Pulse Coding in Seismology

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Pulse Coding

in Seismology

Maurice G. Barbier

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International Human Resources Development Corporation. Boston

Contents v

Preface

1

1 Introduction Historical Development Continuous Transmission of Discrete Pulses Pulse Coding Applications Time and Space Coding 2 Marine Pulse Coding: Sosie

Copyright © 1982 by International Human Resources Development Corpora tion. All rights reserved. No part of this book may be used or reproduced in any manner whatsoever without written permission of the publisher except in the case of brief quotations embodied in critical articles and reviews. For in formation address: IHROC, Publishers, 137 Newbury Street, Boston, MA 02116. ISBN: 0-934634-52-1 Cloth ISBN: 0·934634-40-8 Paper Library of Congress Catalog Card Number: 82-80776

Printed in the United States of America

Definition Characteristics Implementation Instruments Results The Advantages of Pulse Coding in Marine Seismology: Higher Degree of Multiplicity Examples of Results

3 Land Pulse Coding: Seiscode

1

2

4

6

7

9

9

9

11

12

13

15

16

24

24

25

27

27

Definition Theoretical Procedure Characteristics Theoretical Results

iii

iv / Contents

Field Implementation Examples of Results Further Possible Applications

33 34 36

4 Shallow Seismology Pulse Coding: Mini.Sosie

38

5 Pulse Sequences

41

Definition Computation of a Pseudo-Random Sequence Random Pulse Sequence Autocorrelation Functions of Random Sequences Comparison between a Pulse Sequence and a Sweep

6 Correlation Noise Definition Examples of Correlation Noise Signal to Correlation Noise Ratio Improvements

7 Decoding Process Definition Shift and Add Real Time Sosie Processing Use of a Field Correlator

41 42 47 49 53

55 55 59 65

74 74 75 76 82

References

87

Index

88

Preface Coding is used in a number of techniques that derive from com munication theory. Let us take the case of the telephone line, for instance, where the transmission medium is known. Thanks to coding, a single line can pass several independent messages simultaneously, thus improving the economics of the line. In seismic work the transmission medium is unknown, but the comparisqn of the output received signal with the hi put transmitted signal gives some information about this transmission medium. The more discrete messages transmit ted at the input, the better the subsurface will be known. The faster these discrete messages are transmitted, the lower the price for the information. A seismic message will be coded if, due to the energy transmission, the signals received by the geophones ca.nnot be interpreted without applying a special process called decoding. According to the above definition, two types of seismic coding exist. The first was developed by Conoco more than twenty years ago and commercialized under the trademark of Vibroseis. The coded signal is continuous and is sent into the earth using vibrators firmly coupled to the ground. The second type is represented by systems recently designed by Societe Nationale ELF Aquitaine, Production-SNEA (Pl. In this case any pulse seismic source can be used, e.g., a civil engineer ing rammer. In the case of Mini-Sosie, the code consists of a series of different time intervals between the transmitted v

vi / Preface

pulses. It is therefore a discontinuous coded signal. There are at least two reasons to justify the use of seismic coding. The first one is the possibility of increasing the transmitted energy by exploiting the parameter of the length of transmission instead of the peak power of the source. The consequent energy increase is obtained without any loss of resolution on the final seismogram. A vibrator can transmit a sweep of variable length without affecting the shape of the au tocorrelation function of this signal. Only the amplitude changes. A pulse source, when used with a coded system, can be fired as often as its specifications allow without being obliged to leave a listening time after each pulse. It is only the shape of the individual pulse which must be considered with regard to the resolution. A second reason to justify coded systems is the possibility of separately processing several streams of seismic data which have been simultaneously recorded through the same seismic channel. More information can then be obtained during the same recording time and with the same receivers and recorder. Difficulties arise when using coded systems. The most im portant one is the existence of correlation noise. Another one is the strong requirement to make the transmitted signal similar to the code. The existence of correlation noise may degrade the quality of the results in the same way as any other type of noise, e.g., instrument noise or ambient noise. However, there are two types of correlation noise. The first one is caused by the mathematics of the code, and the second one takes into ac count the physical systems, including the earth, that are used in field operations. The requirement to make the transmitted signal as similar as possible to the code applies mainly to continuous signal coding. In the case of pulse coding only the zero time of each transmitted pulse is considered. Pulse coding is a relatively new technique whose only field application is the Mini-Sosie system. Eventually, other ap plications using more powerful sources will be designed.

1

Introduction Historical Development The first coded method used in seismology was the Vibroseis method. Proposed in 1958 by the Continental Oil Company, the Vibroseis method is an application to seismology of a prin ciple already used in Radar Technique known as Chirp Radar. In the early 1960s, another system was proposed by Rogers Exploration Inc. under the trademark of Rogacord. In both cases, seismic energy is transmitted by vibrators coupled to the ground, sending continuous signals into the earth. In the case of the Vibroseis method, this signal is a sine wave, the fre quency of which is linearly varying with time. This is called a sweep. In the case of the Rogacord method, the signal is a por tion of a sine wave at a given frequency. The main characteristic of coded seismology is that the data recorded by' the geophones cannot be interpreted as they are received because they show a complete lack of resolution, and the different reflections overlap each other. To obtain useful results, a special processing, called the decoding pro cess, is needed. In the Vibroseis method, decoding consists of crosscorrelating the received data with the transmitted sweep. In this case the final seismic record is the same as if the autocorrelation of the sweep had been transmitted (Fig. 1). In the Rogacord method, decoding consists of summing different records obtained by successively transmitting different fixed 1

2 / Pulse Coding in Seismology

frequencies. In this case again the final re'cord is the same as if the sum of the fixed frequencies were transmitted at once (Fig. 2).

~f1 VfVf2 Ml\f, \J\M\f ·

-Jv-

Figure 1 Vibroseis method: sweep and its autocorrelation.

Continuous Transmission of Discrete Pulses Another idea was proposed in coding seismology which con sisted of transmitting a sequence of pulses in order to generate a composite signal with a particular envelope. This was in ef fect the transfer to seismic transmission of what is done during the seismic reception with digital recording (Fig. 3). Because it is difficult to control the amplitude of a transmitted seismic pulse and impossible to transmit large negative pulses, the signal is transmitted as shown in Figure 3. No serious tests have been made with this method. One reason for this is that it is difficult to find a seismic source that can produce pulses with a high enough rate of repetition. Prob ably sparkers are the only sources able to produce the required rate of repetition, if the energy of each spark is low enough and it is possible to incorporate several sparkers at the same time. There is, in fact, another reason to doubt whether it would work. A seismic pulse is not a positive spike but a positive

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Figure 2 Rogacord: fixed frequencies and their sum.

3

Introduction / 5

4 / Pulse Coding in Seismology

elongation followed by a negative one (Fig. 4). Because there is no D.C. component ina seismic pulse, you cannot expect to produce with several pulses a lower frequency than the lowest frequency present in each pUlse. Therefore, if we have to use many pulses of low energy we· cannot expect to produce low frequencies.

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Figure 4 Seismic pulse.

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Figure 3 Continuous transmission of discrete pulses.

Pulse Coding Several different patents on pulse coding systems have been filed and registered. (Only some of them will be described.) What was the reason for these ideas? At the time the patents were filed, the method that was used was called normal seismology. This method consists of transmitting one short pulse produced by explosive or mechanical sources, and record ing the seismic data received by geophones or hydrophones for a period of time called the record time. Another well-known

method that was used at the time was called the Vibroseis method. Any pulse coding method can be seen as a combination of these two methods: a transmission of short pulses like the nor mal method and a transmission of a long coded signal like the Vibroseis method. However, there will of course be some im portant differences. There will not be just one pulse per record time like the normal method, but a sequence of at least two of them. The coded signal will not be continuous, but will be com prised of a series of discrete pulses. Therefore, instead of using a vibrator resting on the ground and transmitting a con tinuous signal like a sweep, we must use one or more sources transmitting discrete pulses for a given time. This is called a sequence. Sparkers, Vaporchoc, air guns, Aquapulse, Dinoseis, Thumpers, and most recently civil engineering rammers, have been either tested or used as seismic sources with pulse coding systems. Even vibrators can be used, because after correlation the signal which has been transmitted can be considered as the autocorrelation function of the sweep which is equivalent to a pulse (the Klauder wavelet), The polarity of the correlated pulse depends on the relative phases of the transmitted sweep and the reference sweep. Therefore, after correlation, it can be considered that a given vibrator has transmitted either a large positive or a large negative pulse. We can say that vibrators are the only sources that can transmit large negative pulses.

6 I Pulse Coding in Seismology

The fact that a pulse coding technique is a combination of the normal method and the Vibroseis method is not a good enough reason to justify it. For example, some people will prob ably argue that this new technique will have the disadvantages of both methods. Let us say that pulse coding will complement the others with some specific applications.

Applications When compared with the normal method using explosives, the Vibroseis method proves to be more advantageous when the drilling is difficult because of the lower cost per mile. There is also a higher degree of multiplicity. That is to say, more discrete raypaths, producing better seismic results. Let us note that the limit to the degree of multiplicity has not yet been reached since more and more recording channels are at present being introduced. We shall see later on that pulse coding can increase the number of seismic channels without in creasing the number of recording channels. There are problems when the Vibroseis method is applied to marine seismology. A seismic boat, for example, does not spend enough time at each shot point to transmit several long sweeps. I t takes only a little more than 15 seconds for a boat to move 50 meters and this is less than one normal sweep length on land. This is the reason why a pulse coding technique was first designed for marine applications. The number of discrete pulses transinitted in the time available is unlimited if the energy per pulse is accordingly reduced. On the boat there is a power generator able to deliver one pop of high energy approx imately every six seconds, the record length of the final seismogram. By definition, pulse coding allows delivery of more than one pop per record length; but the energy per pop is then reduced due to the specifications of the power generator. The application of the Vibroseis method to shallow seismology, let us say less than 500 ms twt, faces economical problems. A vibrator is a sophisticated and expensive seismic source. Because the required crosscorrelation is generally per-

Introduction I 7

formed in a processing center, it increases the cost when com pared with the normal method. Even if correlation is performed in the field, the recording instruments are more expensive than the instruments used for normal recording. This is why a pulse coding technique is successful in this seismic domain. Pulse coding applied to shallow seismology will use a rather inexpen sive source; and decoding is performed in real time so that the tapes that are to be processed are like normal method tapes. The instruments necessary for applying a real time decoding are similar to the normal stackers used for the normal method. A pulse coding technique should also be used whenever there is a problem in synchronizing several sources. This is the case with the Thumper. A pulse coding technique has been designed to allow operators simultaneously to use several Thumpers.

Time and Space Coding Let us add some remarks about further possible applications which will illustrate that the coding technical domain is ex tremely powerful. A seismic section or a seismic record is a function of time and space (t,x). We know that any parameter in the time do main, like sample interval or time period, has its equivalent in the space domain, trace interval, and wavelength. In field operations we are used to sources synchronized with an ac curacy of better than half the sample rate. We are also used to designing source patterns, which is nothing but the introduc tion of a time interval between the arrivals at a given geophone station of the two pulses produced by two sources in a pattern. As is well known, the time interval will depend on the distance between the two sources and the apparent velocity of the recorded events (Fig. 5). This operation could be called space coding because we use the x parameter to produce a time inter val between the same type of seismic event generated by two sources. The advantage of this space coding operation is an im provement of the signal to horizontally travelling noise ratio.

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Figure 5 Two synchronized sources, 8, and 8,: A horizontally travelling

event will be convolved with a two-point operator; a vertically travelling

event will have its amplitude multiplied by two.

The price paid for this is a loss of resolution because the two pulses will then be in phase only if the seismic event has an in finite apparent velocity. This, however, is never the case. If there exists a coding operation using the x parameter then there also exists a coding operation using the t parameter. Time coding will correspond to one source (or two sources at the same location) sending two pulses into the ground, the two pulses being separated by a time interval. Let us note that to produce a time interval between two seismic pulses it is the x parameter and not the t parameter that was first used - the reverse of what might be expected. It is the time coding of pulses which will be discussed in this book. Time coding or rather pulse coding will allow more known information to be put into the ground at a given time with the intention offind ing out more about this ground. The price paid for this advan tage will be the presence of correlation noise. From the time-space (t,x) domain of a seismic section we can pass to the frequency-wave number (f,k) domain using the Fourier transform. In this new domain it is easier to under stand time-frequency filtering, space-frequency filtering, and therefore velocity filtering. By analogy we can say that if space coding and time coding exist, we can imagine a time space coding whereby, adding some time coding (Le., pulse coding) to the well-known space coding (pattern design), we might improve the wave number (k) filtering without using patterns that are too long.

Marine Pulse Coding:

Sosie

Definition Sosie is the trademark of a pulse coding technique designed by SNEA(P) for marine seismology. It is an abbreviation of the French expression Source sismique echantillonnee which in English means sampled seismic source. The reason for this name is that digital recording technology had just been in troduced in Europe. With the Sosie method, one or more sources transmit pulse sequences, i.e., more than one pulse is transmitted by each source during each record time. The Sosie principle was first tested using a sparker as a seismic source. The first results were presented in a paper at the SEG meeting of November 1970 and published in Geophysics (Barbier and Viallix, 1973). Later on Vaporchoc was tested and then air guns were used for routine operations on some exploration programs.

Characteristics Energy is transmitted at moments fixed by the Sosie sequence and expressed by the following mathematical formula: 9

10 / Pulse Coding in Seismology i

y =.L

n

i= 1

Marine Pulse Coding: Sosie / 11

d(t -

tiJ

(1)

where n is the number of pulses in the sequence. d(t - td

= 1, when t = tu t

2 , ...

ti, ... ,tn ,

d(t - td = 0, the rest of the time.

If we call T the maximum reflection time or the record time when only one pulse is released, then the Sosie sequence is much longer than T, and the time interval between two suc cessive pulses is much shorter than T. These two conditions can be expressed as: (ti+ 1 -

til

tn

tn being the time at which the last pulse of the sequence is pro duced. This is a measure of the duration of the Sosie sequence. The number, n, of the pulses and the time intervals be tween the pulses are such that the autocorrelation function of the sequence computed over a length of 2T seconds has a cen tral spike of much higher amplitude than the secondary peaks which appear symmetrically relative to the maximum central spike. This autocorrelation function can be expressed as: +T

f

The influence and importance of the correlation noise will be described in chapter six. It is important to have the highest possible ratio between the amplitude of the maximu;m of the autocorrelation function and the amplitude of the maximum secondary peak. This ratio is sometimes called the quality fac tor of the Sosie sequence. From the above description, the Sosie method can be characterized by the transmission into the ground of a coded sequence of seismic pulses released by one or more sources. The sequence itself is characterized by its autocorrelation func tion. This is dependent upon the number of pulses and the time intervals between the pulses.

y(t)y(t+9)dt

-T

where 9 is the time shift in the autocorrelation process and it consists of a central spike of amplitude, n, if the amplitude of each pulse is taken as 1, and n(n-l) secondary peaks of amplitude 1 over the whole length equal to 2tn of the theoreti cal autocorrelation function. The number of secondary peaks over the length 2T depends on the relative values of T and the time intervals between pulses. All these secondary peaks form the correlation back ground noise. The n(n-l) peaks do not necessarily appear at different times. When two peaks appear at the· same time, the amplitude at this time is 2. If three peaks coincide, the amplitude is 3, and so on.

Implementation When using the normal method, the time breaks are recorded on an auxiliary channel. When using the Vibroseis method, the reference sweep, i.e., the coded signal, is recorded on an aux iliary channel. Similarly, when the Sosie method is used, each time break corresponding to the transmission of each pulse is recorded on an auxiliary channel. When the Vibroseis method.is used, the received data are correlated with the reference sweep. When the Sosie method is used, the received data are correlated with the Sosie sequence. At this stage there already exists a difference between the two methods. The reference sweep represents the signal transmit ted into the ground whereas the Sosie sequence only represents the exact moments at which a seismic pulse of unknown shape is transmitted. A pulse sequence consists only of values 1 or O. There is a 1 each time a seismic pulse has been transmitted and there are O's the rest of the time. The correlation process of two func tions consists of first multiplying the corresponding values and then summing the results of the multiplications. In the case of the Sosie method, one of the two functions, the pulse se quence, consists only of values 1 or O. Therefore it is not necessary to perform any multiplication. The value of the func

Marine Pulse Coding: Sosie I 13

12 I Pulse Coding in Seismology tion corresponding to the received data is either unchanged when positioned in front of a 1 or equal to 0 when positioned in front of a O. It is sufficient merely to sum all the values of the function representing the received data which are in front of all the l's of the pulse sequence. This is done for each relative position, and means that this decoding process is much simpler than the full correlation process of the Vibroseis method.

Instruments The signals received by the geophones are the superposition of all the seismograms produced by each successive pulse, and therefore any normal digital recording instruments can be used. Due to the continuous overlapping of strong and weak signals it is possible to record with fixed gain amplifiers. In practice it is preferable to record with binary gain amplifiers to keep a better dynamic range all along the record. The only ad ditional equipment needed on board is a coding-decoding device. The coding unit or generator is essentially made of a 1-K core memory where the different time intervals between pulses are stored in the order they are to OCcur. It is driven by the recorder clock to ensure good synchronization. The clock pulse signals the first time interval. When it arrives at zero, an order pulse is sent to the seismic source, and the measurement of the second time interval is started. After a pulse sequence has been used to produce the first record, a different one is used for the second record. Through the use of multiple coverage, 12 fold for instance, an output seismic trace is the stack of 12 in put traces generated by 12 sequences from the surface of the sea. It is more desirable to have 12 different sequences to build up the 12-fold section, because the sum of the autocorrelation functions of 12 different sequences of 40 seconds in length con taining 30 pulsesis equivalent to the autocorrelation function of a sequence of 480 seconds in length containing 360 pulses. The decoding unit or processor works only on one seismic trace and yields a section on board. The input signal to the pro-

cessor is a coded analog waveform coming either directly from the trace on the streamer or from the amplifier output. In the processor, the signal is converted into digital form, then decod ed with respect to the reference trace from the generator. The decoded results are reconverted from digital to analog form and displayed, usually ona camera, to give a section on board. The length of the output trace can be either 1000 or 2000 samples according to the type of processor. The time intervals between pulses are input using a keyboard or a punched-tape reader. The seismic transmission starts when the boat reaches a precomputed geographic point and it stops after the boat has moved forward a given distance, generally 50 or 100 meters. Then it starts again as rapidly as the tape transport allows it to do so. Continuous recording, such as a mark written on tape each time the boat reaches a precomputed geographic point, can easily be imagined but has not been effectively used. It is a disadvantage to stop recording. The pulses or energy transmit ted over a length equal to the length of the output trace are not completely utilized. The loss is proportional to the depth. An extreme example is this: if we have to stop the tape drive at 20-second intervals, very little is lost on the shallow horizons but as much as 25% of the energy is not used at 5 seconds.

Results In the absence of any noise, a normal seismic record can be ex pressed as: s(t)

* itt)

being the transmitted seismic pulse and itt) being the im pulse response of the earth corresponding to the source and receiver positions. If we call s '(t) the seismic pulse produced by the source at each pulse of the sequence, then the seismic signal transmitted with the sequence can be expressed as: s(t)

14 / Pulse Coding in Seismology s'(t}

Marine Pulse Coding: Sosie / 15

*

(3)

being the pulse sequence. s 'ft) is assumed different from s(t) because the energy per pulse is expected to be reduced in the case of the Sosie method, and so the shape of the signal pulse will be different. The transmitted signal expressed by equation (3) will prop agate into the earth and our record will be the convolution of what has been transmitted with the log of the reflection coeffi cients: S 'ft)

*

y(t)

*

i(t).

(4)

To obtain the final decoded record, the received data given by equation (4) must becrosscorrelated with the corresponding pulse sequence y(t): s 'ft)

*

ACF y(t)

*

i(t)

(5)

where ACF y(t) is the autocorrelation function of y(t). By comparing the final result of equation (5) with the result obtained for the normal record (eq. 2), we see that the dif ference is the presence of the autocorrelation function of the pulse sequence. Therefore, the results would be identical if this autocorrelation function of the pulse sequence was a Dirac pulse. The difference between a Dirac pulse and the autocor relation function of a pulse sequence is the correlation noise produced by the secondary peaks. A way to make sure that this correlation noise is not troublesome is to design the pulse sequence so that the level of the correlation noise is less than the level of the ambient noise. When we compare this process with the final result of a Vihroseis record after correlation, we see that the autocorrela tion of the sweep is replaced by the autocorrelation function of the pulse sequence convolved with the seismic pulse produced each time the seismic source is fired. .These theoretical results do not take into account any kind of noise. With regard to the ambient noise there is little to say except that the signal to ambient noise ratio will be improved

by the decoding process. When we sum the samples of the received data coincident with the transmitted pulses, weare summing not only signals which are in phase but also signals which are out of phase and ambient noise. The summation of the signals which are out of phase form what we call the cor relation noise. This will be discussed later on in chapter six. When summing in phase signals and ambient noise the ex pected improvement in the signal to ambient noise ratio is by a factor of the square root of n, where n is the number of pulses used for decoding. The problem is a little different with regard to the organized noise consisting of horizontally travelling surface waves. If the distance between the source and the receiver varies during the transmission so does the travel time of a given surface wave. Therefore, the decoding process will not sum the surface waves in phase. Some attenuation of this event must therefore be ex pected when compared with vertically travelling events. More details of this noise attenuation effect will be given when the application of pulse coding to land seismology is described. In the case of marine seismology, we know that sources and receivers move forward at the same speed keeping a constant distance between them. Therefore, a horizontally travelling event will be treated by the process in the same way as aver tically travelling one.

The Advantages of Pulse Coding in Marine Seismology: Higher Degree of Multiplicity If we assume the boat is moving at 5 knots, then it takes 20 seconds to cover 50 meters. If we want a record time of 5 seconds, it is possible to transmit a Vibroseis sweep of 15 seconds and to record for 20 seconds, or to transmit 4 pulses spaced by 5 seconds to produce 4 records 5 seconds long. This latter case corresponds to the highest possible degree of multiplicity. The only way to increase this degree of multiplicity is to transmit a second pulse before the end of the 5-second record time. The ability to do this is one of the

Marine Pulse Coding: Sosie / 17

16 / Pulse Coding in Seismology

characteristics of a pulse coding system. In seismology, the quality of the results is a function of the degree of multiplicity. This parameter can be increased if there are more geophones per trace, more geophone stations per kilometer, or more shot points per km. The Vibroseis method suffers in marine seismology from not being able to transmit enough discrete sweeps per transmission. station, losing its main advantage over explosives. Pulse coding can also provide an elegant solution to the problem of increasing the number of discrete raypaths without changing the number of channels of the recording equipment. If we look at Figure 6, we have first one source position and two geophone positions which give two reflection points on each reflector. Let us suppose we want to halve the distance between the two reflection points. We can either double the number of discrete receivers as represented on the second line using new streamers, or we can double the number of discrete sources. Two discrete sources are two sources transmitting two uncorrelated pulse sequences. This is analogous to what was proposed by Pierre Goupillaud (1974) with vibrators transmitting different sweeps. Instead of using the sources along the profile, they could be used normal to the profile (Fig. 7). The recording would be made on the same streamer with the same recorder. The only change in the field would be to add the results of different sources transmitting uncorrelated pulse sequences. During the decoding, the same data would be processed three times according to each pulse sequence.

Examples of Results The first test line. was shot with a sparker unit delivering 25 sparks of 30 kilojoules over a 40-second period, corresponding to a horizontal displacement of 100 meters of the boat. It ap pears that the resolution on the shallow horizons (Fig. 8) down to 2 seconds was enhanced with a better high frequency defini tion. There is also a lack of penetration when the comparison is

G1

G2

(a)

(b)

(c)

Figure 6 Multiplication of discrete raypaths.

made with the dynamite section. A second test line was shot in the North Sea with air guns and a new and improved coding-decoding unit with the follow ing arrays: (1.) Normal air-gun array: 1080 cubic inches (2 X 120 + 6 X 80 + 6 X 40 + 6 X 20) shot twice over 100 meters.

18 / Pulse Coding in Seismology

Marine Pulse Coding: Sosie / 19

(2.) Sosie 15 air-gun array; 160 cubic inches (1 X 40 + 2 X 30 + 1 X 20 + 4 X 10) shot 15 times over 100 meters. (3.) Sosie 30 air-gun array: 80 cubic inches (4 X 20 alter nating with 8 X 10) shot 30 times over 100 meters. The pulse sequence for Sosie 15 had minimum and average time intervals of 2.0 and 2.7 seconds. The pulse sequence for Sosie 30 had minimum and average time intervals of 0.6 and 1.3 seconds. Recording and processing parameters were the same. Figures 9 and 10 show the comparison of the normal air gun on-board section with the Sosie 15 one. The geological target was the Zechstein at about 2 seconds twt. This reflector can be followed on the Sosie section while there is a complete lack of resolution on the normal air-gun section. Figures 11 and 12 show comparison sections after 12-fold coverage but without deconvolution. It will be noted that the definition is better on Sosie sections. Very little reverberating energy is visible, particularly below the Zechstein which makes the end of the useful data. Figure 13 shows comparison sections shot in the North S3 S1

S2

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...' .'....

. ... .

..

G1

Sea in depths decreasing to less than 0.8 meters. The reflec tions extend better on the Sosie section under the extremely shallow water of the left-hand part of the line.

f

f

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aMIlIIiIlli_UlIlri!!il atIiIS;:Jllbilh

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Figure 8 New marine seismic tool. Comparison sections, fiexotir, and the

new method sparker-line in the Bay of Biscay. (a) Flexotir 1 gun 50 gIll.

Deconvolution, 240 msec operator. 12-fold stack. Time variant filter, 20-54

to 10-30. (b) New method sparker-25 sparks of 30 kj on 100 m. Decon

volution, 100 msec operator. 12-fold stack. Time variant filter, 13-48 to

8-32. (Courtesy of Geophysics)

G2

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~

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t

Figure 9 One trace section made on board - conventional air gun - 50 m between pulses. Array of guns = 2 X 120 + 6 X 80 + 6 X 40 X 6 X 20 in inches. Filter = 8 - 62 Hz. (Courtesy of Geophysics)

20 / Pulse Coding in Seismology

Marine Pulse Coding: Sosie / 21

Figures 14 and 15 show comparison sections between nor mal Vaporchoc and Sosie Vaporchoc. It is to be noted that there is better attenuation of the sea bottom multiple on the Sosie section. This effect has been noticed several times on Sosie sections.

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" a Figure 10 One trace section made on board 15 pulses over 100 m. Array of guns 1 X 40 + 2 X 30 + 1 X 20 + 4 X 10 in inches. Filter = 8.62 Hz. (Courtesy of Geophysics)

=

b

Figure 12 (a) Sosie 15 air gun; (b) Sosie 30 air gun. (Courtesy of Geophysics) Figure 11 Conventional air gun. (Courtesy of Geophysics)

22 I Pulse Coding in Seismology

Marine Pulse Coding: Sosie I 23

IN

Figure 14 Conventional Vaporchoc. (From Barbier and Viallix. 1974; courtesy of Geophysical Prospecting. Blackwell Scientific Publications Limited) 2"

24

.I<'igure 13 Sosie air-gun shallow water. (From Barbier and Viallix. 1974; courtesy of Geophysi~al Prospecting, Blackwell Scientific Publications Limited)

Figure 15 Sosie Vaporchoc. (From Barbier and VialIix. 1974; courtesy of Geophysical Prospecting. Blackwell Scientific Publications Limited)

Land Pulse Coding: Seiscode / 25

3

Land Pulse Coding:

Seiscode

tion, but is designed on the time intervals between the pulses transmitted by different sources. In other words, if one source is sufficient to transmit one Sosie pulse sequence, a minimum of two sources are needed to transmit one Seiscode pulse se quence. If the Seiscode method was first designed for application with the Thumper, other possible applications exist with other land seismic sources like Dinoseis, land air guns, and vibra tors. These possible applications will be described at the end of the chapter.

Theoretical Procedure (1.) Energy is transmitted by two or more sources. These

Definition Seiscode is the trademark of a pulse coding technique designed by SNEA(P) for land seismology. Its first application was in association with the weight drop seismic source. This seismic source, introduced in the 1950s under the trademark of Thumper, was an extremely reliable and low cost seismic source. If three or four trucks could be used simultaneously it would have been extremely economical. However, it proved im possible to synchronize any two drops to within the required accuracy of less than one sample interval. The only alternative method of transmitting enough energy was to make many drops at each source position. Because the rate of progress was slowed down, the method, became uneconomical when too many drops were required. The Seiscode method is for use on land with seismic sources that have a low rate of repetition. For example, it takes more than 10 seconds to make two successive drops of the same weight. Moreover, the sources must be moved between successive transmissions in order to construct a source pat tern. These two factors, a low rate of repetition and the necessi ty to stop recording to move the sources, explain why in the case of the Seiscode method the pulse sequence is not transmit ted by one or more sources each working at high rates of repeti

24

are usually nonexplosive surface sources. (2.) Each source transmits only once per record time. The pulse sequence is represented by the time intervals be tween the pulses transmitted. by sources. (3.) After each record time, the recorded data are crosscor related with the short pulse sequence transmitted during that record time. Several different pulse sequences are used at each source position and the corresponding records are summed after the crosscorrelation has been performed as explained above. Let us give an example with three sources and eight suc cessive records. Transmission. TABLE 1 Record Number

Time Interval between First and Second Pulse

Time Interval between Second and Third Pulse

1 2 3

1 4

2 5

6 8 11 14 16 19

7 10 12

4

5 6 7 8

15 17 20

26 / Pulse Coding in Seismology

24

Eight successive records will represent a total of 24 trans mitted pulses. Usually 12 or 16 records are made at each source position in practice. Crosscorrelation. Let us call yift) the 3-pulse sequence belonging to the ith record. Each record can then be expressed as Yi(t) * f(t), f(t) being the record obtained if only one pulse had been transmitted. After correlation of this record with yift). such a record becomes: ACF yift) f(t). ACF yift) is the autocorrelation function of yift). We therefore need to calculate the autocorrelation function of each 3-pulse sequence (see table

1

*

Figure 16 Autocorrelation function of a Seiscode pulse sequence.

-

2).

Characteristics TABLE 2 Record Number

a·Pulse Sequences

Autocorrelation Function

(successive time intervals between the three pulses)

{time intervals between maximum peak and second peaks)

1'':'1''~''1

1 2 3 4 5 6

1

1····1···1···········1 1 2 3 4 5 9 6 7 13 8 10 18 11 12 23 14 15 29 33 16 17 39 19 20

2

4

5

6

7

8 10

11 14 16 19

7

8

12 15 17 20

Summation. We have to sum: i

n

L ACF yift)

i

*

f(t) = f(t)

I

*

i

i=n

L ACF yift). 1

By summing the 8 ACF yift). we obtain an autocorrelation function with a maximum amplitude peak of 24 and secondary peaks at time 1.2.3.4.5.9 •... 19.20,39 from this maximum. The resulting autocorrelation function is represented in Figure 16.

As has already been explained: (1.) energy is transmitted by two or more sources; (2.) only one transmission takes place per source and per record; (3.) the pulse code is represented by the time intervals be tween the pulses transmitted by each source; and (4.) each individual record is crosscorrelated with the cor responding pulse sequence.

We have now to add a fifth point: the sum of the autocor relation functions of each pulse sequence will show a large cen tral peak surrounded by low amplitude secondary peaks. It should be noted that the last secondary peak will appear at a time generally short compared with the record time. In other words. there is a practical difference between Sosie and Seiscode. The autocorrelation function of a Seiscode pulse se quence shows secondary peaks only during the first part of the record time while the autocorrelation function of a Sosie pulse sequence shows secondary peaks throughout the record time.

Theoretical Results A normal record obtained with a Thumper could be expressed i(t); and a Seiscode record could be expressed as: as: 8(t)

*

27

28 I Pulse Coding in Seismology

*

Land Pulse Coding: Seiscode I 29

*

ACF y(t) s(t) i(t). The same s(t) transmitted seismic pulse Occurs in both equations because we assume that it is the same seismic source. That is, we assume that each Thumper in the Seiscode sequence generates the same pulse s(t) at the shot point. ACF y(t) is the sum of the autocorrelation functions of the individual pulse sequences as has been explained above. In the previous expression, no noise apart from correlation noise has been taken into account. With regard to ambient noise there is nothing to add to what has been said for the Sosie results. The signal to ambient noise ratio will be improved in the same way with Seiscode as with Sosie. That is to say, by yn, if n pulses have been transmitted. As has already been explained, the pulse decoding process consists of summing in phase events which occur exactly at the same time after each transmitted pulse. This is precisely the case for any vertically travelling seismic event, but it is not the case with horizontally travelling events when the source receiver distance varies during decoding. Moreover, let us remember we have at least two sources when Seiscode is used, and it is more than likely that they will be spaced out on the ground surface. The problem of the influence of Seiscode on the signal to organized noise ratio is therefore much more com plicated. Let us compare what happens with horizontally travelling seismic events when the normal method is used and when Seiscode is used. To simplify the equations and the figures, we will use only two sources with both the normal method and the Seiscode method. . In the normal method, the two pulses are synchronized. These two pulses produce two synchronized reflections and two surface noises which are time shifted by dlV, if d is the distance between the sources along the profile and V the veloci ty of propagation of the noise (Fig. 17). When the two sources are moved along the profile, the reflected signals stay syn chronized, but the noises are continuously time shifted as shown in Figure 18. After summation of the 8 successive records, we see that the vertically travelling events (reflec tions) have been multiplied by 16, whereas the hOrizontally travelling events (surface noises) have been convolved by a long operator of 16 points spaced by dl8 V. The result is an im provement in the signal to surface noise ratio.

..........-

S1

First Position

S2

d

S1

x

G

Second Position

S2

•

G

...+

•

+

--------------------------------------S1

S2

•

•

G

Eighth Position

+

Figure 17 Successive source and receiver positions when using a source pattern.

Vertically Travelling

Horizontally Travelling Events

Event (Reflections)

(Surface Noises)

t, (S1)

t, (SI)

t,

Second Record

i

(S1)

t, (S2}~Z

First Record

x +v~~m~ 7dl8 __

S (1)

(S2)

~

(S2)

x---v-d 1(S2) 8 !1

1!

------- ------------------------1

~-----_______r

---~

t, (SI) Eighth Record

to (S2)

1

dl8

~+

~

v

(S1)

x_

7dl8

-_-:-_'v-::= ____ ~(S_2:...)

1

I ! _ _ _ _ _ __j

16

Summation

1

1

1111111111111111

Figure 18 Travel times corresponding to the normal method.

30 I Pulse Coding in Seismology In the Seiscode method there is a time interval between the two pulses transmitted by SI and S2. This time interval is different at each record to realize a Seiscode pulse sequence. This is represented in Figure 19. In the same figure we have also represented the ACF of the individual pulse sequences and the sum of them. A reflection obtained by the Seiscode method, (after decoding), suffers a convolution with the operator. This is represented at the bottom of Figure 19. Figure 20 shows what happens to a hOrizontally travelling event. The normal time shift between two noise arrivals, due to the different positions of the sources, is now increased or decreased. This depends on which source is shot first and by the time interval between the transmission from the two sources. The second column of Figure 20 shows the time shifts when SI is shot first. The fourth column of this same figure shows the time shifts when S2. is shot first. During decoding these two-point operators are crosscorrelated with the cor. responding pulse sequences and the effect of decoding upon the noises in the individual records is shown in columns 3 and 5. After summation of the individual records, we obtain the final operator by which this given noise is convolved. This operator should be compared to the operator we obtained with the normal method in Figure 18 at the bottom right. In contrast to the time intervals between the transmitted pulses which depend only on the chosen code, the time inter vals between two arrivals of the same noise, that have been called time shift, depend on:

Land Pulse Coding: Seiscode I 31 Seiscode: 2 Sources, 8 Records

Record NB

Pulse Sequence yi(t)

ACF yi(t)

2

11

1

U

ill

2

U

3

U

L1 W

4

LJ L

5 6

L.J

L

7 2

The distance d between the sources.

(2.) The choice of the source which is shot first.

(3.) The apparent velocity of the noise, V.

(1.)

8

I 16

For example, we have chosen in Figure 20 a time shift, dlV equal to the maximum time interval of the pulse code. As a result we can see that the two noises arrive in phase when SI is shot before S2 (column 2). If S2 is shot first then the time shift is equal to twice the time interval (column 4). The two resulting operators with which the noise will be convolved are completely different. The first one (SI shot first) is completely inefficient with regard to the attenuation of the

Summation

Figure 19 Result of decoding for vertically travelling events (reflections).

32 I Pulse Coding in Seismology Land Pulse Coding: Seiscode I 33

~fJ Jd '

~

organized noise due to the presence of a large peak of ampli tude 10. (Note that if a split spread is used, we shall have the first operator on one side and the second one on the other side. Therefore, the noise attenuation is not symmetrical.) At this point it can be understood that the effect of pulse coding on any event which is not travelling vertically can be extremely complex, even if only two sources have been used. The final result can be completely different from what is ex pected. The fina,! operator with which a noise is to be convolved should be computed for each type of organized noise, taking in to account the position of the sources and the order in which they will shoot.

N

C\I T""

~ JJJJJJJ

Field Implementation

~

~<.~mJ

t ~ "~I c

dl

~IJ ~ ~ -3 ~ ~ J] ~ .

~~.

••• ., ~ :g

]

l'!

" ""

]

]

]

II

]

II

e,z' *

~

* * *

.,

~Jr

II

:0 ----l

*

j

N

:

]

]

]

~

~ ~ ~ ~ E E'a c::

be

A possible field implementation is represented in Figure 21. A coding unit would be installed in the recording truck and would delay the start orders to each truck by predetermined in tervals of time. The corresponding time breaks would be used in a decoding unit before the data are written in the memory of the stacker. J.

Star! Pulse

CODING

UNIT

J.

_ truck n· 1 J.J.- trucKI~· 2

_

trucK n·3 Radio Transmission

DEcODING

Radio J. TB 1 } Reception J. TB 2 l. TB 3

T~K~ or; TAPE RECORDER

0

*

*

*

'" '

:J

of!

2

<

::J

Q)

<.)

-~

~ ,,0 t,,~~

II

... "

0

:l

CI)

]

]

]

~

:~

l

fEISMli AMPLIFIERS

I

I

Figure 21 Seiscode implementation. (From Barbier and Viallix, 1974;

Courtesy of Geophysical Prospecting, Blackwell Scientific Publications

Limited) c'" '-, -, (, r' ",'

£J.,.",,) l~

,.,,,, UIO COlO"""'" Co

n1rCl

d~

'1 UEl "IUOC'.

l[llOnna<;\on

Land Pulse Coding: Seiscode / 35

34 / Pulse Coding in Seismology

In the case where the sources cannot be synchronized, the

exact time breaks must be transmitted back to the

truck. It is therefore preferable to transmit one start pulse on

ly and to have one coding unit per source truck. This will

delays of different predetermined time intervals in each source·

truck. Each real time break is radio transmitted back to

recording truck. Such a system is represented in Figure 22. It

can be seen that one transmitter and three receivers are re

quired. for the recording truck.

Recording Truck

I

~

·e~ '"~

Receiver 1 \--- J.

~ Receiver 2.\--- .L TB2

Tape Recorder

I-

o

:g

a::

..l...

1'[F '--R-ec-e-Iv-er-s-f-.

.L TBS

Seismic Amp.

Start Pulse .

---------Source Truck No.1

g

TBl

~ Receiver

Start Pulse

1.

---------Delayed TBl ..L

Start Pulse

~.L o<,~

"'"

E

'"c:

>='" o

ia:

Figure 22 Possible implementation of Seiscode with the Thumper.

Examples of Results The Seiscode method was tested in Africa and three com parisons are shown in Figure 23. The first comparison is 16 drops per shot point for the normal method versus 48 drops with 3 coded Thumper trucks per shot point for Seiscode. The time spent was equivalent, and an improvement can be seen in the signal to noise ratio particulary below 1 second. The next comparison presents the same section, this time with 48 drops in both cases. If there is a difference it is in favor of the normal method. However, the time spent with one truck in the conventional method was nearly three times more than

]

Figure 23 Examples of results with Seiscode. (From Barbier and Viallix. 1974; courtesy of Geophysical Prospecting. Blackwell Scientific Publica tions Limited)

36 / Pulse Coding in Seismology

with the Seiscode method and three trucks. The last example is a compromise with 24 drops for Seiscode section and 16 for the normal section. The time for the 24 drops was shorter than the time for the 16 drops But the quality was slightly better below 1.5 seconds because of the increased multiplicity.

Further Possible Applications Two possible applications concerning the advantages of pulse coding in marine seismology have been discussed: (1.) number of discrete raypaths can be increased without chang ing the number of channels of the recording equipment; and ( 3-D recording. Another possible application has been implicitly men tioned - the improvement of the attenuation of organized noise. With a given source pattern, a pulse code can improve the theoretical noise attenuation. More important, the same at tenuation can be obtained with a shorter pattern. A possible specific application of Seiscode is with the use of vibrators and negative pulses. Let us give a short descrip tion of what can be done in this domain. Let us suppose the field equipment consists of one record ing truck and two vibrator trucks,· Vi and V 2• The reference sweep in the recording truck has a given polarity, the pilot sweep in Vi has the same polarity as'the reference sweep, whereas the pilot sweep in V 2 has the opposite polarity. The crosscorrelation function of the reference sweep with the Vi pilot sweep will produce a positive pulse whereas the crosscor relation function of the reference sweep with V 2 pilot sweep will produce a negative pulse. Therefore, a pulse sequence designed for vibrators can consist of .both positive and nega tive pulses. . Let us now compare the autocorrelation function of two se quences of n pulses-the first one with only positive pulses and the second one with both positive and negative pulses. These two autocorrelation functions will have the same max imum amplitude. However, the correlation background of a

Land Pulse Coding: Seiscode / 37 pulse sequence consisting of both positive and negative pulses can be less troublesome because there will be a reduced number of secondary peaks. This is easily shown in Figure 24 where two examples concerning very short sequences are given - four sequences of two pulses in the first example and two sequences of three pulses in the second example. In the first case, the cor relation baCkground has completely disappeared. In the se cond case, there are fewer secondary peaks and the length of the autocorrelation function is shorter. This represents two ad vantages with regard to the final correlation noise. Second Example:

First Example 2

W

U

~a is to be compared with ~b.

lLu

LLJ

2

~ LJ

~

I

1~1

~a

W

~ 1

8-1

~~

~ LLJ

I

I I

II I I I

~ I II II I I

~~

Figure 24 Effect of using both positive and negative pulses on the shape of the ACF of the sequence.

Shallow Seismology Pulse Coding: Mini-Sosie / 39

4

Shallow Seismology Pulse Coding: Mini-Sosie It was early in 1973, about 5 years after the Sosie pulse coding method was applied to marine seismology, that the idea of using an earth tamper as a seismic source came to mind. The Mini Sosie method can be defined as pulse coding application to shallow land seismology. In the beginning only shallow refrac tions and/or reflections up to 200 or 300 ms were expected. Since then reflections below one second have been obtained. The earth tamper (Fig. 25) is a common civil engineering tool which has been adapted to provide continuous, randomly spaced seismic pulses. In order to make the pulse sequence ran dom, all that is required is to modify the throttle control to make the engine speed variable. Such a source is highly reliable and easy to operate. It can be operated over all sorts of terrain, including roads and agricultural areas without surface damage. To record the exact transmission instants, a sensor is fixed to the rammer base plate and connected by wire to the recorder. The output signal of the sensor is shaped into a short pulse to be compatible with a Sosie decoder unit as used in marine Sosie operations. We first had a one-channel, recording-decoding in strument, which was expanded to a two-channel one. In both cases, we had to use the transposed method, which is quite familiar to those involved at the start of Thumper and/or Vibroseis operations.

38

In the transposed method, two geophone stations are laid out at one spread distance, the seismic source(s) being operated at equally spaced positions (generally 12) between the two geophone stations. The method is obviously called transposed because the two geophone stations occupy conventional source positions while the source occupies geophone stations. After energy has been transmitted at these 12 different positions, 24 seismic traces are recorded. These can be played back on a 24-channel recording oscillograph. In the case of Mini-Sosie, as we have only a one-for two-) channel(s) recorder, the play-back has to be made after each energy transmission. An analog out put to display the decoded results on a memory scope is used. After each energy transmission for each geophone position, the contents of the memory of the decoder are transferred to the memory scope, and the spot is shifted down the screen. When the screen of the scope is full with 6 or 12 traces, depending on the scale chosen, a picture is taken with a Polaroid camera (Fig. 26).

As the decoding process is performed in real time, a great deal of time and money is saved by the Mini-Sosie method.

-~~

Figure 25 Earth tamper. (From Barbier et aI., 1976; courtesy of Geophysical Prospecting, Blackwell Scientific Publications Limited)

40 / Pulse Coding in Seismology

5

Pulse Sequences Definition

Figure 26 Seismic reflection. 24 geophones over 15 m minimum 65 m, max imum offset 175 m. (From Barbier et al., 1976; courtesy of Geophysical Prospecting, Blackwell Scientific Publications Limited)

A pulse sequence is a time series consisting of O's and l's. Each 1 in the series corresponds to the transmission of a seismic pulse at the corresponding time. As has already been explained, it is not the sequence itself which is important but its autocorrelation function. In the frequency domain, a pulse sequence is characterized by an amplitude spectrum A(f) and a phase spectrum CP(f). Its autocorrelation function will have a zero-phase spectrum like any autocorrelation function and an amplitude spectrum which is equal to A2(f). This means that certain different pulse sequences can have the same autocorrelation function, and therefore there is no difference between these pulse sequences for seismic applications. There is a need only for an optimum autocorrelation function of the pulse sequences. A pulse sequence can be pseudo-random or purely random. In the first case, all the time intervals between pulses are com puted and known in advance. Such a procedure is used when the number of pulses is not very large, let us say a few tens. This is the case for the Sosie sequence in marine seismology. In the case of a purely random pulse sequence, the time in tervals between successive pulses cannot be predicted. They generally depend on the operator. driving the source. This is the case when the source is a civil engineering rammer as in the Mini-Sosie application.

41

42 / Pulse Coding in Seismology

Pulse Sequences / 43

The autocorrelation function of a pulse sequence is com prised of a central large peak of very large amplitude and secondary peaks which form what is called the correlation background of the autocorrelation function. This correlation background gives rise to the correlation noise which is present on the seismic records. This point will be treated in detail in chapter six. First, we shall study the way to compute a pseudo-random sequence and the properties of random sequences produced by one rammer or three rammers.

I I I Idl I" I

I I' I

/1/1/

1/

a

=

e

I I I II I I I 1

2

t1

t2 t3

Computation of a Pseudo-Random Sequence Let us consider a sequence of pulses at times tlo t 2 ,. .. ti, ... t n and its replica just below (Fig. 27). In this position we can compute the maximum of the autocorrelation function, the amplitude of which will be n if there are n pulses, and we give the amplitude 1 to each pulse. Since an autocorrelation function is always symmetrical, the correlation background is symmetrical. It is therefore sufficient to compute it for one side only, for exam. pIe, by moving the replica towards the right of the figure. When this operation is performed, each pulse of the replica will pass in front of the next pulse of the sequence as it is represented on the upper part of Figure 27. Looking at this d, then the figure, if the minimum time interval is (tij - t 4 ) first secondary peak which is the first peak of the correlation background will occ;:ur at time d in the autocorrelation func tion. Further secondary peaks will follow for each time interval of the sequence. If the same time interval is present twice in the sequence, there will be a value of 2 at that time in the autocorrelation function. As the replica continues to move, each pulse will pass in front of the second pulse after itself as it is represented in the lower part of the figure. This will happen when the displacement is equal to the sum of two successive time intervals, for example. at times (t a t i ) = (a + b), (t 4 - t 2 ) = (b + c), etc. To summarize what has been described above, the correla-

c

b

3

4 5

6

7

t4 t5

t6 t7

II I

8

(n - 2)(n - 1) n

ts

tn

Correlation background at: (to - t,) = a

(t, - to) = b

Un -

tn-i)

=

It\ I

II

//!/ I I I II I I I

/I I

I a I I c Idl b

e

1

2

3

4 5

6

7

8

t1

t2

t3

t4 t5

t6 t7

t8

Correlation background at:

(n

tn

(t. - t,) = (a (t. - to) = (b (tn -

I

2)(n - 1) n

tn -

2)

Figure 27 Autocorrelation of a Bosie sequence.

=

+ +

b)

c)

44 ! Pulse Coding in Seismology

Pulse Sequences ! 45

tion background of the autocorrelation function of a pulse se. quence consists of secondary peaks which occur at times equal to each time interval between two successive pulses, the sum of two successive time intervals, the sum of three Successive time intervals, etc. Therefore, when we build a pulse sequence using successive known time intervals, we can predict the in fluence of each of them. If we start with a time interval a, then there will be a peak at time a in the autocorrelation function of the corresponding sequence. If we add a time interval b after the first time interval a, then we know there will be a peak at time a, a peak at time b, and a peak at time (a + b). These three peaks will have the same amplitude. If we choose b a, then our autocorrelation function of the corresponding pulse se quence will show an amplitude 2 at time a and an amplitude 1 at time 2a (Fig. 28). Autocorrelation Function Sequence

3

Ia I

ULt

b

I •

a b (a + b)

Ia I

a

I •

LLl a

~---~

2a

Figure 28 Autocorrelation function of a pulse sequence.

When the replica of the pulse sequence is moved relative to the sequence to compute the autocorrelation function, the .total movement necessary is equal to the length of the final decoded record. This is a short time when compared with the length of the pulse sequence itself. Therefore. when we sum the suc cessive time intervals of the pulse sequence, and we find a value greater than the length of the final record, this value will not appear in the part of the autocorrelation function we are considering. If we call a,b,c,d, etc. the successive time intervals of a pulse sequence, then the best way to compute the correlation background of the corresponding autocorrelation function is described in table 3.

TABLE 3 Time Intervals

Sum Two

Sum Three

a b c d e

a+b b+c c +d d+e

a+b+c b + c +d c+d+e

•

•

• •

• •

When a value is greater than the length of the final de· coded record, it is not written in table 3. All the values in table 3 represent a time where there is a correlation background peak. If the same value is represented twice, then at that time the amplitude will be 2 instead of 1. When designing a sequence for marine seismology, a minimum time interval is fixed, taking into account various parameters such as the type of source(s) used. This is done because there is a minimum time which must elapse before the same source can be fired again. Also a minimum time incr€" ment is chosen, generally equal to the sample rate or a multiple of this sample rate. The length of the sequence and the length of the final record are chosen in advance. Another parameter to be considered is the maximum value of the correlation background to be allowed. Most of the time this value is 1. Having decided all these parameters, the Sosie sequence can be automatically designed by computer. Time intervals are ad ded one by one to the sequence, the corresponding autocorrela· tion function being computed after each addition. If no value of the correlation background is above the indicated limit, the new time interval is accepted. Otherwise, it is rejected and a new one, the value of which was the old one plus the increment, is tried. This procedure is stopped when the sequence reaches the required length. This is a pragmatic approach to the prob· lem. The computer program uses a trial and error method. We do it this way because we have had no success in optimizing the computation using purely mathematical processes. Let us give an example: a sequence about 10 seconds long with a minimum time interval of 1 second, an increment of 4 ms and no correlation background peak having an amplitude of more than lover a period of 4 seconds (see table 4).

46 I Pulse Coding in Seismology

Pulse Sequences / 47

TABLE 4

Pulse Nb 2 3 4 5 6 7 8 9

Elapsed Time in ms

Time Intervals

1000

2004

3012 4024

5040 6060

7084 8112 lO 9144

........ .... . .... ......................_--.... ...... . - ....

11 10,180

__-- _

__

0

1000 1004 1008

1012 1016

1020 1024

1028

1032

10

Correlation

Peaks (a)

1000

10042004

1008 2012 3012

1012 2020 3024 4024

1016 2028 3036

1020 2036 3048

102420443060

1028 2052 3072

1032 2060 3084

II I II II I 1000

1032

2004

I

I

2060

3012

3084

10

1036

(b)

The autocorrelation function of the sequence in table 4 is

represented in Figure 29. Such a sequence is quite monoto

nous, and sometimes it is preferable to mix long and short time

intervals. For example, two short ones followed by a long one.

Let us therefore design such a sequence which is still 10

seconds long but with a minimum short time interval of 800

ms and a minimum long one of 1600 ms. As before, the incre

ment will be 4 ms and there must be no correlation background

peak greater than lover a period of 4 seconds (see table 5).

The autocorrelation function of the sequence in table 5 is also represented in Figure 29. TABLE Pulse Nb 1 2 3 4 5 6

Elapsed Time in ms 0 800

1604

3204

4012

4824

7 6432 8 7248 9 8068

10 9680 ...... ....--............_--. --.... ..........- ...... 10,504

_-

_---

Time Intervals inms

Correlation

Background Peaks

0

800 804 1600 808 812

1604 1608

816

820 1612

800

8041604

160024043204

808 2408 3212

812 1620 3220

rejected

1608 2420 3228

816 2424 3236

820 1636 3244

1612 2432 3248

824

800 820

1600

1636 2404

3204

Figure 29 (a) Autocorrelation function of pulse sequence 1 (see table 4). (b) Autocorrelation function of pulse sequence 2 (see table 5).

The two autocorrelation functions of pulse sequences 1 and 2 have the same maximum amplitude (10), the same max imum of secondary peaks (1), and the same number of secon dary'peaks (24) between 0 and 4 seconds. However, the distri bution of these peaks is different. In the. first autocorrelation function we have a regular distribution of these peaks in three different zones, a I-second zone with an increment of 4 ms be tween peaks, a 2-second zone with an increment of 8 ms, and a 3-second zone with an increment of 12 ms. In the second auto correlation function we have four zones and a less regular distribution between peaks. Such a change in the distribution means a change in the seismic correlation noise as will be de scribed in chapter six.

Random Pulse Sequence We shall call a pulse sequence random when it has not been precomputed. A random pulse sequence is only dependent on

48 /

Pulse Sequences / 49

Pulse Coding in Seismology

the type of sources and on the way these sources are controlled by an operator. This is the case when rammel'S are used to im plement the Mini-Sosie method. In order to treat random pulse sequences and their autocorrelation functions, some mathe matical assumptions have to be made. One possibility is to assume that the time intervals between successive pulses pro duced by the rammer follow a Gaussian distribution of mean value m and standard deviation a. With a Gaussian distribution, the probability E. of value x is: E.(x)

=

aV'2i! e

-(x - 2 mp

2a

(6)

The shapes of such curves for different values of a are well known. Figure 30 shows one of them computed with m = 0 and a = 7.8. The value of the maximum amplitude is 0.051, and the value of x corresponding to a probability of 1% is 14.1. A random pulse sequence is therefore characterized if we assume a Gaussian distribution and the values of m and a are known. The mean value of a rammer is a little less than 100 ms. We also have access to the minimum (U and maximum (tz) time intervals betwen two successive pulses. Among the characteristics which are given by the manufacturer of the BS60Y rammer, the percussion rate/minute is 450-630. This corresponds to tl = 95 ms and t z = 133 ms. We then have to measure the probability of these two values. This can be done using the autocorrelation function of the sequence. Equation (6) can be written as: (t -

m) = ±aV 2 Log

(7) (tz - t) = 2aV 2 Log f. f. f.

= 3 X 10-3

"

€oJrn.

corresponds to (tz - t I ) = 37.2 with a = 7.8. = 2.5 X 10-3 corresponds to (t z - t l ) = 30.7 with a = 6. = 2.5 X 10-3 corresponds to (t 2 - t I ) = 43.2 with a = 9.

= 28.2 with a = 7.8.

E.

= 10- 2 corresponds to (t 2

E.

= 10- 2 corresponds to (t z - ttl = 31 with a

tj)

=;:

9.

Let us remember that the value given by the manufacturer for a BS60Y is equal to 38 ms.

Autocorrelation Functions of Random Sequences As has already been explained, the correlation secondary peaks represent the correlation background. These occur at in stants equal to each time interval dti of the sequence and also at instants equal to the sums of successive time intervals: (dtj + A ti+l), (A ti + A ti+1 + A ti+2), etc. If we consider a long enough sequence, the number of times each A tj is present in the sequence is equal to the pro bability of this value occurring. Therefore, the first group of correlation peaks is the Gaussian distribution of the time inter vals of the sequence. The first group is centered at the mean value to of the time intervals. It should be noted that this result represents a possible way of measuring the distribution of the time intervals. The sum (dtj + dti+ V is the sum of two values of the in dependent variable of a certain Gaussian distribution. dtj +1 does not depend on A ti, but is produced by the same source driven by the same operator. In such conditions, the sum is itself a Gaussian distribution of mean value twice the mean value of the original distribution. The standard deviation, a', is defined by the relation a'2 = 2a2 • The second group of cor relation peaks is therefore centered at 2to and is represented by a Gaussian distribution of standard deviation a'. The above reasoning can be applied to the other sums. The correlation background therefore consists of successive Gaus sian distributions centered at instants nto with standard devia tions varying as aVn.

50 / Pulse Coding in Seismology

Pulse Sequences / 51

E:

The amplitudes of the successive secondary maxima cen tered at to, 2to,... nto are given by the formula:

g o

An

~

o

---L .._ = V2ri oVn

.

(8)

The exact values are given in table 6 with the correspon ding attenuation in decibels relative to the maximum peak amplitude which is taken equal to 1. The plot of these values for the three different values of a is shown in Figure 31.

~ o

,...

8

o

~

TABLE 6

o

o

0=3

tin ms

~ o

0.133 0.094 0.077 0.066 0.059 0.054 0.050 0.047 0.044 0.042

100 200 300 400 500 600 700 800 900 1000

0. 10

~

o

N o

o ,... o o

..

17 db 20 db 22 db 24 db 25 db 25 db 26 db 26 db 27 db 27 db

o = 7.8

0.051 0.036 0.029 0.026 0.Q23 0.021 0.019 0.018 0.017 0.016

26 29 db 31 db 32 db 33 db 34 db 35 db 35 db 36 db 36 db

0=9 0.044 0.031 0.026 0.022 0.020 0.018 0.017 0.016 0.015 0.014

27 db 30 db 32 db 33 db 34 db 35 db 35 db 36 db 36 db 37 db

(")

oo

The following remarks can be made:

en ................. '" o o

o

(1.) The

10

8

o x

-25

-20

-15

-10

-5

o

5

Figure 30 Gaussian distribution: [(x) =

1 0\7'2ii

e

-(x-m)'

20'

10

15

20

25

maximum of the autocorrelation function consists of a single peak d(t) whereas the other peaks are Gaus sian distribution curves, the maximum amplitude of which are not the only parameter to be considered. (2.) We are not interested in all the maxima, but only in those which occur within the record length of the decoded record. Let us assume a maximum record length of 1 second (most of the time it will be less than this). If to, the mean value, is equal to 100 ms, then n " 10.

where m

= 0 and

0

= 7.8.

(3.) With regard to the seismic correlation noise, it is a favorable factor that An be decreasing with n.

Pulse Sequences I 53

52 I Pulse Coding in Seismology

(4.) At a given time kto, the amplitude of the. secondary peaks varies as 110. This is proof that the correlation background decreases when the modulation of the source is improved.

An .130

3

Comparison between a Pulse Sequence and a Sweep

.120 .110

A sweep and a pulse sequence represent two coded seismic signals which must be known so that the signal received by the geophone is intelligible to the interpreter. However, there are more differences than similarities between a sweep and a pulse sequence.

.100 .090 .080

(1.) A

.070 .060

7.B

.050 .040 .030 .020 .010

01

.1

.2

.3

.4

.5

.6

.7

.8

.9

1.0

~ec

Figure 31 Amplitude versus time of the secondary maxima of the ACF of a Gaussian distribution for different values of the standard deviation a and mean value to = 100 ms.

sweep is a continuous signal whereas a pulse se quence is a discontinuous one. The same applies to their autocorrelation functions . (2.) A sweep represents the transmitted seismic signal which is reflected at each geological interface, whereas a pulse sequence only represents the instants at which seismic pulses are transmitted . (3.) A sweep is frequency band limited and the end fre quencies are selected according to the ground and the geological target. Such a consideration is not involved in designing a pulse sequence. (4.) The autocorrelation function of a sweep has a higher dynamic range than the autocorrelation function of any pulse sequence which has been effectively used. This dynamic range is measured as the ratio between the maximum amplitude of the autocorrelation func tion and the amplitude of the correlation background. (5.) The correlation background of the autocorrelation function of a sweep is continuous and rich in the end frequencies of the sweep. The correlation background of the autocorrelation function of a pulse sequence is

54 I Pulse Coding in Seismology

discontinuous and it contains frequencies which are outside the frequency bandwidth of the seismic record. Thanks to these properties the signal to cor relation noise ratio of a pulse coded record can easily be improved. (6.) To transmit a sweep effectively, important problems of phase control between the reference sweep and the transmitted sweep must be solved. When using pulse sequences we are faced only with the problem of record ing the zero time of the seismic pulses.

6

Correlation Noise Definition Correlation noise is associated with any type of coded seismic method, including Vibroseis, Sosie, and Mini-Sosie. The presence of significant correlation noise will degrade the quali ty of the final seismic section, and we have to consider a signal to correlation noise ratio in the same way as a signal to instru ment noise ratio, a signal to ambient noise ratio, and a signal to interference or organized noise ratio. To improve and op timize the signal to correlation noise ratio. we first have to understand precisely how this type of noise is generated. We have already seen that the autocorrelation function of a pulse sequence consists of a maximum central peak sur rounded by secondary peaks which represent what we called the correlation background. We also know that after decoding a pulse coded record can be expressed as: ACF y(t)

* s(t) *

(9)

i(t)

when the normal equivalent record would be expressed as:

*

s(t)

i(t)

(10)

(any type of noise except correlation noise being neglected in . eqs. 9 and 10). 55

56 I Pulse Coding in Seismology

Correlation Noise I 57

It is easy to understand what the correlation noise is by comparing the amplitude of the same given refection Rl in equations (9) and (10). Let us represent the absolute amplitude versus time of. equation (10) in Figure 32. We first have a very low amplitude, then a very high one due to the first refraction arrivals, followed by a decrease in amplitude due to the attenuation of the waves travelling into the earth. If we wait a long enough time, the amplitude level will return to the level of the start of the record before the first breaks. Now this curve will tell us the ampli tude of the chosen reflection at time t J• According to the curve it is ARl. Let us try to find out what would be amplitude of same reflection if we had used a pulse coding method. Let us suppose we have transmitted a sequence of n pulses, the autocorrelation function of which is represented in Figure 33. We may consider that the maximum amplitude is n, or we may consider that the maximum amplitude is 1, in which I case the amplitude of each secondary peak has been divided by n. Let us choose the latter. Equation (9) says that we have to convolve equation (10) represented by Figure 32 with this autocorrelation function. The relative positions of equation (10) and the autocorrelation function needed to obtain the

value of the reflection time tJ are shown in Figure 34. From this we can calculate the value at time tJ: we multiply the two functions ordinate by ordinate and we add the products. This will give us:

3~n

+ ARl + +

(AI

(A4

+ A2 + A3)

+ A5 + As)·

(11)

The value of the correlation noise is obviously:

+

_I_fAI n

+ A2 + A3 + A4 + A5 + As)·

(12)

The value of this correlation noise must be kept as low as possible, preferably, at the level of the ambient noise. At this level, there is no more uncertainty in the amplitude of the reflection when using a pulse coded method than when using a normal method. As we can see from equation (11) the value of the correla tion noise is the product of two series of terms.

Amplitude

The amplitudes of the secondary peaks of the correla tion background which have been taken as all equal to lin in the chosen example. (2.) The amplitudes of the seismic record obtained by

(1.)

AR1,·········.···· .....

I

1/n

~

Figure 32 Absolute amplitude versus time curve of a one-pulse record.

•

TI~

Figure 33 ACF of a pulse sequence.

Correlation Noise / 59

58 / Pulse Coding in Seismology

ground and on the ratio between the largest and the smallest amplitude events in the corresponding pulse record. As this ratio also varies with the source-receiver distance, the same transmitted pulse sequence will therefore produce a higher level of correlation noise on a near offset trace than on a far off set trace. This is to be kept in mind when attempting to im prove the signal to correlation noise ratio.

Amplitude

AR1 A,

A, ~ - - - - -

Al

t-_. ---,- -------

-I" ---- -~----~--------~-~ I I I

I

:: ::::-- -~: -:: t::.:-::.:-::1.:-~ 1::::: ~ -

A, _____________ ,_________ J _I- .1 _____ I :

An I

I

I

•

I

I

•

.

•

I t

I I

I I

..1 __

J

f

I

f

I

I

I

•

I

I

Examples of Correlation Noise

J __ I I

Time

1

11n Figure 34 Relative position of the one-pulse record, amplitude curve, and the ACF pulse sequence to obtain the amplitude of reflection R i •

sending one seismic pulse into the ground. In our ex ample we can see that there are some large amplitude events (first breaks, shallow reflections) and some small amplitude events (ambient noise, deep reflec tions). It is obvious that the predominant part of the correlation noise will come from the large amplitude events. What we call seismic correlation noise or more simply cor relation noise is therefore not just the correlation background of the autocorrelation function of the pulse sequence. It also depends on the characteristics of the impulse response of the

Figure 35 shows the autocorrelation functions of two pulse se quences convolved with the filter response of the seismic amplifiers. At the top of Figure 35 the pulse sequence has been pro duced by three rammers each of which have a good rate of modulation. At the scale of the figure, the filtered correlation background is hardly visible. At the bottom of Figure 35 the pulse sequence has, been produced by one rammer which has been deliberately run at a constant rate of transmis.sion. The repetition interval is ap proximately 92 ms. Due to the fact that this is not exactly 92 ms, there is a slight decrease in the amplitudes of the second ary peaks as well as a broadening of the filtered pulses. The right-hand part of Figure 36 shows the autocorrela tion functions of different pulse sequences filtered by the analog signal delivered by the source sensor bolted on the base plate of the source. Each function has been obtained with a dif ferent number of pulses, from 10 to 1600. We still see an improvement when we pass from 400 up to 800 pulses, but no improvement at the scale of the figure when we pass from 800 to 1600 pulses. Let us point out that such a high number of pops is necessary for random pulse sequences. For pseudo random pulse sequences much better results can be obtained with far fewer pops. The left-hand part of Figure 36 shows the signal received by a geophone at a depth of 153 meters in a well. The signal which can be expected is shown on the first line where 1600

8l o

3

2

5

4

6

8

7

"

~

(a)

~

1000 Pops Random (3 Rammers)

~-~--~--.------~--~---------"--

..--.-.-"-~- .

-~--,----

-.

"-~-----~----"--

~.

.. ---"

~. --~-----.----

-~----

.~-."-----.--------.----.-."--."~"==-:---------.--"~~~-~----"-=---~-"--~--'-----~-

~

.

~ ?;;.

-.-.--.-

-~--"-------------~---.~--

~

a. o

~

(b)

1000 Pops

Periodic (1 Rammer)

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

-~"". --~"~-==::.:.-=:::::=::--=--::::-"-.____r, __ _~-

~--~.~

..

._~._-

. ---.--~--- - .".----------~

..;.-.-----..,..,'"V--.-."'--"--------.... ----

".-~-:

Figure 35 Example of correlation noise: (a) random, 3 rammers; (b) periodic, 1 rammer. (Courtesy of Horizon Exploration Ltd.)

No. of Pops

Max. Trace Amplitude em/sec

1600

~

800

~

0.215 0.105

400

0.049

Vv'r

200~

0.033

100 0.015

40

0.0061

~

.....,.. 'V\I'I>

'V'

hI>

~

~

20

S" '"t

0.0027

o· ;::!

0.0013

,

o

100

o

200m sec

100

200m sec

Source Monitor Correlation

153m Downhole Seismometers BS 60

Figure 36 Example of correlation noise

= downhole geophone record. (Courtesy of Horizon Exploration Ltd.)

....~ 1:1) ~

"

~

62 I Pulse Coding in Seismology

pulses have been transmitted. The first arrival is about 100 ms. The correlation noise is clearly visible on the last five or six traces. It must be noted that, since the autocorrelation func tion of the pulse sequence is symmetrical, the correlation noise is also symmetrical. Any large amplitude event will therefore give a repetition to ms before and to ms after its own time of ar rival, to being the mean interval of the pulse sequence. When the large event is the first break, the repetition before is mixed only with ambient noise and is clearly visible. The repetition after is mixed with other seismic arrivals. This is shown on the last trace. The first arrival shows its repetition about 90 ms before the first arrival and 90 ms after it. However, if the time of arrival of the first event is shorter than to. then its repetition before will not appear on the record. Figure 37 is an example of a field monitor where strong first breaks produce a high level of correlation noise represen ted by a succession of repetition throughout the record. However, a reflection is still visible at 230 ms. The higher the dynamic range of a field record, the higher the correlation noise level. Figure 37 is a good example of this effect. Any change in the field parameters which would decrease the amplitude Qf the first breaks without affecting the amplitude of the reflections would improve the signal to correlation noise ratio by decreasing the amplitude of the repetitions of the first breaks. Therefore, if no pattern is used, and if the source-receiver distance is short, the conditions for correlation noise are at their worst. Unfortunately, such a choice of field parameters is quite common with regard to shallow seismology. A case is illustrated in Figure 38 where the target is the reflection at 75 ms. The source is a rammer ramming on the spot and the receivers are single geophones per trace. In Figure 38 the same record is represented three times, twice with AGC on (records 1 and 3) and once with AGC off. What is seen below 150 ms is correlation noise. This time the repetition of the shallow reflection is more visible than the repetition of the first breaks. This correlation noise is not troublesome at all since the repetition occurs after the record time of the useful data. The question which then arises is

Correlation Noise I 63

I'

I'

<0

i.... ,§..., 0:1

LO

! IZ1

§

..,.

'§ ::t:

'0

»

...,...gj

:::s

en

o

2

ai

~

+ N

S ~
1\ Ol

~l

II

II

o

E!l

1 ....o

1 IZ1

!;:;

~

Ill)

r;::

64 I Pulse Coding in Seismology

lID"f(Jl'\ iV ( Y

Correlation Noise I 65

1I11Hl"I'l ,r I J 4I)(\i\~)l{ \ . 7 J\~ j

00 C\J

~

§

J Pil

§ .~ o

))\1 )!(rr)~

HUHlII) II

\)K0~

~

T""

::t: 'Cl ~

i

whether we still need to transmit a coded sequence of pulses, or whether we can afford to keep the source running at a constant rate of repetition. To answer this question, let us turn to Figures 39 and 40 which portray slightly modified versions of Figure 32. In Figure 39 the autocorrelation function of the pulse se quence has been shifted to the position which corresponds to the deepest useful reflection. This autocorrelation function ex hibits a high level of correlation background. The period of repetition of the secondary peaks is longer than the deepest reflection time, a. In such conditions the correlation noise is not troublesome because its level is considerably inferior to that of the signal. In Figure 40 the autocorrelation function of the pulse se quence is the same, but the pulse response of the ground is dif ferent. The presence of a strong event, quite possibly organized noise, can be seen after the deepest reflection. In such condi tions the combination of this high amplitude event and the high correlation background will produce correlation noise which will obscure the useful seismic data.

2 ui ~

'8 I \J

(\ lAf'J'4J\)

g

T""

S

]

oS .!!l

g

=

.S!

IIIl l)')t5P>

III mo?;}}

1111 k»J?

~

~... ~

....o ~

..:l!

~

~

~

'r":;

~

Signal to Correlation Noise Ratio Improvements Correlation noise exists with any coded seismic method. This must be understood and accepted. When using any electronic equipment,there is always some instrument noise. Inthe same way, when using a pulse coded method, some correlation noise will be added. Instrument noise and correlation noise must be minimized relative to the seismic signal. Correlation noise will not necessarily have a constant amplitude throughout the record, and we shall, of course, be most concerned with the amount of correlation noise in the zone of interest of the final record. For example, it does not matter if we have visible correlation noise before the first breaks because there is no useful information in this part of the record. In the same way, it does not matter if we have impor tant correlation noise at the end of the record because the

Correlation Noise I 67

66 I Pulse Coding in Seismology

a: record time of the deepest event b: rate of repetition of the pulse sequence c: high level of correlation background

Amplitude

time

a

c

b

c

Figure 39 In such conditions a high level of correlation background is not troublesome.

a: record time of the deepest event b: rate of repetition of the pulse sequence c: high level of correlation background

Amplitude

-i-----------------------------time

a

c

b

c

Figure 40 In such conditions, although the high-level seismic event is oc curring after the record time of useful data, it becomes troublesome in presence of a high level of correlation background.

record time is always longer that the reflection time of the deepest expected reflection. Since the seismic correlation noise is the convolution of the correlation background with the pulse response of the ground, the signal to correlation noise ratio can be improved by acting on either of these two functions. The first action on the correlation background is the im provement of the autocorrelation function of the pulse se quence. It is obviously impossible to increase the amplitude of the maximum of the function without simultaneously increas ing the number and/or the amplitude of secondary peaks. Therefore, we have to increase the amplitude of the central peak more rapidly than the amplitude of the secondary peaks. This is what is done when a time interval is added to the se quence so that there is no secondary amplitude larger than 1. Not all peaks of the correlation background have the same importance. An early secondary peak is less harmful than a late secondary peak for the following reason: the correlation noise is considered to be the repetition of any seismic event. So an early secondary peak, let us say at 500 ms. will give a repeti tion of each seismic event 500 ms before and 500 ms after the event itself. The repetition 500 ms before will be mixed with an event having an amplitude in general larger than the primary having produced the repetition. Therefore. we can expect the repetition to have a smaller amplitude than the primary occur ing at the same time. In contrast, the repetition 500 ms after will be mixed with an event having an amplitude smaller than the primary having produced the repetition. In this second case. there is a risk that the repetition will have an amplitude larger than the primary occurring at the same time. This is more likely to happen if the primary producing the repetition and the primary occurring at the time of the repetition have a large amplitude difference. that is to say, if they are separated by a long time. For the same reasons as those given immediately above, a secondary peak of amplitude greater than 1 is more acceptable near zero than when it is rejected at alonger time. In fact an autocorrelation function with secondary peaks of decreasing amplitudes would be quite acceptable if the dynamic range was

Correlation Noise / 69

68 / Pulse Coding in Seismology

constantly superior to the dynamic range of the incoming data. That is to say, that the ratio between any two peaks of the autocorrelation function is greater than the ratio of any two in coming seismic events separated by the same time (Fig. It is also possible to try to take advantage of portions of the autocorrelation function of the pulse sequence which do not contain any secondary peak. The result is that some por tion of the final record will also show less correlation noise. As it is the first arrival and/or some shallow reflections which pro duce the most harmful correlation noise, there will be very lit tle correlation noise when no secondary peak is in front of this part (Fig. 42). Let us now see how to act on the pulse response of the ground. There is an improvement if we reduce the dynamic range of the recorded data. That is to say, if we decrease the amplitude of the strong events. This can be obtained by in creasing the offset and using longer source and geophone pat terns. Such a technique was also in use for the very early analog Vibroseis when the dynamic range of the correlator was not as good as it is now. Because the pulse sequence is well known after it has been recorded on one auxiliary channel, we could propose to design its inverse filter and to convolve the final record with this in verse filter. This would be equivalent to what is done to remove the effect of the multiples and/or the transmitted signal in normal seismic deconvolution.

Amplitude

Time

81

A1

A2 A3

L______ time

Figure 41 AliA. and A,IA. is larger than B,IB, and B,IE•• respectively. This is favorable to reduce the amount of correlation noise.

Figure 42 The most troublesome correlation noise is produced by the hatched zone. It is favorable when no secondary peak of the ACF of the pulse sequence is in front of this zone.

70 I Pulse Coding in Seismology

Correlation Noise I 71

We have not done this experiment ourselves. but we an ticipate the following difficulties because the inverse filter must be time variant. • The autocorrelation function of the pulse sequence is to be taken from - T up to +T, T being the record time. • At 0 second, the relative position of the autocorrelation function and the seismic data is represented on the second diagram of Figure 43. • At T/2 second and T second the relative positions are dif ferent (each time it is the maximum of the autocorrelation function which gives the time of the seismic data). At first sight it does not seem possible to neglect the later secondary peaks because· their influence on the correlation noise level is the most important, especially at the end of the record where the correlation noise is the most harmful. We can probably obtain an improvement of the signal to correlation noise ratio using this method. but we do not know how much. It might be more difficult than expected at first sight. Taking into account both the correlation background and the response of the ground. there is another way to minimize the correlation noise: it is to have a correlation background and seismic data with different frequency spectra. As the frequen cy spectrum of the correlation noise is the product of the fre quency spectrum of the seismic data by the frequency spec trum of the correlation background, we can reduce the level of this correlation noise by ensuring that the two frequency spec tra are different. If we consider Mini-Sosie with a rammer repetition rate fo. there is no doubt that the frequency spectrum of the correla tion background will be rich in foHz. In fact without any modulation, the frequency spectrum will be a line spectrum with foHz, 2foHz, 3foHz.... Due to the modulation, there will be less 2foHz than foHz, less 3foHz than 2foHz, etc. The top of Figure 44 shows the amplitude spectrum of the

~

~

+T

-T

Convolution Operator

at 0 ms

~

Convolution Operator at T/2 ms

/'

~

Convolution Operator at T ms

~ Figure 43 The portion of the autocorrelation function of the pulse sequence which is to be considered is from - T up to +T •.T being the length of the final decoded record. When we say that a pulse coded record is equal to a normal record convolved with the autocorrelation of the pulse sequence. this filtering is in fact a time variant filter. This figure shows three dif· ferent operators at three different times.

72 /

Pulse Coding in Seismology

Correlation Noise / 73 correlation background of the ACF of a pulse sequence. The bottom part represents the amplitude spectrum of two seismic pulses. a low frequency one and a high frequency one. The cor relation noise is the convolution of the correlation background with each seismic pulse. In the frequency domain it will be the multiplication of the two amplitude spectra. The use of high frequency pulse gets rid of the correlation noise produced by fo and even 2fo. For example. when using a rammer at an average rate of repetition of 10 Hz. the signal to correlation noise ratio is improved by using low cut filters that strongly attenuate 10 and 20 Hz.

A

(a)

fo

A

Low f Pulse

(b)

" I

I

High f Pulse .-/

/

\,

\

".,f

Figure 44 (a) Amplitude spectrum of the correlation background of the ACF of a pulse sequence having an average rate fo Hz; (b) amplitude spec tra of a low frequency pulse and high frequency pulse. The amplitude sec trum of the correlation noise will be the product of the two spectra and the use of a high frequency pulse will reduce the level of the correlation noise.

Decoding Process / 75

Shift and Add

7

Decoding Process Definition Decoding means the process that transforms a very long record without any seismic resolution (because the data pro duced by the pulses are overlapping each other) into a short seismic record on which the reflections are in the right order and can easily be picked by an interpreter. The basic idea of this processing is to crosscorrelate the received data with the pulse sequence. As is well known, to crosscorrelate two functions means to multiply them ordinate by ordinate and to add the products over the duration of the two functions. This operation is done for each relative position of the two functions. When one of the two functions is a pulse sequence, i.e .• a function containing values 1 or 0, all the multiplications contain either a 1 or a 0 which is an important simplification of the process. Decoding a pulse coded record will therefore be much faster and much cheaper than decoding a Vibroseis record. Two different ways to decode pulse coded records will be described. The first one is called the shift and add process. It is used to decode the marine Sosie records when the processing is done in a processing center using large computers. The second one is called real time Sosie processing. It is performed by the specialized Mini-Sosie recorder. In both cases the final result is obviously the same: the convolution of a one pulse record with the autocorrelation function of the pulse sequence.

74

In the field. the pulse sequence is recorded as a reference trace on an auxiliary channel. and the geophone data are recorded on normal seismic channels. As an example, let us consider a pulse sequence 40 seconds long with seismic data 45 seconds long, which corresponds to a 5-second record time after the last pulse has been transmitted. Let us look at Figure 45. If we consider each transmitted pulse individually, we would have recorded for 5 seconds after each pulse. If we look at a given reflection e at a time of 2 seconds. and if n pulses have been transmitted at instants t i • t z, ts.... ti, ... t n , then our given reflection e will have been record ed 2 seconds after t i • 2 seconds after t~. 2 seconds after tit and 2 seconds after tn. We must also note that each reflection is recorded each time and mixed up with all the other events. The basic principle of the shift and add process is to divide the 45-second record into n windows of 5 seconds start ing at each transmitted pulse (Fig. 46). Then each window is SOSIE DATA PROCESSING REFERENCE TRACE

W--l-

t, t2 t3 I

tj

18 I

II

I 1

,I I ';

81

I

,I

I 1

+

~

Recorded at ti me

t1+ 8

I II

----------•..

_-

t:2+ 8

=

I I

I

I

I

I

1

h+8

=

-

81

tj +8

~ 1

1

e t

tn+8

1

=

-T FIELD SEISMIC TRACE EQUIVALENT TO THE STACK OF n TRACES FINAL TRACE AFTER PROCESSING

Figure 45 Shift and add process.

-

~

~

Decoding Process / 77

76 / Pulse Coding in Seismology

shifted in succession to the time at which the last pulse was transmitted, i.e., by tnt (t n tl), ...(tn - td, ...O. Finally these n successive 5-second windows are added together. When the addition is made, the data corresponding to the reflection E> add in phase while the events mixed with each E> reflection will add out of phase because they appear at dif· ferent times. In other words, when an event is not in its right position it adds out of phase.

Real Time Sosie Processing The shift and add process would not have been possible if the pulse sequences had not been of limited length because seismic computers are unable to accept multiplexed records beyond a

INPUT

I

FIELD DATA

c=:: : : : : : : SItqoence #

REFERENCE TRACE

CROSSCORELATION

I fI I

I

I

I

I'

,

OR

1:1

D

.,

I - . -- - I Sequence :tt. 2 Sequence # mOD: 0 DOD I

. -.....-.- -

-

I~:

c:

f

CJ

~-,-I

I

I

3

.. --..,.-- --

oi

- - , - - - - - - ; - - - .. - ,

I

• The top line of each diagram represents the successive in coming time breaks with their corresponding numbers (1), (2},...(k).... etc. As time elapses, each time break moves from left to right. • The dot represents the incoming sample at the time in stant of the diagram.

;::::::;:::=.-;......----'~~ ~~

+ I I%·$$~ +

PftOCESS

given maximum length. In marine seismology, this presents little problem because the boat is continuously moving for ward and does not spend a long time on each spot point. A transmission time of 45 seconds is the maximum possible, and with a sample rate of 4 ms only 11,250 samples per trace have to be demultilplexed. With the Mini-Sosie technique, it is not unusual to transmit the energy for 3 minutes. The most com monly used sample rate is 1 ms because it is a high resolution tool and high frequencies are expected. 180,000 samples per trace would therefore have to be demultiplexed and it is quite obvious that the decoding must be performed in real time. A real time pulse decoder must consist of a solid memory,

the length of which will be the length of the final decoded

record. If the memory length is 1000 words, then we shall have

a I-second final record with alms sample rate, and a 2-second

final record with a 2 ms sample rate. Figure 47 represents a series of diagrams (a), (b), (c},...(h) that illustrate various moments of the real time decoding pro cess:

I

• The bottom line represents the memory which is reserved for the data belonging to a given input channel.

SHifT

....

•

STACK

= [

OUTPUT

rface#l Record #1

TrJlCtJ#1

_tt2

Figure 46 Seismic processing regarded as (1) a crosscorrelation of field data and reference trace, or (2) a stack of field data shifted in time. (From Bar bier and Viallix, 1974; courtesy of Geophysical Prospecting. Blackwell Scientific Publications Limited)

The dashed lines indicate the memory locations to which the incoming seismic sample is to be directed.

At time to, diagram (a), the first time break (1), initiates the decoding process and the first incoming sample is directed to the first memory location. As time elapses each sample is placed in successive memory locations just as in a normal recording procedure. At time t I , diagram (c), we are faced with the pulse coding

78 I Pulse Coding in Seismology

Decoding Process I 79

,

,

(1)

(1)

•

411

(a) :

(b)

""

L

="t

(2)

(1)

(2)

t

~ •,,,, '. (c) ,:

(d)

\ (2)

(1)

~

~

'

W

(f)

.,

(3)

(2)

t

t

,

(1)

" ....' ....... . ,, , , .

\

d

,

\

" ,

,,

"

"

(h)

'"

(3)

(2)

~

(1 )

~

~

..

,

(k

+

,,"".... ....

,,,'. .. ,

.,

" "'.

't-,••

I \".

(g)

t

~',...

, ..

(3)

,

(1)

t t.

,,'. "

t

(e)

..

.'"

"

&'\ . . , 1) (k)

,

(k -

.• •

\ ..... ,',........ , , , , , , ...... .... , ,

1)

\

\

\

1

,

'

'"

"

.....

Figure 47 .Real time Sosie processing; ~ number of time breaks correspond ing to each transmitted pulse; • incoming sample; , memory location where the incoming sample is to be addressed; (a) start of decoding when first time break arrives; (b) still only one transmitted pulse; (c) arrival of a second time break corresponding to a second pulse; (d) still only two transmitted pulses; (e) arrival of a third time break corresponding to a third pulse; (f) still only three transmitted pulses; (g) time elapsed since the start of decoding is longer than record length (first time break no longer useful); (h) one incoming sample at a given time with three time breaks dur ing a time equal to the record length just preceding this sample.

problem because a second pulse has been transmitted before the data corresponding to the first one have been completely recorded. On receipt of the second time break (2), the incoming seismic sample is placed in the next memory locatiori in accor dance with the first time break following the dashed line num bered 1. This sample must also be placed in the first memory location where it is to be added to the data already contained in that memory cell following the line. numbered 2. The recording then continues, diagram (d), where each incoming seismic sam ple is placed in two memory locations. At time t 2, diagram (e), the third time break arrives and the incoming seismic sample is placed in the appropriate locations following the lines numbered 1 to 3. The recording then con tinues, diagram (f), where each incoming seismic sample is placed in three memory locations_ In diagram (g), the time elapsed is longer than the record length of the memory. Therefore the line numbered 1 is beyond the memory length, and the time break (1) is no longer useful. In short we can say that at a given time instant, the incom ing seismic sample must be placed in the memory locations ac cording to the time breaks present in a time window equal to the record length, following the lines numbered. This is what is shown in diagram (h). The decoded record is progressively built-up. When an oscilloscope is connected to a channel of the memory, the effect of continuously increasing the number of pops can easily be seen in real time. In this type of decoding there are also some limitations imposed by the characteristics of the recording in struments. Each time a new seismic sample arrives on a seismic chan nel, it must be addressed to as many locations as there are recorded time breaks during the record length just preceding this incoming sample. For example, if the record length is 1 se cond and 10 pulses transmitted during the second just pre ceding the incoming sample, this sample must be addressed to 10 different locations and summed to the values already ex isting in each of these locations. These operations Qf addres sing and summing take some time, and must be done for each seismic channel before the next sample arrives, i.e., during one

80 / Pulse Coding in Seismology

sampling time interval. There is, therefore. a limit to the rate at which pulses can be accepted. The limit will depend on the number of seismic channels and on the sample rate. Let us assume the decoding unit can just accept 10 pops at 1 ms sam ple rate, and let us see what could happen if this number is greater than 10. . When more pops than the equipment can process are pro duced. we have three options. can ignore the extra time breaks. These extra time breaks will therefore correspond to pulses which have produced seismic energy not considered as signal but as noise. (2.) We can accept the extra time breaks but use only the first ones during processing. Then any remaining time breaks will only be taken into account when the first ones have disappeared (Fig. 48). If the limit is 10 at the beginning of the processing, time breaks 1 to 10 will be used. After a time equal to the record time, time breaks 2 to 11 will be used, etc. This means there will be no useful energy brought in by time break 11 during the first part of the record. The first part of the final record will show low amplitudes if there are too many incoming pops (more than the decoding can ac cept) during the seismic transmission. This happens because the degree of summing is inferior to the degree of summing of the rest of the record. This effect is known as the end of stack effect. (3.) We can accept the extra time breaks but use only the last ones during processing. As soon as a new time break arrives, the oldest one is abandoned. For exam ple, when time break 11 arrives, time break 1 is aban doned although it has not been used throughout the record length. This means there will be no useful energy brought in by time break 1 during the last part of the record. The signal to noise ratio will therefore become less than it should be at the end of the record. This effect will be less apparent than the end of stack effect because it is more common to have a low signal to noise ratio (and a low amplitude) at the end of a

Decoding Process / 81

...

..

Record Time

Normal Processing 109 8 7

5

6

43

2

(1.) We

First Option: TB 11 is ignored 11109 8 7

6

5

End of Stack Zone

I

Second Option: TB 11 will not be used before TB 1 reaches the record time limit End of Stack Effect

11

First Useful Position of TB 11

Understacked Zone Third Option: TB 1 is ignored as soon as TB 11 arrives

\ Last Useful Position of TB 1

Figure 48 Instrument limitations to decoding.

82 I Pulse Coding in Seismology

Decoding Process I 83

record. However, it should not be forgotten that in such conditions no improvement will result from in creasing the total number of pulses since none will contribute to the end of the record.

Use of a Field Correlator In a field correIator that performs the correlation in real time, the memory size of each seismic channel relates to the length of the crosscorrelated record, i.e., 1000 or 2000 words instead of the 5000 or 6000 words needed to record seismic data before correlation. There is also one auxiliary channel that records the reference sweep. Let us see how this recorder crosscorrelates a Vibroseis sweep with the seismic data and could be used to process pulse coded records. Let us describe a normal crosscorrelation when the reference signal is six samples long and the received data eight samples long: ala2a3a4a6a6

Reference signal: Received signal: blb2b3b4b6b6b7bs

The correlated output signal will be three samples long corresponding to three relative positions of the signals (see table 7). To obtain this result using a real time correlator, we only need a 3-word memory to record the reference signal, and a 3-word output memory to record the correlated values (see table 8). The processing is stopped when a sum of 6 values is reached in each output word. It should be noticed that: • Each incoming sample is only multiplied by three values of the reference signal. This number 3 is equal to the number of output samples. This is the reason why we don't need more than a 3-word memory to record the reference signal. The contents of this memory changes at each incoming

TABLE 7 Amplitude of the Output

Relative Positions a 1 a2 a3 a, aD all

(alb I +a2 b2 +aaba+a~b4+a5bB +aabe)

x x x x x x b, b,b, b. b, b, b, b, a 1 a2 aa a,aGCZe x x x x x x b, b, b, b. b, b, b, b,

(alb2+a2bB+a3b4+a4b6+aebs+asb7)

al az as a.. a6 all x x x x x x b, b, b, b. b, b, b, b,

(alba +a2 b, +aab e+a,b e+aa b7+ aebs)

TABLE 8

OUTPUT MEMORY

When the first sample b, arrives, it is multiplied by a, and located in the first word. When the sec_ond sample bll arrives, it is multiplied by a" and located in the second word, and multiplied by a" and located in the first word where it is added to the existing value.

First Word alb}

+

Second Word a1b2

Third Word

+ a:.b 2

aBba

alba

When the third sample b, arrives ...

asb a

+

+

When the fourth sample b. arrives ...

a,b,

aa b,

aBbe

a,bf,

asb e

When the sixth sample b, arrives ...

+

+ +

a2b,

When the fifth sample b. arrives ...

a.b.

ae b6

a,b e

a.b,

ar.b,

When the seventh sample b, arrives ... When the eighth sample b. arrives ...

+

+

+

+

+

+

+ +

aab s

84 / Pulse Coding in Seismology

Decoding Process / 85

sample. We successively have: a] 00, a 2 a l 0, aa a 2 a l ,a4 aa a2 , • • • etc., the last contents being 0 0 as.

• •

The results of the three multiplications are addressed to the three different words of the output memory. The order of summation in each word of the output memory is equal to the number of samples in the reference signal.

Let us now describe how the equipment can be used for pulse decoding. The following illustrate the different applica tions of this equipment that can be considered.

•

For normal recording, the time break is represented by the value 1 recorded on the auxiliary channel. As time elapses, this time break moves from left to right and each incoming sample is recorded according to the position of the time break (see Fig. 49).

Auxiliary , Channel

1·'

Seismic Channel

b1

I I

Auxiliary

I Seismic I I I Channel b1

I I I

I I I

Chao".'

b2

First Position

I

I I

IP",lIo" I I I Second

Figure 49 Use of a field correlator for normal recording.

•

each value of the filter function as shown in Figure 50. As time elapses, the whole filter function is moved from left to right (see Fig. 50).

For normal recording with digital filtering, the reversed function representing the desired filter is recorded on the auxiliary channel. It is necessary to reverse the function because the instruments are performing a correlation and not a convolution. Each incoming sample is multiplied by

First

Position

I

8,

I

8,

I

8,

I . r=J..

"'----'---1 ,,+---r-,a, 1 b,a,-'---'II

8,

Second

Position

I e, I

e,

1

",J::.tJJ I

e,

I

~~"" 1 1';' 1:f: 1'-1 b 18 1

b 2 8 'l

b 1 a,l

_

-

-

-

-

'

I

1

8,

u~

8,

1

I

L

1 ·-1

1

Figure 50 Use of a field correlator for normal recording with digital filter ing.

• Let us explain the decoding of a pulse coded record. At a given instant the pulse sequence which is present in the memory of the auxiliary channel comprises all the pulses which have been generated between this instant and a time equal to the record length (just previous to this instant). Figure 51 shows there are three time breaks located in the second, fifth, and ninth memory locations. Therefore the incoming sample, bi, at this instant is addressed to the sec ond, fifth, and ninth memory locations of the seismic chan nel where its value is added to the already existing value. One sample time later each time break has moved forward by one memory location and the next incoming sample bH 1 is addressed to the third, sixth, and tenth memory location where its value is added to the existing value.

86 I Pulse Coding in Seismology

I

I

1

I

1

1 Ith

I +bj I

I +bl I

I Hi I

I

CI

I l T T J - lI C C 11 I

I

1+~i+ll

I Hi

I +bl J+bi+1J

I

I Hi

Position

I (I + l)th I position

/+bl+ll

Figure 51 Use of a field correlator for real time decoding of a pulse coded record.

• In pulse decoding with digital filtering each pulse which was previously represented by a 1 is now replaced by a function with which it is desired to crosscorrelate (or to convolve) the incoming seismic data. As time elapses the whole function is moved from left to right. Each incoming sample like b£ is then multiplied by the value present in each memory location like a h a2 • aa before adding the result of the multiplication to the corresponding memory loca tion of the seismic channel (see Fig. 52). Such an application would be useful because this filter would be common to all the seismic channels and much easier and cheaper to design (see Fig. 52).

I

e,

I

s,

I =a;J~

CI

8,

I

e,

I

e,

J

References Barbier, M.G., Bondon, P., Mellinger, R., and Viallix, J.R., 1976, Mini-sosie for land seismology: Geophysical Prospecting, v. 24, p. 518-527. Barbier, M.G., and Viallix, J.R., 1973, SOSlE: a new tool for marine seis mology: Geophysics, v. 38, p. 673·683. Barbier, M.G., and Viallix, J.R., 1974, Pulse coding in seismic prospecting SOSIE and SEISCODE: Geophysical Prospecting, v. 22, p. 153·175. Goupillaud, P.L., 1974, Signal design in the VIBROSEIS technique: pre sented at 44th Annual International SEG Meeting, November, Dallas, Texas. Vidal, J.C., 1978, Mini-SOSlE: un nouvel outi! pour l'exploration sismique it faible profondeur: Bull. Cent. Rech. Explor. Prod. ELF Aquitaine, v. 22, p. 469-489.

ith

1-".:.1,:., 1,;.,11·1 I I k I,:., I,;, I

eo,;","

r=r=r~I8J80~]

·CI

e,

I

s,

+

bi+1 81

+

I

+

biBI bjB::

Figure 52 Use of a field correlator for real time decoding with digital filter ing of a pulse coded record.

87

Index I 89

Random pulse sequence. See Pulse sequences, random

Raypaths. See Pulse, seismic

Real time decociing, 74. 76-82

Rogacord method, 1- 2

Index

Instruments

coding-decoding, 12-13, 33, 39,

84-86

computers, seismic, 76-77

earth tamper, 38

recording, 7, 12, 13, 16, 34, 38,

39

sweeps. 1, 5, 11, 36, 53-54

Thumper, 7, 24-25, 28

vibrators, 1, 5, 6

Interference noise. See Organized noise

Ambient noise, 14-15,28 Autocorrelation function, 10, 11,

14, 27, 36, 41, 42, 44, 53, 55,

67-68

Chirp Radar. 1

Computers, seismic, 76-78

Correlation, 7, 11, 36-37, 42~44,

49,53-54.55,67,82

crosscorrelation, 6-7, 36, 74

Correlation noise, 8, 10, 14, 15, 42,

67

definition, 55-59

examples, 59-65

improvements, 65-73

Crosscorrelation. See Correlation, crosscorrelation

Mini-Sosie method, 38-39, 74, 77

Multiplicity, degree of, 6, 15-16

Noise. See Ambient noise; Corre

lation noise; Organized noise

Normal seismology method, 4, 5,

11, 28, 34-36

Decoding process, 1, 7. See also Instruments, coding-decoding; Pulse coding definition, 74

field correlator, 82-86

real time Sosie processing, 74,

76-82

shift and add, 74,75-76 Degree of mUltiplicity. See Multiplicity, degree of Dirac pulse, 14

Organized noise, 15, 28, 33, 36

Peaks, secondary, 11, 27,44, 67,

70

Pseudo-random pulse sequence. See Pulse sequences, pseudo random Pulse, seismic, 2-4, 12, 13, 36

Pulse coding, 2-6, 7, 8, 15-16,33,

36, 65, 74, 85. See also Mini

Sosie method; Seiscode

method; Sosie method

Pulse sequences, 5, 10, 11, 13-14,

24-26, 27, 36, 37, 53-54, 59,

74, 75

definition, 41-42

pseudo-random, 41, 42-47, 59

random, 41, 47 -53, 59

Earth tamper, 38

End of stack effect, 80

Equipment. See Instruments

Filters, 8, 70, 73, 84-85, 86

Frequency spectrum, 53. 54, 70,

73

Gaussian distribution. 48, 49. 50

88

Secondary peaks. See Peaks, secondary Seiscode method

applications, 36-37

characteristics, 27

definition, 24-25

examples, 34-36

implementation, 33-34

procedure, 25-26

results, 27 -33

Seismic computers. See Com puters, seismic Seismic correlation noise. See Correlation noise Seismic pulse. See Pulse, seismic Seismology, coded. See also Normal seismology method; Rogacord method; Transposed method, Vibroseis method Land. See Mini-Sosie method;

Seiscode method

Marine, 6, 36, 45. See also Sosie

method

Shallow land seismology, 6-7, 16,

62. See also Mini-Sosie method

Shift and add process, 74, 75-76

Signal to correlation noise ratio.

See Correlation noise . Sosie method, 27, 45, 74

advantages, 15-16

characteristics, 9 -11

decoding, 74, 75-82

definition, 9

examples, 16-23

implementation, 11-12

instruments, 12-13, 16

results, 13-15

Source patterns. See Space coding

Space coding, 7 -8, 13

Sparkers, 2, 9

Sweeps, I, 5, 53-54

reference, II, 36

Thumper, 7, 24-25, 28

Time coding. See Pulse coding

Time intervals. See Space coding

Time shift, 30

Transposed method, 39

Vaporchoc, 20

Vibrators, I, 5, 6

Vibroseis method, I, 5, 6, 11, 12,

14, 16, 68