“2D Transforms”;
2D Transforms
4.1 introduction
In this chapter we will work with the following processes:
1- FX-FK filter for ground roll and random noise.
2- Forward Tau-P transform.
3- Inverse Tau-P transform.
4- Radial trace forward transform.
5- Radial trace inverse transform.
6- Radon transform, forward, inverse, and multiple removal.
4.2 2D Transforms
4.2.1 FX-FK filter application to remove or isolate Linear Noise and 3D Linear Noise
4.2.1.1 INTRODUCTION:
Here we will apply (FK- FX) filter on 2d and 3d land data. The Filter is applied to remove or isolate linear noise. Close to pie-shape operator is designed in FK domain within defined the apparent velocity range, as well as the noise temporal and spatial frequency ranges. Operator is converted in FX domain and applied using the exact shot/receiver coordinates. The level of noise removal is controlled by the length of the applied operator.3D case: operator is applied on shot gathers in moving azimuthal sectors. As a next step noise is obtained by subtracting FX-FK filtered data from the initial data. Adaptive subtraction is used to accurately remove noise without damaging the signal.
The F-X prediction filter was first introduced by Canales (1984), and formulated to the F-XY filter later by Chase (1992). It is widely used as a tool of random noise attenuation. It appeals to seismic data processing mainly due to its general signal model assumption, i.e., signal is predictable by convolution filters. This is a better signal model than that of other noise attenuation algorithms. For example, the K-L transform assumes that signal is horizontally aligned events with only amplitude variations. The Radon transform is more flexible than the K-L in allowing signal to follow varied trajectories than simply being flat in time, but a few fixed types of trajectories (hyperbolic, parabolic and straight lines to name some) could not fully cover all signal behavior.
4.2.1.2. Theory, work method and results
4.2.1.2.1 Theory
FK FILTERING is transforming the data to the FK domain, raising the amplitude spectrum to an exponential power and performing the inverse transform is a method sometimes used to reduce the levels of random noise.
FX DECONVOLUTION, This is the commonest modern technique for attenuating random noise since it has few artifacts and can be run in 2D or 3D modes. An important feature is the addback of original signal which can be tailored by the processor to produce a section with a pleasing appearance. Small temporal (e.g. 10 traces) and spatial (e.g. 20ms) windows of input data are Fourier transformed to the FX domain. Deconvolution operators are designed in the lateral (X) dimension to predict the coherent parts of the signal. Subtracting the coherent parts will leave the incoherent parts i.e. random noise which can then be inverse transformed and subtracted from the signal. The next window would then be selected, ensuring some overlap with the previous window.
4.2.1.2.2 Work method and results
The process done by four steps, first applying linear noise removal using FK-FX filter on our data, the input is 2d land data for linear noise and 3d land data for 3d Linear Noise Removal. For the Trace Distance Noise Filter 10 m the average step for offsets, Length of the filter in FX domain 2000 m, Apparent minimum slowness of noise 8 ms/trace ,Apparent maximum slowness of noise 9000 ms/trace ,Maximum frequency for band-pass 100 HZ ,Max Frequency (Linear Noise) Maximum frequency of ground roll for operator 50HZ.,Muting (% of Nyquist) Percentage of Nyquist spatial frequency for wave-number muting 60%.For 3D Linear Noise Removal, 3D Azimuth Slice Size 45 degree the size of azimuthal sector. Minimum Offset (0 m), Distance from the shot for borrowing traces to compensate for lack of near offsets in the sector. Second step, is linear noise extraction, subtract filtered data from the input data, the input is the input and output of first, and output is extracted noise. Third step, applying a band pass filter on the extracted linear noise, the input is extracted noise (output second step), the output is filtered noise. The ormsby band pass filter parameters ,low truncation 10HZ ,low cut frequency 15 HZ,high cut frequency 55 HZ,high truncation 60HZ ,filter in frequency domain ,percent zero padding for FFT 10.Step four, Adaptive subtraction input data (first step input) minus filtered noise (third step output ), the input for this step have two inputs, one is the input of first step and the second is filtered noise (output third step).the operator lag for time domain Adaptive subtraction 10 ms ,moving window shift 50%.
The four steps done can be illustrated in fig (4.2.1-1).
Fig (4.2.1-1) shows the flow used for this work
In fig (4.2.1-2) shows the raw data and fig (4.2.1-5) 3d raw data shot point sort, 192 traces, used for flow in fig (4.2.1-1). The first output which is output of first step can be represent in fig (4.2.1-3) for 2d land data, and fig (4.2.1-6) for 3d land data. After applying the flow in fig (4.2.1-1) the output of step four (Adaptive subtraction) is removal noise, which can be illustrated in fig (4.2.1-4) for linear noise removal (2d land data), and 3d linear noise removal for 3d land data.
Fig (4.2.1-2) 2d land data raw data shot point sort, 120 traces
Fig (4.2.1-3) Fk-fx data, 2d land data after applied fk-fx filter, shot point sort, 120 traces
Fig(4.2.1-4)After applied flow fig(1), Removal noise
Fig (4.2.1-5) 3d raw data shot point sort, 192 traces
Fig (4.2.1-6) Fk-fx data, 3d land data after applied fk-fx filter
Fig (4.2.1-7) 3d land data after applied flow in fig(1), 3D Linear Noise removal
4.2.2 A review of forward Tau-p transform in F-K and F-X domain (remove surface noise).
4.2.2.1 Introduction:
The Tau-p transform is an attempt to preserve the wave field characteristics of the seismic data. A seismic section in theTau-p domain offers an alternative view in which all subsurface reflectors are illuminated by incident energy of a fixed ray parameter. One advantage of working in theTau-p domain is that we can study the different wave modes as function of their corresponding slowness values (p=1/v), where v is the propagation velocity. Then, the Tau-p transform is useful processing tool because it provides an increased separation between different seismic waves (i.e., multiples, ground-roll, P and S waves among others).
Given that there is minimal deterioration of the seismic data due to transform artifacts, a simplified interpretation of field records and better noise suppression can be obtained in the t-p transform. This transformation has been world-wide used and well researched for two-dimensional seismic data recording during decades. For 3D data there are some mathematical developments and several approaches taking advantage of particular symmetries in the data (Evans, 1991).There are many references in the literature to this transform. – Dunne, J. and Beresford, G., 1995, "A review of the tau-p transform, its implementation and its applications in seismic processing": Expl. Geophys., 26, no. 01, 19-36.
4.2.2.2. Theory, work method and results
4.2.2.2.1 Theory
The forward Tau-P Transform works by using an FK or TX (slant-stack) method to calculate the forward tau-p transform of the input traces. The output of this process is a set of traces (possibly but not necessarily equal to the number of input traces) whose samples are amplitudes corresponding to a certain tau and a certain "p" or slope interpolated for each trace between the minimum and maximum desired slope.
4.2.2.2.2 Work method and results
The input data are normally raw uncorrected shots (no NMO), but they can also be pre-stack data sorted by some key (e.g. Shot, or CMP). In these cases, the forward Tau-P will automatically stop at the end of each "group" (be it Shot, Receiver or CMP gather). In other words, no "mixing" will occur between adjacent shots, or CMP's.in this paper we will use shot group .There are two options for Forward Tau-P Transform, one is Forward Tau-P Transform in F-K domain, and this use a Fourier transform method to calculate the forward tau-p transform. And the second is Forward Tau-P Transform in T-X domain, this calculate the tau-p transform in the T-X domain (in other words) calculate the components of the tau-p transform by slant stacks. The distance between traces of the input data is 20 M, the lowest frequency we wishes to keep is 3HZ ,All lower frequencies will be set to zero. Minimum Tau-P Slope is (-0.00033 s/m), this value has units of seconds/meter. Maximum Tau-P Slope (0.00033s/m). Number of Slopes is equal to Number of Input Traces, then Forward Tau-P transform will have the same number of "traces" as the input data. Each "trace" of the forward tau-p transform corresponds to a "slope" – or "p" value. These "p" values are linearly interpolated between the Minimum Tau- P Slope and the Maximum Tau-P Slope above. Noise is obtained by subtracting Tau-Pi filtered data from the initial data. Adaptive subtraction is used to accurately remove noise without damaging the signal. The linear noise is filtered by taking the forward Tau-Pi transform in cascade Noise is obtained by subtracting Tau-Pi filtered data from the initial data and the Adaptive subtraction is used to accurately remove noise without damaging the signal. The operator lag for time domain Adaptive subtraction 10 ms, moving window shift 100%. The mute data trace was as follow, TAPER Mute Zone 4 samples, Mute Location X: 680.000 Y: -0.000.
Fig (4.2.2-1) shows the flow use for done this work.
In case 1, the flow in fig (4.2.2-1), the first case is tau-p extracted Nosie, and there are two outputs for tau-p transform in F-K, and F-X.and they are represented in Fig(4.2.2-4), shows the outputs of first case in flow(fig4.2.2- 1),(a) tau_pi_noise ,2d land data ,tau-p transform in F-K .(b) tau_pi_noise ,2d land data ,tau-p transform in T-X .(c) Different between tau_pi_noise in F-K and tau_pi_noise in F-X .
The case 2, is Tau-p filtered data, we will work with one input 2d land data, and the Adaptive subtraction can be in time domain Adaptive subtraction or in frequency domain Adaptive subtraction. While Ormsby band filter also can be filter domain frequency or filter domain time. So Fig (4.2.2-2) shows the possibility of work in flow in fig (4.2.2-1) case (2), for input, tau-p transform, Adaptive subtraction and Ormsby band filter.
For case 1 there will be two outputs. While for case 2 there are eight outputs as its shows in fig (4.2.2-2).
Tau- p transform Adaptive subtraction Ormsby band filter
Input data F-K time domain domain frequency
F-X frequency domain domain time
Fig (4.2.2-2) the possibility of work in flow in fig (4.2.2-1) for input, tau-p transform, Adaptive subtraction and Ormsby band filter.
(a) (b)
(c) (d)
Fig (4.2.2-3) ,(a)show the input data ,2d land Raw +Statics ,sorted in shot point .(b,c,d) Amplitude spectrum for input data .
(a) (b)
(c)
Fig(4.2.2-4) shows the outputs of first case in flow (fig 4.2.2-1), extracted Nosie ,(a) tau_pi_noise ,2d land data ,tau-p transform in F-K .(b) tau_pi_noise ,2d land data ,tau-p transform in T-X .(c) Different between tau_pi_noise in F-K and tau_pi_noise in F-X .
(a)
(b)
(c )
(d)
(e)
(f)
(g)
(h)
Fig (4.2.2-5) shows the outputs of case 2 , Tau-p filtered data , blue color is average.(a ) amplitude spectral shot 163 + tau_pi F-K domain + time domain Adaptive subtraction +time domain orsmby filter,(b) amplitude spectral shot 163 +tau_pi F-K domain + time domain Adaptive subtraction +frequency domain orsmby filter,(c)shot_163+tau_pi F-K domain + frequency domain Adaptive subtraction +frequency domain orsmby filter,(d) amplitude spectral shot_163+tau_pi F-K domain + frequency domain Adaptive subtraction +time domain orsmby filter,(e) shot_163+tau_pi T-X domain + time domain Adaptive subtraction +time domain orsmby filter,(f) amplitude spectral shot_163+tau_pi T-X domain + time domain Adaptive subtraction +frequency domain orsmby filter,(g) amplitude spectral shot_163+tau_pi T-X domain + frequency domain Adaptive subtraction +frequency domain orsmby filter,(h) amplitude spectral shot_163+tau_pi T-X domain + frequency domain Adaptive subtraction +time domain orsmby filter.
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i)
Fig (4.2.2-6). (a) Amplitude spectral raw data. case 2, (b), amplitude spectral shot_163+tau_pi F-K domain + time domain Adaptive subtraction +time domain orsmby filter,(c) amplitude spectral shot +tau_pi F-K domain + time domain Adaptive subtraction +frequency domain orsmby filter ,(d)shot +tau_pi F-K domain + frequency domain Adaptive subtraction +frequency domain orsmby filter,(e ) amplitude spectral shot +tau_pi F-K domain + frequency domain Adaptive subtraction +time domain orsmby filter,(f) shot +tau_pi T-X domain + time domain Adaptive subtraction +time domian orsmby filter,(g) amplitude spectral shot +tau_pi T-X domain + time domain Adaptive subtraction +frequency domian orsmby filter,(h) amplitude spectral shot +tau_pi T-X domain + frequency domain Adaptive subtraction +frequency domain orsmby filter,(i) amplitude spectral shot +tau_pi T-X domain + frequency domain Adaptive subtraction +time domain orsmby filter.
4.2.3 A review of inverse Tau-p transform in F-K and F-X domain (remove surface noise).
4.2.3.1 Introduction:
Here will work by same way, we worked in (4.2.2) for forward tau-p transform, but here add to flow in Fig (4.2.2-1) inverse tau-p transfer this, shows in Fig (4.2.3-1), for other parameters will be the same.
4.2.3.2. Theory, work method and results
4.2.3.2.1 Theory
The Tau-p inverse works by using an FK or TX (slant-stack) method to calculate the inverse tau-p transform of the input traces. The output of this process is a set of traces (possibly but not necessarily equal to the number of input traces) whose samples are amplitudes corresponding to a certain tau (usually equal to the input time) and a certain "p" or slope (each trace has constant "p") interpolated for each trace between the minimum and maximum desired slope.The cascade of a forward and inverse tau-p transform preserves the relative amplitudes in a data panel, but not the absolute amplitudes meaning that a scale factor must be applied to data output by such a cascade before the output may be compared to the original data. This is a characteristic of the algorithm employed in this program.
4.2.3.2.2 Work method and results
The input data are normally raw uncorrected shots (no NMO), but they can also be pre-stack data sorted by some key (e.g. Shot, or CMP). In these cases, the inverse Tau-P will automatically stop at the end of each "group" (be it Shot, Receiver or CMP gather). In other words, no "mixing" will occur between adjacent shots, or CMP's.in this paper we will use shot group .There are two options for inverse Tau-P Transform, one is inverse Tau-P Transform in F-K domain, and this use a Fourier transform method to calculate the forward tau-p transform. And the second is inverse Tau-P Transform in T-X domain, this calculate the tau-p transform in the T-X domain (in other words) calculate the components of the tau-p transform by slant stacks, No rho filter is 71. The linear noise is filtered by taking the inverse Tau-Pi transform in cascade Noise is obtained by subtracting Tau-Pi filtered data from the initial data and the Adaptive subtraction is used to accurately remove noise without damaging the signal. The operator lag for time domain Adaptive subtraction 10 ms, moving window shift 100%. The mute data trace was as follow, TAPER Mute Zone 4 samples, Mute Location X: 680.000 Y: -0.000.
Fig (4.2.3-1) shows the flow use for done this work.
In case 1, the flow in fig (4.2.3-1), the first case is tau-p extracted Nosie, and there are two outputs for tau-p transform in F-K, and F-X.and they are represented in Fig(4.2.3-4), shows the outputs of first case in flow(fig (4.2.3-1),(a) tau_pi_noise ,2d land data ,tau-p transform in F-K .(b) tau_pi_noise ,2d land data ,tau-p transform in T-X .(c) Different between tau_pi_noise in F-K and tau_pi_noise in F-X .
The case 2, is Tau-p filtered data, we will work with one input 2d land data, and the Adaptive subtraction can be in time domain Adaptive subtraction or in frequency domain Adaptive subtraction. While Ormsby band filter also can be filter domain frequency or filter domain time. So Fig (4.2.3-2) shows the possibility of work in flow in fig (4.2.3-1) case (2), for input, tau-p transform, Adaptive subtraction and Ormsby band filter.
For case 1 there will be two outputs. While for case 2 there are eight outputs as its shows in fig (4.2.3-2).
Tau- p transform Adaptive subtraction Ormsby band filter
Input data F-K time domain domain frequency
F-X frequency domain domain time
Fig (4.2.3-2) the possibility of work in flow in fig (4.2.3-1) for input, tau-p transform, Adaptive subtraction and Ormsby band filter.
When forward tau-p in F-K domain or F-X, the inverse tau-p also in same domain. Fig (4.2.3-5). Shows the outputs of case, comparison, for fig ((4.2.3-2) the possibility of work.
(a) (b)
Fig (4.2.3-3) ,(a)show the input data ,2d land Raw +Statics ,sorted in shot point .(b) Amplitude spectrum for input data .
(a) (b)
(c)
Fig(4.2.3-4) shows the outputs of first case in flow (fig 4.2.3-1), extracted Nosie ,(a) tau_pi_noise ,2d land data ,tau-p transform in F-K .(b) tau_pi_noise ,2d land data ,tau-p transform in T-X .(c) Different between tau_pi_noise in F-K and tau_pi_noise in F-X ,(a) is base for comparison .
Fig (4.2.3-5), shows the outputs of case 2, in flow (fig 4.2.3-1). Tau-p filtered data , blue color is average.(a ) forward tau_pi in F-K domain + time domain Adaptive subtraction +time domain orsmby filter,(b) amplitude spectral shot 163 +tau_pi F-K domain + time domain Adaptive subtraction +frequency domain orsmby filter,(c)shot_163+tau_pi F-K domain + frequency domain Adaptive subtraction +frequency domain orsmby filter,(d) amplitude spectral shot_163+tau_pi F-K domain + frequency domain Adaptive subtraction +time domain orsmby filter,(e) shot_163+tau_pi T-X domain + time domain Adaptive subtraction +time domain orsmby filter,(f) amplitude spectral shot_163+tau_pi T-X domain + time domain Adaptive subtraction +frequency domain orsmby filter,(g) amplitude spectral shot_163+tau_pi T-X domain + frequency domain Adaptive subtraction +frequency domain orsmby filter,(h) amplitude spectral shot_163+tau_pi T-X domain + frequency domain Adaptive subtraction +time domain orsmby filter.
(a)
(b)
(c )
(d)
(e)
(f)
(g)
(h)
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i)
Fig (4.2.3-5). (a) Amplitude spectral raw data. case 2, (b), amplitude spectral shot_163+tau_pi F-K domain + time domain Adaptive subtraction +time domain orsmby filter,(c) amplitude spectral shot +tau_pi F-K domain + time domain Adaptive subtraction +frequency domain orsmby filter ,(d)shot +tau_pi F-K domain + frequency domain Adaptive subtraction +frequency domain orsmby filter,(e ) amplitude spectral shot +tau_pi F-K domain + frequency domain Adaptive subtraction +time domain orsmby filter,(f) shot +tau_pi T-X domain + time domain Adaptive subtraction +time domian orsmby filter,(g) amplitude spectral shot +tau_pi T-X domain + time domain Adaptive subtraction +frequency domian orsmby filter,(h) amplitude spectral shot +tau_pi T-X domain + frequency domain Adaptive subtraction +frequency domain orsmby filter,(i) amplitude spectral shot +tau_pi T-X domain + frequency domain Adaptive subtraction +time domain orsmby filter.
CONCOLUTION (chapter 4)
Minimum apparent slowness must be smaller than real minimum slowness of linear noise because we limit operator length when we apply.Max slowness can be just huge number, if we want to eliminate all low velocity linear noise. The shorter is operator length, the milder application of operator will be. To eliminate all linear noise this procedure can be applied in iterative manner. The fk-fx linear noise removal was reviewed and tested on 2d land and 3d land seismic data , Fig (4.2.1-2) 2d land data raw data shot point sort, 120 traces , Fig (4.2.1-3) Fk-fx data, 2d land data after applied fk-fx filter, shot point sort, 120 traces , Fig(4.2.1-4)After applied flow fig(1), Removal noise , Fig (4.2.1-5) 3d raw data shot point sort, 192 traces, Fig (4.2.1-6) Fk-fx data, 3d land data after applied fk-fx filter, Fig (4.2.1-7) 3d land data after applied flow in fig(1), 3D Linear Noise removal. It was found that on noisy synthetic images, numerical measurements indicate the fk-fx filter performs better at attenuation random noise than the f-k filter only. The residual noise after f-x filtering still appears fairly random, and the filter does not give rise to the same type of coherent In addition, the f-x filter is able to extract the signal without any guidance from the user, whereas an f-k dip reject filter must. The linear noise is filtered by taking the forward Tau-Pi transform in cascade Noise is obtained by subtracting Tau-Pi filtered data from the initial data and the Adaptive subtraction is used to accurately remove noise without damaging the signal. Each trace of the forward tau-p transform corresponds to a slope or "p" value, these "p" values are linearly interpolated between the Minimum Tau- P Slope (our value in this work 0 S/M) and the Maximum Tau-P Slope (our value in this work 0.005 S/M). The distance between traces of the input data was 10 M, and the lowest frequency we wishes to keep was 3HZ ,All lower frequencies set to zero. After applied tau-p transform the Amplitude spectrum for input data in fig (4.2.2-3,b,c,d) increased and so the average trace also and from results we see that tau-p transform give s very good results and comparison of tau-p in F-K domain with tau-p in ,the Fig (4.2.2-5)( e) shot_163+tau_pi T-X domain + time domain Adaptive subtraction +time domain orsmby filter,(f) amplitude spectral shot_163+tau_pi T-X domain + time domain Adaptive subtraction +frequency domain orsmby filter ,from results we found that applied TAU-P in T-x domain was giving better results .
References
1. Canales, L.L. 1984, Random Noise Reduction, 54th Annual SEG meeting, Atlanta
2. Chase, M.K., Random noise reduction by 3-D spatial prediction filtering, 62nd Annual SEG Meeting, New Orleans, USA. 1992.
3. Dunne, J. and Beresford, G., 1995, "A review of the tau-p transform, its implementation and its applications in seismic processing": Expl. Geophys., 26, no. 01, 19-36.
4. Jones, I.F., and Levy, S., 1987, Signal-to-noise ratio enhancement in multi-channel seismic data via the Karhunen-Loeve transform: Geophysical Prospecting, v. 35, 12-32.Holden-Day.
5. Treitel, S., 1974, The complex wiener f'flter: Geophysics, v. 39, 169-173.
6. Lawton, D., and Harrison, M., 1990, A two-component reflection seismic survey, Springbank, Alberta: in this volume.
7. Robinson, E.A., 1967, Multichannel time series analysis with digital computer programs: San Francisco,
8. Wang, Xi-shuo, Random noise attenuation of pre-stack seismic data by surface consistent prediction in frequency domain, CSEG National Convention, Calgary, Canada, 1996.
9. Wang, Xi-shuo, Surface consistent noise attenuation of seismic data in frequency domain with adaptive pre-whitening, 67th Annual SEG Meeting, Denver, USA. 1997.
References
1. Chapman, C.H., 1978, A new method for computing synthetic seismograms: Geophy. J. Roy. Astr. Soc., v. 54, p. 481-518.
2. Chapman, C.H., 1981, generalized radon transforms and slant stacks: Geophy. J. Roy. Astr. Soc., v. 66, p. 445-453.
3. Evans, B., 1991, ET- a slant-stack transform of three dimensional data: Expl. Geophy., v. 22, p. 135-142.
4. Dunne, J. and Beresford, G., 1995, "A review of the tau-p transform, its implementation and its applications in seismic processing": Expl. Geophys., 26, no. 01, 19-36.
5. Diebold, J.B. and Stoffa, P.L., 1981, The traveltime equation, tau-p mapping and inversion common midpoint data: Geophysics, v. 46, p. 238-254.
6. Kak, .C. and Rosenfield, A. 1982, Digital picture processing -Volume 1: Academic Press, Inc.
7. McCowan, D.W.and Brysk, H.,1989, Cartesian and cylindrical slant stacks, Paul L. Stoffa (ed.), Tau-p: A Plane Wave Approach to the Analysis of Seismic Data, p. 1-33.
8. Pan, N.D. and Gardner, G.H.F., 1984, Forward and inverse p-tau transformations using k-f transforms: Seismic Acoustics Laboratory Semi- Annual Progress Review, 14, 241-270.
9. Phinney, R.A., Chowdhury, K.R., and Frazer, L.N., 1981, Transformation and analysis of record
10. sections: J. Geoph. Res., 86, 359-377. Tatham, R.H., 1984, Multidimensional filtering of seismic data: Proceedings of the IEEE, 72, No. 10, Oct.
11. Stoffa, P.L., Buhl, P., Diebold, J.B., and Wenzel, F., 1981, Direct mapping of seismic data to the
12. domain of intercept time and ray parameter: Geophysics, V.46, p. 233-267.
13. Wade, J.C. and Gardner, G.H.F.,1988, Slant-stack inversion by hyperbolae extraction in the Fourierdomain: 58th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, p. 676-679..
14. Wade, J.C. and Lu, L., 1991, Some fundamentals of slant-stack methods: Slant-stack processing, SEG(Appendix 1), p. 457-481.
15. Yilmaz, O., Seismic data processing, 1987: SEG
.