Pulse Coding in Seismology

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wV': 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

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FIELD DATA

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REFERENCE TRACE

CROSSCORELATION

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• 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.

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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:

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

SHifT

....

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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

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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

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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

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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.

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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).

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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

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• 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

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• 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).

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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.

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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