vV

t'~x

"

Observed precipitation

Theoretical earth tide (nano strain)

^ A ^ A A A A X x ^.,....,_A ^WAWAWAWAWA.A.A.,.,,,..,,,, ^^ W t.,v~ u165165 ,,4wv

0 rw WW WW WWWWlNp u u165

-6o

~

1~

1'6

"1']me (day)

2'1

~

3'1

Fig, 2. The observed groundwater level, barometric pressure, precipitation and theoretical earth tide at the Haibara observation well in July, 1982. The blank parts of the line denote missing data.

239

latitude, longitude and altitude are 34.7903~ 138.1881~ and 58 m, respectively. Fig. 1 denotes the location of the Haibara well. The diameter and depth of the well are 0.2 m and 170 m, respectively. The surrounding rock from the depth of 3 m to 170 m is sandstone and mudstone of late Miocene to Pliocene at the Haibara well. The well is screened from the depth of 71 m to 154 m. The transmissivity of the wall rock obtained by the hydraulic test in January 1979 was 4.6 x 10 -6 m2/sec. In March 1993, cleaning of the well and another hydraulic test were carried out and the transmissivity was 1.6 x i0 -~ m2/sec. The accuracy of the observed water level, barometric pressure, precipitation is -t-1 ram, 1 hPa and 1 mm, respectively. The water level, barometric pressure and precipitation data are observed every 2 minutes, and the data is send to the National Institute of Advanced Industrial Science and Technology (AIST) every 1 hour. The observed water level, barometric pressure, accumulated precipitation and theoretical earth tide at the Haibara well are shown in Fig. 2. The water level data resampled every I hour is analyzed by our method.

4

Changes of Residual Water Level

Matsumoto et al. (2001) estimated the residual water level t,q,~, the three aseismic responses and noise component from the observed water level at Haibara weU (Fig. 3). Fig. 4 shows observed and residual water level during the period from April 1981 to December 1997 using the model (1). When the residual water level is compared with the earthquake catalog of the Japan Meteorological Agency, 28 coseismic changes of the water level are recognized more than 0.66 cm during a 200 month period (Matsumoto et al., 2001). Table 1 shows the list of the earthquakes which induced the changes of the water level. Fig. 5 shows the relationship between the magnitude of the earthquakes M and the hypocentral distance D i s from the Haibara well (Matsumoto et al., 2001). Of the entire 28 earthquakes, which caused residual water level drops, 26 earthquakes satisfy the relationship M > 2.45 log D i s + 0.45 during the period from April 1981 to December 1997. This means that there is a threshold between the magnitude and hypocentral distance of earthquakes, which caused the coseismic water level changes. There is the hypothesis that groundwater level of a confined aquifer changes in proportional to volumetric strain (Bredehoeft, 1967). The 28 coseismic changes are used to check whether or not the hypothesis is applicable to the water level in the Haibara well. Coseismic volumetric strain changes are estimnted by Okada's method (Okada, 1992) for point sources. Harvard CMT catalog (http://www.seismology.harvard.edu/CMTsearch.html) is used for the point source mechanisms. Table 1 shows estimated coseismic volumetric strain steps in each earthquake. Although all of the residual water level is decreased, 33 % of the estimated volumetric strain denotes contraction. Fig. 6 shows the relationship between the estimated coseismic steps of volumetric strain S~ and coseismic changes in the residual water level hco~ (Matsumoto et al., 2001). The relationship S~ = 0.59 h~os is obtained by the least square method with a low correlation. It means that the water level sensitivity to the strain is 1.69 cm/10 -g volumetric strain. Meanwhile, the tidal response in the water level is 0.016 cm/10 -9 volumetric strain at Haibara which is 1/106 of the strain sensitivity obtained by the coseismic changes. These two results show that the water level at Haibara cannot be explained by the hypothesis that the water level in the confined wells changes in response to volumetric strain.

240

198eLed Wier Level .

i t0o

Barometric R~sponse

I

Tidal Response Rain Response Noise Component Corrected water level I

May

~MT.0,375km

I

Jun. Jul. Time (month)

I

Aug.

Fig. 3. Observed water level, barometric and tidal responses, response to precipitation, noise component and residual water level from May to August 1982.

241

1990 15 "-%-.

~ - " ' Z

1992

-

r'7"

-~ .-~ _

--.--1993clearing of well ~l~l and

- .

Il~ 195 ~

.---'-'-" ,

~' J F MA MJ 1985 ~ .

J A S O N D J .

.

.

.

.

.

F MA

MJ

~22 ,.

13~ 23~

1988

D

..~.~._._.,~---..~__...

1995 1987

J A S ON

.

~

. . . .

~24

~25

~26

...

sensor

199._._7 ,27

f~.._!' ~

,

J

F MA

MJ J A S O N D J Time (month)

F MA

ff

I

v,'v

MJ J A S O N D Time (month)

Fig. 4. The observed water level (tbJn/Lnes) and the residual water level (thick line) from Apr;J 1981 to December 1997 (Matsumoto et al., 2001). The number on the earthquake is are same a.s Table 1.

242

Table 1, Earthquakes that induced changes in the groundwater level (Matsumoto et al., 2001). Magnitudes of the residual water-level changes and estimated coseismic steps of volumetric strain are also shown. The h co, denotes the magnitude of decrease in the residual water level. 'Est. strain' denotes the estimated coseismic strain step calculated by Okada's method (Okada, 1992). The ' - ' for h co, indicates that the magnitude of the decrease cannot be measured because of missing data. The 'N/A' in the 'Est. strain' denotes that the CMT mechanism of the earthquake is not available in the Harvard CMT Catalog. No.

date

Dis (krn)

M

heo,, (era)

Lat. (deg.)

Lon. (deg.)

Est. strain (10-9)

1 2 3 4 5 6 7 8 9 10 ll 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Aug.15,1981 Jul.23,1982 Dec.28,1982 Mar.16,1983 May.26,1983 Aug.8,1983 Oct.3,1983 Nov.24,1983 Mar.6,1984 Sep.14,1984 Jun.24,1986 Nov.22,1986 Dec.17,1987 Oct.15,1989 Feb.20,1990 Sep.24,1990 Apr.25,1991 Sep.3,1991 Ju1.12,1993 Oct.4,1994 Dec.28,1994 Jan.17,1995 Feb.l,1996 Mar.6,1996 May 27,1996 Oct.5,1996 Mar.16,1997 Oct.11,1997

41.9 375.0 155.9 65.9 621.9 113.1 150.4 57.0 741.6 127.9 241.7 126.2 226.7 122.1 95.9 199.7 43.9 139.9 888.8 1253.7 794.3 289.8 13.2 104.4 33.7 36.2 73.3 54.4

4.8 7.0 6.4 5.7 7.7 6.0 6.2 5.0 7.9 6.8 6.5 6.0 6.7 5.7 6.5 6.6 4.9 6.3 7.8 8.1 7.5 7.2 3.6 5.8 4.2 4.3 5.8 4.9

6.4 3.5 3.6 4.4 1.8 2.6 1.9 14.9 1.3 3.1 3.5 1.7 8.1 1.3 1.1 3.0 1.0 7.4 1.3 3.9 0.8 2.2 3.1 1.1 8.8 6.2

34.80 36.18 33.87 34.79 41.26 35.52 34.00 34.73 29.34 35.82 34.82 34.55 34.37 34.82 34.76 33.1 35.06 33.68 42.78 43.37 40.43 34.59 34.76 35.47 34.96 34.97 34.92 34.42

138.05 141.95 139.45 137.61 139.00 139.03 139.51 137.71 139.21 137.56 140.72 139.53 140_50 129.50 139.23 138.63 138.21 138.83 139.18 147.71 143.75 135.04 138.33 138.95 138.21 138.05 137.53 138.23

N/A 1.10 2.43 1.43 -2.12 -0.59 1.80 0.32 0.26 2.14 3.47 0.50 2.16 0.40 13.37 4.16 N/A 5.64 -1.07 -4.00 -0.18 7.05 N/A -0.10 NIA N/A 1.86 -0.91

243

M = 2.45 log Dis + 0.45 ~ ~,~ _

9" With coseismic change x No change

s s

s,i'

., .E 9 R

~7,"

H B B []

[]

e-

J~ ~N

1.1.16-

~ ~&x

x

/ x ~," x 9

x

x

x

~

x

,'x x wx x s9 x z~ lxx x ,.~ x xlc xxx ~m~

x

," o*X

x

.,

x xm s n e a ~ s t

9

x9 x x 9

x x ~ : e n a ~ n ~uq m

,+-

o

x ~ ,'

x

9 ~ x z m m

,4,,-'

~5-

[ ] m / na ,, 9 x

wx

~

aN

N

~ x

4-

," ,"

,,'

x I~xlc x l c z

z ii

x

-' 2.~ .'T~ -

H

I

I

I

I

50

100

500

1000

Hypocentraldistance Dis (km)

Fig, 5. Scatter plot between the magnitude of the earthquakes, M, and hypocentral distance, Dis, during the period from April 1981 to December 1997 (Matsumoto et al., 2001).

244

14 '9'-

12

'~ 8

4 2

E

-2

m

-4 0

L~cos 1;%" S' ~"

2

9

4 8 10 12 14 Coseismic groundwater-level drop, hcos (crn)

16

Fig. 6. The relationshipbetweenthe estimatedcoseismicstep S,~ of volumetricstrain and coseismicchanges hco, in the residual water level. Dashedline denotesthe relationshipbetween these two changes, S,, = 0.59 h~os determiaedby the least square method(Matsumotoet al., 2001). In other words, there might be other mechanism which affect the changes of the water level. In Fig. 4, there are four anomalous increases of more than 1.5 cm in the residual water level, which were independent to heavy rainfall: 1) March 1983, 2) September 1984, 3) September 1994 and 4) November 1994. Fig. 7 shows the magnification of each change. Except case No.4, the increases occurred within 6 days before the earthquakes. Event No.4 occurs between the Hokkaido-toho-oki (Kuril) earthquake (M8.1, No.20 in Table 1) and the Hyogoken-nanbu (Kobe) earthquake (M7.2, No.22 in Table 1). Cases No.3 and No.4 have increases of more than 2.5 cm. These increases seem to be pre- or inter-earthquake changes of the residual water level probably affected by changes of the aquifer system related to local crustal deformation.

5

Statistical and Conceptual Modeling for the Response to Precipitation

In the previous section, the third order model is an optimal model for estimating the response to precipitation at the Haibara well. In this section, the optimal model is considered to be the proper response to precipitation and compared to a linear conceptual runoff model, the linear TANK model with three tanks (Sugawara et al., 1983; Sugawara, 1995). The third order model of the (4) is expressed by Rn=clP~_l

+ c2R~_2 + c 3 R n - a + d o r n + d l r n - 1 + d 2 r n - 2 .

(27)

Using the backward shift operator B ( B / ~ = / ~ - 1 ) , (27) is expressed by (1 - c l B - c2B" - c3B3)p~ = do(1 + do

+

B2)rn"

(28)

Then, 1 - clB-

c2B 2 - c3B 3 = 0

245

(29)

J 1984

F

,.. _ . ~ j - , . , , . _

M

_

A

~ 411

Case B

I5~'n

"x,~ I

I

M

I

J

J

I

1

A

S

O

1994-1995 /{21

~..--J'

T

/

Case C

22 ~

2

i'= 3

Case D !

A

I

S

I

I

O N D Time (month)

!

I

d

F

Fig. 7. Magnification of the four pre-earthquake rises of more than 1.5 cm in the residual water level. The number on the earthquake is same as Table 1.

~

Kr.

x,l

1 Ik2

x21-L x,l Fig. 8. Schematic figure of the linear TANK model with three tanks.

246

Table 2. The coefficientsof the responseto precipitationek (no unit) and d, (x 10-4 m/mm) obtainedby applying this methodfor entiredataset (Matsumotoet aI., 2001). k 0

e~

dk 1.664

1 1.931 43.002882 2 -1.043 -1.387 3 0.1107

is the characteristic equation for the R,~ part (autoregression part) and dl B l+d0 + ~d2 B.~ =0

(30)

is the characteristic equation for the r , part. There are three constraints for the coefficients of (27) to make the proper response to precipitation: i) all absolute values of the roots of the characteristic equations (29) and (30) should be larger than 1 for stationarity (Harvey, 1981), ii) all of roots of the characteristic equation (29) should be real to avoid an oscillatory response to precipitation (Spolia and Chander, 1974; Harvey, 1981), Table 2 shows the coefficients cl, c2, c3, do, dl and d.~ as a result of the application for the period from April, 1981 to December, 1997 (Fig. 4, Matsumoto et al., 2001). They satisfy the constraints i) and ii) although we have no constraints when we estimate those optimal coefficients by maximizing the log likelihood (21) using non-linear optimization. When (27) is expressed by oo

R~ = y ~ g~r~--i,

(31)

i=0

the relationship between ci, di and g~ are:

do g,~ =

(n=0)

--.

d,~ + ).-]i=1 c~9--i (0 < n < 3) k E~=I c~g._~

(32)

(n > 3)

(Harvey, 1981). Fig. 9 shows responses to the unit precipitation using coefficients in Table 2. The response function of the precipitation is estimated properly as shown in Fig. 9. The linear TANK model with three tanks shown in Fig. 8 is d X l,~

dt dX2~ dt dX3.

=

Kr~ - (kl + k2)Xl,~

(33)

=

k 2 X l ~ - (k3 + k4)X2,~

(34)

k4X2~ - k s X 3 .

(35)

k l X l , ~ + k a X 2 n + ksX3n.

(36)

-

dt I~

=

The discrete representations of (33) - (35) are XI,~ - XI,~_I

=

K r ~ - (kl + k 2 ) X l ~

(37)

X2~ - X 2 n - I

=

k 2 X I ~ - (ka + ka)X2~

(38)

X 3 ~ - X3~_1

=

k4X2~ - k s X 3 . .

(39)

247

O.._.

~a~E E o,5 ~ E 0.4 ._E E

o.a

o .~ 0.2 ~ .1 t--0._Q~ , ~O O,C O

o

2oo

n"

Time (hour)

Fig. 9. The responsefunctionto the unit precipitationusing the coefficientsc 1, c~, c3, do, dt and d2 shown in Table2 (Matsumotoet al., 2001). Using these equations, the equivalent expression of the response to precipitation is shown in (49) of Appendix A. The relationship will be obtained between the coefficients of the ARMAX type model and coefficients of the tank model by comparing (27) and (49): ci

=

do =

af+~7+~/a aft7

, c2 -

a+f+^f off"/

K fl? + k29' + k2k4 af'~,

1 , Ca = a/37,

K f l +"/ + k2,d2 = K , ~1 = -

c,/~

(40) 1

(41)

c,f---~"

In order to be able to express (27) equivalent to the linear TANK model (49), the coefficients c~, c2, ca, do, dl, d~ of (27) must satisfy the following relationships by the comparison between (27) and (49) additionally:

>0, c2<0~ca>0,

(42)

do > 0, d, < 0, d2 > 0.

(43)

cl

Because a,/3, 7, K, k2, k4 > 0 in (40) and (41), since K, kl, .. 9 k5 > 0 in (48). The estimated coefficients are properly estimated as we mentioned previously, but are not regarded in the linear TANK model because d2 < 0.

6

Conclusions

The time series analysis method using state space modeling is proposed to detect anomalous changes of the water level. Using this method, not only the coseismic changes but also the possible preseismic changes can be detected because we can estimate the barometric and tidal responses with a lagged term, the response to precipitation, and the noise component and eliminate those responses from the original observed groundwater level. After applying the method for the groundwater level at the Haibara well, 28 coseismic changes are detected during the period from April 1981 to December 1997. There is the relationship M >__2.45 log Dis+0.45 between the magnitude, M, and hypocentral distance, Dis, of the earthquakes, which affect the coseismic changes in the residual water level at Haibara, The water-level changes at the Haibara well cannot be explained by the hypothesis

248

that the water level of confined wells is proportional to volumetric strain because o f a low correlation between the amount o f the coseismic water level and estimated coseimic step of volumetric strain. There are four anomalous pro- or inter-earthquake changes in the residual water level at Haibara well. The T A N K model, one of the well known conceptual runoff models, and statistical method to estimate the response to precipitation in the p r o p o s e d method are compared. Although the estimated coefficients at Haibara are not applicable to the T A N K model because d2 < 0.0, the estimated response is sufficient to describe the response to precipitation because there are neither an osciUatory nor unstable response to the unit precipitation. The proposed method is also useful for the leveling, tiltmeter and strainmeter time series data if they contain signals related to earthquakes and are contaminated with responses of the barometric pressure, earth tide, rainfall and observation noise.

Acknowledgments We greatly appreciate E. A. Roeloffs for her many suggestions and detailed comments.

References Akaike, H., 1973, Information theory and an extension of the maximum likelihood principle, in Second International Symposium on IrfformationTheory, edited by B. N. Petrovand and F.Cald, Akademiai Kiado, Budapest, 267-281. Akaike, H., 1974, A new look at the statistical model identification, IEEE Transactions on Automatic Control, AC- 19, 716-723. Akalke, H., Ozald, T., Ishiguro, M,, Ogata, Y., Kitagawa, G., Tam~a, Y-H., Arahata, E., Katsura, K. and Tamura, Y., 1985, TIMSAC-84 Part 1, Computer Science Monographs, No.22, The Institute of Statistical Mathematics, Tokyo. Box, G. E. R and Jenkins, G. M, 1970, Time series analysis, forcasting and control, Holden-Day, San Francisco, Calif. Bredehoeft, J. D., 1967, Response of well-aquifer system to Earth tide, J. Geophys. Res., 72, 3075-3087. Duncan, D. B. and Horn, S. D., 1972, Linear dynamic recursive estimation from the viewpoint of regression analysis, J. American Statistical Association, 67, 815-821. Harvey, A. C., 1981, Time series models, Philip Allan Pub. Ltd, Oxford. Igarashi, G. and Wakita, H., 1991, Tidal responses and earthquake-related changes in the water level of deep wells, J. Geophys. Res., 96, 4269-4278. Kalman, R. E., 1960, A new approach to linear filtering and prediction problem, Trans. ASME, Journal of Basic Engineering, SenD, 80, 35-45. Kitagawa, G,, 1993, Fortran77 Programming for time series analysis, Iwanami Publishing Co. Ltd (In Japanese). Kitagawa, G. and Gersch, W., 1984, A smoothness priors - state space modeling of time series with trend and seasonality, J. American Statistical Association, 79, 378-389. Kitagawa, G. and Matsumoto, N., 1996, Detection of coseismic changes of underground water level, J. American Statistical Association, 91, 521-528. Koizumi, N., 1993, Frequency dependence of the groundwater discharge at an artesian weU as recognized from tidal fluctuation records, J. Geophys. Res., 98, 825-835. Kowali_k.J. and Osborne, M. R., 1968, Methods for unconstrained optimization problems, Elsevier Publishing Company, Inc. Matsumoto, N., 1992, Regression analysis for anomalous changes of ground water level due to earthquakes, Geophys. Res. Lett., 19, 1193--1196. Matsumoto, N., 1999, Detection of groundwater level changes related to earthquakes, in The practice of time series analysis, edited by H. Akaike and G. Kitagawa, Springer-Verlag New York, Inc., 341-352. Matsumoto, N., Kitagawa G. and Roeloffs, E. A., 2001, Hydrologic response to earthquakes in the Haibara welt, central Japan: I. Groundwater-level changes revealed using state space decomposition of atmospheric pressure, rainfall, and tidal responses, submitted to Geophys. J. Int.

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Okada, Y., 1992, Internal deformation due to shear and tensile faults in a half-space, Bull. Seismol. Soc. Am., 82, 1018-1040. Quflty. E. G., and Roeloffs, E. A., 1991, Removal of barometric pressure response from water level data, J. Geophys Res., 96, 10209-10218. Roeloffs, E. A., 1988, Hydrologic precursors to earthquakes: a review, Pure Appl. Geophys., 126, 177-206. Rceloffs, E. A., 1996, Poreelastic methods in the study of earthquake-related hydraulic phenomena, in Advances in Geophisics, edited by R. Dmowska, Academic, San Diego, Calif. Spolia, S. K, and Chander, S., 1974, Modeling of surface runoff systems by an ARMA model, J. Hydrol.. 22, 317-332. Sttgawara, M., Watanabe, I., Ozaki, E. and Katsuyame, Y, 1983, Reference Manual for the TANK model, National Research Center for Disaster Prevention, Tokyo. Sugawara, M., 1995, Automatic calibration of the tank model, in Computer models of watershed hydrology, edited by V. P. Singh, Water Resources Publication, Colorado, 164-215. Tamura, Y., Sato, T., Ooe, M. and Ishiguro, M., 1991, A procedure for tidal anlysis with a Bayesian information criterion, Geophys. J. Inter., 104, 507-516.

A

Appendix: Response to Precipitation by using the Linear TANK Model

The discrete m o d e l (37) - (39) are represented by (1 - B ) X 1 .

=

K r . - (kl + k2)Xl,~

(44)

(1 - B ) X 2 ~

=

k 2 X l . - (ka + k 4 ) X 2 .

(45)

(1 - B ) X 3 n

=

k4X2,~ - k~X3n.

(46)

using the backward shift operator B. the Rn becomes =

+

k2

k2k4

( a - B ) ( ~ - B ) + ( a - B ) ( 5 - - - B ) ( 7 - B-)

)

r,~

(47)

from (44) - (46), where a=l+ki+k2,

fl=l+k3+k4,

7 =l+k~.

(48)

Finally, P ~ is expressed by

c~+~7+ ~ 7 7~P~-1

~+~+ 1 ~/~7 7R~-~ + S-~ P~-3

+ K f l ' y + k27 + k2k4 K fl + 7 + k2 1 aft 7 rn -aft7 rn-1 + K - ~ r n - 2 .

250

(49)

On the Realtime Monitoring of the Long-Period Seismic Wavefield Hitoshi Kawakatsu Earthqtkake Research Institute, University of Tokyo, 1-1-1, Yayoi, Bunkyo-ku, Tokyo, 113-0032, Japan [email protected]

Abstract. A possibility of monitoring the long-period seismic wavefield in realtime is suggested. The seismic wavefield below 0.1 I-Iz may be consistently modeled by the earthquake activity field defined by a point source moment tensor on 10 kin-mesh grid points. With the current level of personal computers, it should be possible to perform moment tensor inversions for all the mesh points to find the best moment tensor every second. A sparse regional broadband seismometer network appears suffice to perform such realtime monitoring, which may eventually enable us to predict the short-period ground motions in realtime as well.

1 Introduction As a result o f continuous activities of the earth -- earthquakes and volcanoes are familiar examples for geophysicists, but flows in the mantle, ocean, and atmosphere are also such manifestations (e.g., Suda et el., 1998) -- the solid part of the earth vibrates elastically to generate the seismic wavefield (SWF). Due to the great advances in global seismology, led by the deployments of global digital seismic networks (e.g., IDA, GDSN, GEOSCOPE, POSEIDON etc...), the very-long-period part of the seismic wavefield is now well understood, and corresponding activities of the earth (let us call this "the earthquake activity field (EAF)") are n o w routinely determined by various institutes around the world (e.g., Dziewonski et el., 1981; Sipkin, 1993; Kawakatsu, 1995). From the view point o f seismic source analysis, the eternal goal of seismology may be defined as to monitor in realtime the seismic wavefield to infer the corresponding earthquake activity field. The purpose of this short note is to suggest that such realtime monitoring of the long-period seismic field may now be possible using data from sparse broadband seismic network on a regional scale.

2

Long-Period Seismic Wavefieid vs. Earthquake Activity Field

Seismic moment tensor determination of regional earthquakes is now becoming a common approach for monitoring regional seismieity (e.g., Dreger and Helmberger, 1993; Romanowicz et al., 1993; Thio and Kanamori, 1995; Fukuyama et al., 1998). At the Earthquake Research Institute, we have developed an automated scheme using data from the regional broadband seismic network deployed in the Kanto area (Fig. 1). The system is initiated by e-mail from JMA (Japan Meteorological Agency) when JMA detects an earthquake in the area. For the actual moment tensor inversion, broadband data are low-pass filtered at 0.1 I-Iz, and a laterally homogeneous flat layer structure is assumed to calculate Green's function. JMA's initial location can be off as large as 10 km from the final JlVIA location, but such a location error usually does not alter the inverted moment tensor solutions significantly (Fig. 2; Ito and Kawakatsu, 1997; Ito, 1997). This observation indicates that the seismic wavefield below 0.1 Hz may be consistently 251

modeled by a point source moment tensor located on one o f the grid points o f 10 /an-mesh: i.e., the seismic wavefieId below 0.1 Hz can be modeled by the seismic activity field represented by a 10 kin-mesh. So the question is now whether or not such modeling can be done in realtime, and we suggest in the following that it is possible.

Broadband stations 138"

139"

140"

141"

142"

38"

38"

37"

37" r~aA

NUJ

Q KuJ

.~

/

9 GNZ

o(~-IlT

36"

36"

35"

35"

34"

.0 138"

139"

140"

141"

34" 142"

Fig. 1. Location of re~onal broadband seismic stations available in the Kanto area, Japan. The closed circles indicate the stations operated by the Earthqtmke Research Institute, and the stars indicate the stations of FREESIA network

252

Mechanism variation

(a)

r 0 +

Ol +

+ 0 0

=? 0|

-0.3

-0.2

-0.1

0.0

Longitude

+0.1

+0.2

+0.3

(degree)

Fig. 2 (a) Moment tensor solutions of an intermediate depth earthquake (t996/10/12 21:40 Mw=4.2) obtained on each grid point of I0 km-mesh. Numbers next to the focal mechanisms are estimated seismic moment (• ~5Nm). Only the best double couple component is shown. The location (0.0, 0.0) corresponds to the preliminary location given by JMA (after ko, 1997).

253

(h)

1996/10/25 12:25 M w 4.4 JMA 22.61tm

60

'

I

T

i

i

t

Depth(kin) Fig. 2 (b) Variance reduction as a function of depth of a shallow event (1996/10/25 12:25 Mw=4.4). The epicenter is fixed at the best location. Corresponding moment tensor solutions (best double couples) are also shown. The variance reduction has a peak at the depth near the JMA's final depth estimate (22. 6kin), although the mechanisms are not so dependent on the depth, q-hcrefore, the variance reduction, which is a function of the residual (4), should allow earthquakes to be located.

3

Realtime

Monitoring

Let us think about a moment tensor inversion problem when the origin time and the source location are given. The observation equation to be solved for a source s and station k is

(1)

Z G~ (t)m] = d k(t), i

where G : * ( t ) a n d d k ( t ) a r e theoretical and observed seismograms at kth station (superscript k is used to represent all three component seismograms o f a station k) respectively, and m: is the /th component o f the m o m e n t tensor. The normal equation based on (1) is

~ , A:,m 7 = b;

(2)

i

where

9 = y,A::,

A j, =

Ia;,t (t)a;,t (t)d,,

k

b;" = Z b,,e

bj"

= I G j k ( t ) d ~(t)dt

k

(for simplicity we omit the superscript s when it is not confusing). Thus the least squares solution for the m o m e n t tensor is given in vector form by

254

ffa=A-Jb.

(3)

Because A is a cross-correlation between Green's functions, it can be readily calculated and stored once the structure model is chosen. Therefore, the moment tensor nh can be obtained by a simple matrix multiplication if b is determined. This shows that the procedure for estimating a moment tensor when a source location is given is almost equivalent with the calculating the cross-correlation between Green's functions and data. It can be further showla that model prediction error (residual between data and synthetic seismograms calculated for the estimated ffa is

Res = ( ~ ~dk (t)2dt) - b'A-~b,

(4)

k

which can be also easily calculated if we have b. It should now be clear that in order to monitor EAF fyom long-period SWF, we only need to be able to calculate the cross-correlation b for all possible source points on the 10km-mesh (hereafter referred as to "virtual sources"). For this to be done in realtime, two conditions must be satisfied: (1) all Green's functions can be stored in the computer memory, (2) the cross-correlation b can be calculated within a certain short time (the first can be considered as a necessary condition for the second). For the region of our interest CKanto area (34~ ~ 138~176 Fig. 1), these conditions appear to be satisfied. For stations with an epieentral distance of at most 400 km, all the major phases arrive within the first two minutes. Considering that we are dealing with a long-period wavefield above 10 sec, with one sample per two-second, each waveform contains 60 points. I f the horizontal and vertical grid sizes are taken to be 0.1 ~ and 10kin respectively, there will be 40• virtual source points in 4~215176 krn size area. The total size of the Green's function for each station to "memorize" is 60 (points) x 3 (components) x 16,000 ~rids) • 5 (moment tensors) • 4 bytes 57 Mbytes, which can fit in the memories of some recent PCs. As for the second condition, for one station, calculating b~ = ~G~ (t)d a (t)dt (j' = 1..... 5 for a deviatoric moment tensor) for all virtual sources (s = 1. . . . , 16000) takes only a second with recent fast PCs. It should, therefore, be possible to monitor the long-period wavefield for every second, if we assign one PC for each station. The best moment tensor solution (in the least-squares sense) for each virtual source s is fn ~ = ( A * ) - j . E b

'k ,

(5)

k

and the corresponding prediction error is (4). ~a s which gives the smallest prediction error is the "earthquake activity" most consistent with the long-period seismic wavefield of the time.

255

4

S e i s m o m e t e r as a Cross-Correlator

In the view of monitoring the long-period SWF presented above, a seismometer (or seismic station) can be considered as a machinery to correlate the long-period vibration with the vibration predicted by virtual sources: Conceptually, the role o f a seismic station is now said to be to estimate b ~ for all possible s every second, and to send them to the central computer, where b sk from different stations are summed to estimate b ~ = ~ k bSk for all s. The central computer multiplies(A') -~ tobSto obtainda" for all s, and chooses the best one using (4). This "solution" may be shown visually on a display, which then gives the EAF of the time (with few minutes delay). Of course, this whole process can be done on a single main-frame machine, not necessarily in the way suggested above by assigning a PC to each station.

5

Discussion

As shown above, it appears feasible to monitor the EAF in realtime using data from a sparse regional broadband network. It should then also be possible to "predict" in realtime the shorter period wavefield (if an earthquake occurs, it becomes a so-called strong motion wavefield) everywhere consistent with the estimated EAF. Thus we may be able to say that we have a realtime strong motion prediction machine based on data from a sparse regional broadband network. O f course, at first, the predicted strong motions may be quite different from the actual observations. But the system can be improved as our understanding of the each step o f the above procedure advances in the futttre; e.g., a better knowledge of the regional structure improves the Green's function, which may result in a smaller mesh size; a better knowledge of the site effect improves strong motion prediction; advanced source analysis such as that attempted by Kaverina et al. (1997) improves the estimation of the effects of rupture propagation, etc. What seems to be important is to realize that seismology is now at the stage where it is possible to start such realtime monitoring and prediction. The realtime monitoring of long-period SWF need not be restricted to the regional scale problem. Instead of the Green's function, we can correlate an observed wavefield with incoming plane waves. With this kind of monitoring, we may start seeing exotic seismic events which might have been overlooked by the conventional method o f event detection, in which seismic events are "detected" when coherent short-period signals are observed within a seismic network. For example, Kawakatsu et al. (1994) reported 10sec period volcanic signals observed at remote broadband seismic stations. Reports on longer-period signals on a global scale can also be found in many geophysical literatures (Kanamori and Given, 1980; Kawakatsu, 1989; Rouland et al., 1992; Shearer, 1994). Finally, we note that the realtime monitoring of the long-period seismic wavefield suggested in the present chapter seems even practical at Aso volcano, where long-period tremors of 15sec period are continually emitted from a known source (Kaneshima et al., 1996). Legrand et al. (2000) performed the grid-point moment tensor inversion (of 100m-mesh) and Kawakatsu et al, (2000) suggests the possibility of the realtime monitoring o f the volcano using long-period waveforms.

References Drcger, D. S. and Helmberger,D. V., 1981, Determinationof source parameters at regional distances with 256

single station or sparse network data, J. Geophys. Res., 98, 8107-8125. Dziewonski. A. M., Chou, T. -A., and Woodhouse, J. H., 1981, Determination of earthquake source parameters from waveform data for studies of global and regional seismieitT, J. Geophys. Res., 86, 2825-2853. Fukuyama, E., Ishida, M., Dreger, D. S., and Kawai, H., 1998, Automated seismic moment tensor determination by using on-line broadband seismic waveforms, Zisin, 5l, 149-156 (in Japanese with English abstract). Ito, W., 1997, Automated near-realtime CMT inversion for regional earthquakes, MS thesis. U. of Tokyo, pp. 66. Ito, W., and Kawakatsn, H., 1997, CMT inversion for earthquakes around the Kanto District. Abstr. Japan Earth and Planetary Science Joint Meeting, 786 Kanamori, H., and Given, J. W., 1980, Analysis of long-period seismic waves excited by the May 18, eruption of Mortar St. Helens: A terrestrial monopole, 1982, J. Geophys. Res., 87, 5422-5432. Kaneshima, S., Kawakatsu, H., Matsubayashi., H., Sudo, Y., Tsulsui, T., Ohminato, T., Ito, H., Uhira, K., Yamasato, H., Oikawa, J., Takeo., M., and Iidaka, T., 1996, Mechanism of phreatic eruptions at Aso volcano inferred from near-field broadband seismic observations, Science, 273,642-645. Kaverinm A., Dreger, D., and Antolik, M., 1997, Toward automating flrlite fault slip inversions for re#onal events, E.O.S., 78, F 45. Kawakatsu~ H., 1989, Centroid single force inversion of seismic waves generated by landslides, J. Geophys., R.es., 94, 12363-12374. Kawakatsu, H., 1995, Automated near-realtime CMT inversion, Geophys. Res. Lett., 22, 2569-2572. Kav,~akatsu, H., Ohminato, T., and Ito, H., 1994, 10s-tperiod volcanic tremors observed over a ~-ide area in southwestern Japan, Geophys. Res. Lett., 21, 1963-1966. Kawakatsu, H., Kaneshima, S., Matsubayashi, H., Ohminato, T., Sudo, Y., Tsutsui, T., Uhira, K., Yamasato, H., and Legand, D., 2000, Aso 94: Aso seismic observation with broadband instruments, J. Volcanol., Geotherm. Res., 101,129-154, Legrand~ D.: Kaneshima, S., and Kawakatsu, H., 2000, Moment tensor analysis of near field broadband waveforms observed at Aso volcano, Japan, J. Volcanol. Geotherm. Res., 101,155-169. Romanowiez, B., Dreger, D., Pasyanos, M., and Uhrammer, IL, 1993, Monitoring of strain release in central and northern California using_broadband data, Geophys. Res. Lett., 20, 1643-1646. Rouland, D., Condis, C., Parmentier, C., and Sourian, A., 1992, Previously undetected earthquakes in the southern hemisphere located using long-period GEOSCOPE data, Bull. Seism. Soc. Am., 82, 2448-2463. Sipkin, S., 1994, Rapid determination of global moment-tensor solutions, Geophys. Res. Lea., 21, 1667-1670, 1994. Shearer, P. M., 1994, Global seismic event d~teetion using a matched filter on long-period seismograms, J. Geophys. Res., 99, 13713-13725, 1994. Suda., N., Nawa, K., and Fukao, Y., 1998, Earth's background free osciLlations, Science, 279, 2089-2091. Thio, H.-K., and Kanamori, H., 1995, Moment tensor inversion for local earthquakes using surface waves recorded at TERRAscope, Bull Sei~n-a,Soc. Am., 85, 1021-1038

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