Least-squares inverse filters have found widespread use in the deconvolution of seismograms and the removal of multiples. The use of least-squares prediction filters with prediction distances greater than unity leads to the method of predictive deconvolution which can be used for the removal of long path multiples. The predictive technique allows one to control the length of the desired output wavelet by control of the predictive distance, and hence to specify the desired degree of resolution. Events which are periodic within given repetition ranges can be attenuated selectively. The method is thus effective in the suppression of rather complex reverberation patterns. A back propagation(BP) neural network is constructed to perform the detection of first arrivals of the multiples and therefore aid in the more accurate determination of the predictive distance of the multiples. The neural detector is applied to synthetic reflection coefficients and synthetic seismic traces. The processing results show that the neural detector is accurate and should lead to an automated fast method for determining predictive distances across vast amounts of data such as seismic field records. The neural network system used in this study was the NASA Software Technology Branch's NETS system

Feuerbacher, G. A.

Moebes, T. A.

English

NASA Technical Reports Server

A Feasibility Study for Long-Path Multiple Detection Using a Neural Network 
G.A. Feuerbacher, Texaw Inc. and T.A. Moebes, SAIC 
Section 0.0 Abstract 
Least-squares inverse filters have found widespread use in the deconvolution of 
seismograms and the removal of multiples. The use of least-squares prediction filters with 
prediction distances greater than unity leads to the method of predictive &convolution which 
can be used for the removal of long path multiples. 
The predictive technique allows one to control the length of the desired output wavelet by 
control of the predictive distance, and hence to specify the desired degree of resolution. 
Events which are periodic within given repetition ranges can be attenuated selectively. The 
method is thus effective in the suppression of rather complex reverberation patterns. 
A back propagation(BP) neural network is constructed to perform the detection of first 
arrivals of the multiples and therefore aid in the more accurate determination of the 
predictive distance of the multiples. The neural detector is applied to synthetic reflection 
coefficients and synthetic seismic traces. The processing results show that the neural detector 
is accurate and should lead to an automated fast method for determining predictive distances 
across vast amounts of data such as seismic field records. The neural network system used in 
this study was the NASA Software Technology Branch's NETS system 
Section 1.0 Introduction 
The Wiener filter (least-squares inverse filter) is one of the most effective tools for the 
digital reduction of seismic traces. It is the most important element of many deconvolution 
methods. In one application this filter is used to deconvolve a reverberating pulse train into 
an approximation of a zero-delay unit impulse. More generally it is possible to arrive at 
Wiener filters which remove repetitive events having specified periodicity. Multiples are 
such events and the periodicity are the arrival times or "predictive distances" of the 
multiples. 
In this paper we develop a method using the BP neural network to detect multiples and 
their first arrivals. This would enable us to automatically determine predictive distances for 
each seismic trace and thus remove multiples more accurately and with a minimum effect on 
good data. The neural detector is applied to synthetic reflection coefficients and synthetic 
seismic traces. The processing results show that the neural detector is accurate and should 
lead to an automated fast method for determining predictive distances across vast amounts of 
data such as seismic field records. The neural network system used in this study was the 
NASA Software Technology Branch's NETS system. 
Section 2.0 Synthetic Data: Reflection Coefficients 
Figure 1. represents an idealized noise-free model of an offshore seismic situation(Peacock 
and Treitel, 1968). Reflector 1 is the water surface, reflector 2 is the water bottom, reflector 
3 is a strong interface beneath the water bottom, and S is the surface location just beneath the 
water surface. The associated normal incidence reflection coefficients are 1, cl,  and c2, 
respectively, while the transmission coefficient across reflector 2 is tl.  If c is the downward 
reflection coefficient, the corresponding upward reflection coefficient is -c. From physical 
considerations, we know that the magnitude of all reflection coefficients are less than unity. 
Figure 2. shows the deconvolution of a first-order ringing system 
(l,O,O, ... n..O,cl,O,O,...n..O,c12,0,0....n.O, -c$,o,o, ...XI.. 0, ~ 1 4 ,  OO, ... n..O ..........I ...........(I) 
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https://ntrs.nasa.gov/search.jsp?R=19960022633 2020-06-16T04:50:21+00:00Z
where n is the predictive distance. 
-el, c12 413 ,  c14) is (c~,O,O,...n..O,l). 
signal (l,O,O ,... LO). 
Figure 3. shows the deconvolution of a second-order ringing system 
The deconvolution operator that removes the multiples 
The results after deconvolution is the multiple free 
(l,O,O, ... n..O,-2c~,O,O,...n..O,3c~~,O,O ,... n..O, -4C13,O,O ,... n..O, 5 ~ 1 4 ~  O,O, ... n.O ..........) ....... 0 
where n is the predictive distance. The deconvolution operator that removes the multiples 
The results after deconvolution is -2c1, 3c12 -4~13, 5 ~ 1 4 )  is (c12,0,0 ,... n..0,2c1,0,0 ,... n..O,l). 
the multiple free signal (l,O,O, ..n. 0). 
We simulated the neural detector for the above synthetic seismic trace (I) above by training 
an NN with data of the form (-cl, c12 -c13, c14) , 0 c c l  c 1, as input where 4.5 indicated a 
multiple, and with data not of the form (-c1, c12 -c13, c14) , 0 c c l  c 1, as input where -0.5 
indicated an event that is not a multiple. The topology of the NN is shown in Figure 4. The 
network has four input nodes, two hidden nodes, and one output node. An example of 
training input indicating a multiple is (-0.5. 0.25, -0.125, 0.0625) for input and +0.5 for 
output, An example of training input indicating a non-multiple is (-0.5, 1.25, -0,145, 0.1117) 
for input and -0.5 for output. Another example of training input indicating a non-multiple is 
(2.0,-0.5, 0.25, -0.125) for input and +0.5 for output. This last example would simulate a 
window moving over a multiple but not quite covering the multiple. We trained the network 
with 5 multiples and 5 non-multiples and achieved 100% accuracy for 30 test cases. 
100% accuracy. 
We performed a similar experiment for a second-order ringing system and also achieved 
Section 3.0 Synthetic Data: Seismic Data 
Marine seismic data are frequently plagued by the presence of multiple reflections from the 
water bottom and by water-layer peg-leg multiples. This problem is especially severe in 
"hard bottom" areas where the reflection coefficient at the water-sediment is large, resulting 
in high-amplitude multiple reflections. Essentially, the water-bottom multiples arise because 
the water layer acts as a wave guide, resulting in repetitions of the water-bottom bounce. 
The peg legs arise from primary reflections that take an extra bounce or two in the water 
layer. There are two approaches to suppression of multiples, each depending upon one of the 
two distinguishing characteristics of multiples, namely periodicity and velocity. 
At shallow water depths (say, less than 250 ft.) the multiples are periodic, after normal 
moveout(NM0) correction, with a repetition period equal to the two-way travel time through 
the water layer. Predictive deconvolution is very effective in suppression of such multiples. 
When the water is deep, successive multiples are no longer periodic at far offsets, nor do 
they have the proper amplitude relations for predictive deconvolution to be successful. 
However, multiples typically spend more of their travel time in the lower velocity water layer 
than the primaries do, and as such have lower velocities. The differential moveout between 
multiples and primaries caused by the difference in their velocities has been successfully 
exploited in the common depth point (CDP) stacking scheme, as well as in exponential stacking 
rOUtines. 
At intermediate water depths (250 -1250 ft.) the multiples are not periodic, nor is the 
velocity difference between the primary and its associated (peg legs) multiples sufficient to 
allow for the application velocity-separation schemes mentioned above. The non periodicity 
of the multiples is shown on a synthetic field record in Figure 5 ,  where the spread is over 
578 
10,000 feet and the two-way water-bottom time is 200 msec. The two-way travel time to the 
primary is 1 second, and the velocity of the primary event is 6000 feedsecond. Notice that 
on the near trace the period of the (peg leg) multiples is 300 msec, whereas on the far trace 
the multiples are no longer periodic. This synthetic field record confirms the lack of 
periodicity of the multiples at a large offset, which precludes the use of conventional 
deconvolution schemes. Deconvolution schemes operate with a specified distance dependent 
upon the time span between a primary and its first multiple, and this time span is assumed to 
apply between successive multiples. 
Observing that (peg-leg) multiples on intermediate water depths are no longer periodic with 
increasing offset Hilderbrand( 1978) proposed a non periodic form of prestack gapped 
deconvolution to attenuate (peg leg) multiples. This report uses synthetic data to 
demonstrate the feasibility of such a deconvolution procedure being improved upon and 
extended to deep water depths using a neural network to determine the predictive distance 
for multiples. Extensive recording of a program originally coded by Hildebrand would be 
required. 
Section 3.1 Description of The Synthetic Seismic Traces. 
1) The "water layer" model(fie1d record) was created by generating spikes with a normal 
The reflection coefficients move-out equation and a model velocity of 5000 feet per second. 
were determined by the equation 
r = (V1 - V2)/(V2 + Vl), neglecting density. 
The half spaces were assumed to have velocities of 1100 ft./sec.(air) and 6500 ft./sec/ (rock). 
The data is sampled every two milliseconds. Convolution of the spikes(reflecti0n coefficients) 
with a minimum phase wavelet produced the final seismic trace(see Figure 6.). The first trace 
of the primary starts at 200 msecs and extends to 300 msecs. The first trace of the first 
multiple starts at 400 msecs and extends to 500 msecs. The first trace of the second multiple 
starts at 600 msecs and extends to 700 msecs(the second multiple is faint). We trained a BP 
network with 70 input nodes, 20 hidden nodes, and 2 output nodes to detect the multiples. 
Traces 1, 3, 5, 10, and 15 were input as part of the training data. The first 70 samples from 
each trace multiple were used. For the output nodes, true was indicated as +0.5 and false was 
indicated as -0.5. Five traces that were not multiples were generated and entered as training 
data in a similar manner. For test data we 
entered the first 70 samples of the remaining multiples and five new non multiple examples. 
We created one network for the first-order multiples and a second network for the second- 
order multiples. We achieved 100% accuracy in both tests. 
This gave the network a grater training scope. 
2) The Three-Layers Model (20 trace field record) data were generated by a wave-equation 
program (PARX) at Texaco, Incorporated. The assumed reflection times (at zero-offset) were 
350 msec, 500 msec, and 750 msec. The velocities of the three rock formations were 5000 
ftJsec., 6500 ft/sec., and 9500 ft./sec., respectively(see Figure 7). 
The three primaries start at 400, 500, and 750 milliseconds, respectively. The three 
corresponding first-order multiples start at 1200, 1450, and 1650 milliseconds, respectively. 
The topology and setup of the network was the same as in the "water layer" model. We 
worked only with first-order multiples. Three networks were created for each of the three 
different primaries' respective multiples. We achieved 100% accuracy in all three tests. 
The topology for the above networks is shown in Figure 8. 
Section 4.0 Mathematics Of Gapped, Predictive Deconvolution. 
579 
For zero-offset traces, and for normal incidence ray paths, peg legs from a primary reflector 
are periodic, the period being equal to the two-way travel time in the water-bottom(Backus, 
1959). Mathematically, the (peg-leg) multiple generation process can be described by the 
difference equation: 
m(n) - -2Ehn(n-T) - (R**2)mn(n-2T) + p(n) 
where 
n = sample number for some fixed sampling interval 
m = composite(primary + pegleg) signal received 
R = water-bottom reflection coefficient 
T = two-way travel time in water layer in samples 
p = primary signal giving rise to peg leg) multiples 
and, 
p(n) = m(n) + 2Rm(n - T) + (R**2)(n - 2T). 
The primary p(n) can be recovered, theoretically, from a weighted sum of the trace and its 
delayed samples. This is an finite impulse response operator with two gaps of T each-hence 
the terminology "double gapped " operator. Non periodic models of p(n) and m(n) have been 
postulated where both m(n) and p(n) are functions of T1 and T2 where T1 is the separation 
between primary and first (peg-1eg)multiple in sample intervals, and T2 is the separation 
between (peg-1eg)first multiple and second (peg-leg) multiple in sample intervals. = 
T2, this later model collapses to the periodic (peg-leg) multiple model. 
If T1 
The arrival time of the (peg-leg) multiples can be computed using Dix's formula in 
intermediate water depths. Applications have shown many inaccuracies in intermediate 
depth water. It is even recommended not to use this approach in deep water due to 
inaccurate calculations of T1 and T2, the predictive arrival times for the (peg-leg) multiples. 
Our feasibility study suggests that the predictive arrival times can be found automatically by 
identifying the multiples with a neural network. We could approximate the location of the 
multiples with Dix's equation, and fine tune their location with the neural networks. 
Section 5.0 Summary 
Neural Networks are now part of the leading edge in Geophysical data processing and 
interpretation. They have been recently successful in locating subsurface targets (Poulton, et 
al, 1992) and in obtaining seismic reflectivity sequences from seismic data(Wang, 1992). In 
this study we have shown the feasibility of developing a BP neural network for estimating the 
predictive distances of multiples where other traditional methods are not as adequate as 
desired. This seems to be particularly true in the case of deep water bottom multiples. The 
simulation data processing results showed that 1) the accuracy of the predictive distance of 
multiples can be enhanced with use of a neural detector over existing methods, and 2) the 
software implementation could be much faster since NN applications are potentially faster 
than traditional numerical and statistical methods. We look forward to the opportunity to 
implement an NN application and apply it to real data. 
580 
FIGURES 
Reflector 1 
ReYlector 2 
Reflector 3 
FIRST-ORDER R l N G l N G  SECOND-ORDER RING\ NG 
FIG, 1.  first- and second-order ringing in 3 2-layer marine model. 
1 
FIG. -2. Deconvolution of a first-order ringing system. 
The operator is shown in time-reversed form. 
1 
FIG. .3. Deconvolution of a secondsrder ringing sys- 
tem. The operator is shown intime-reversed form. 
00 0-0 Input Layer 
00 Hidden Layer 
00 Output Layer 
Figure 4. NN Topology For The Reflection Coefficients Data 
581 
f : : : : ~ S f l ? F k P r : f Z ' t ~ ' c r r n  ,. 
Figure 5. Synthetic gather with primary and multiple reflections 
WATER-MODEL 3-LAYERS 
Figure 6. 
Field Record 
Water-Layer Model of a 20 Trace Figure 7. Three Layer Model of a 20 Trace 
Field Record 582 
00 001 00 00 ... ............. 70 s............. ... ............. * ............... I 
00 00 .. ..... * ........ ... .... ..... 20 ........ * ...... * ............... 
Figure 8. Network Topology For Multiple Detection BP Network on Synthetic Seismic data 
REFERENCES 
1. Bachus,* M.M. (1959), Water reverberations-Their nature and elimination. Geophysics, 
~01.24, p. 233-261. 
2. Hildebrand, H.A. (May 1980), The estimation of primary waveforms in the presence of peg- 
leg multiples. Geophysics, vol. 12, p. 2353-265. 
3.) Poulton M., Stemberg, and GLass, C.E.(December 1992) Location of subsurface targets in 
geophysical data using neural networks. Geophysics, vo1.57, p. 1534-1544. 
4) 
Neural Networks, Vol3, No. 2, March 1992, p. 338-340. 
Wang, Li-Xin, A neural detector for seismic reflectivity sequences. IEEE Transactions On 
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A feasibility study for long-path multiple detection using a neural network

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