GB2082771A - F-K Geophysical operations including filtering of seismic records - Google Patents

Abstract

Seismic signals are transformed into a F-K array of digital samples which represents amplitude as a function of frequency and wave number. The F-K array is then filtered by weighting all the samples in closed frequency regions with the weighting dependent upon signal and noise. Seismic record having an enhanced representation of the earth's formations is then generated from the filtered array.

Description

SPECIFICATION F-K geophysical operations including filtering of seismic records Background of the Invention This invention relates to geophysical exploration and more particularly to geophysical operations performed on f-k transforms of seismic records.

In seismic exploration the seismograms obtained in the field are processed to make them easier to interpret. Field seismograms include random, or incoherent, noise which is caused by the instruments used or the particular obscuring nature of the geophysical formations, and coherent noise which includes ghosts, multiple reflections, and surface waves. Geophysical operations which are performed on seismograms to make them more discernible include convolution, deconvolution, signature estimation, designaturizing, demultiplexing, and correlation. Some geophysical operations which reduce noise can be performed in the field. For example, geophones can be arranged in a particular pattern to deconvolve, or filter, a particular type of noise.However, the more prevalent practice is to perform these geophysical operations on the seismograms after they have been recorded and transported to a central processing center.

During the early development of seismic exploration, the seismograms were recorded as analog voltages on magnetic tape. Today, the seismograms are still commonly recorded on magnetic tape but they are recorded as digital samples Tepresenting the amplitude of a received seismic signal as a function of time. Since seismograms are usually obtained along a line of exploration on the surface of the earth, the digital samples can be formed into x-t arrays with each sample in the array representing the amplitude of the seismic signal as a function of horizontal distance and time. When such arrays are visually reproduced, by plotting or the like, seismic sections are produced. A seismic section depicts the subsurface layeringof a section of the earth. It is the principal tool which the geophysicist studies to determine the nature of the earth's subsurface formations.Before an array of seismic samples can be converted into a seismic section which can be interpreted by the geophysicist, the array must be extensively processed by one or more of the geophysical processing operations mentioned previously.

Of these geophysical processing operations, one of the most common is filtering (convolution).

Workers in the field have transformed x-t arrays into arrays representing amplitude as a function of frequency and wavenumber. This is commonly referred to as an f-k transformation. Kutrona, et al., Optical Data Processing, I.E.E.E. Proceedings, (1959) describesf-kfiltering in optical processing of data recorded as variable density photographs. In this type of processing, plane monochromatic light passed through a variable density photographic film, then through a spherical lens to produce a two dimensional Fourier transform of the object on the film. Jackson, P. L., "Analysis of Variable Density Seismograms by Optical Data Processor", Geophysics, No. 1, (1965) describes filtering f-k seismic sections by optical processing. U.S. Patent 3,370,268 Dobrin et al and Dobrin, M.V., "Short Note on Optical Processing and Filtering", Geophysics, No. 6, (1965) also describe optically filtering f-k seismic sections. The Dobrin article discusses the limitations on optical processing. Because of these limitations most geophysical processing is done on digital data processors, not optical processors.

In digital data processsing, the f-k transformation has been used as a tool to study seismic filtering. U.S. Patents 3,284,763 Burg et al. and 3,274,541 Embree describe velocity filtering which is carried out in the time domain on digital seismograms. These patents describe a type of velocity filtering which is commonly referred to as "pie slice" because of the shape of the filtered region in the f-k transform of the seismic section. Embree and Burg et al. do not perform a filtering operation on the f-k section; all filtering is in the time domain on sections in the normal x-t arrays. U.S. Patent 3,550,073, Foster et al. is an improvement on "pie slice" filtering.

British Patent 1,099,483 to Texas Instruments Incorporated describes a geophysical processing operation sometimes referred to as horizontal stacking. The f-k transformation is useful in understanding horizontal stacking, however, all operations in horizontal stacking are performed in the time domain, not on f-k transformed sections.

All of the foregoing types of spatial filters have the drawback of having a gentle slope between the pass band and the rejection band. Thus these filters lack selectivity in discriminating between desirable and undesirable events which are near one another in the f-k transform. It is an object of the present invention to provide a filter which discriminates between events with velocities or dips which are very close together in the f-k transform.

The reason that geophysical processing operations have not been previously performed on f-k transformed seismic sections is that it was thought that such an operation would violate a fundamental sampling theorem. However, I have found that certain geophysical processing operations, particularly filtering, can usefuily be performed on f-k transforms of seismic sections.

Accordingly, it is an object of the present invention to perform geophysical processing operations on seismic sections (arrays) representing amplitude and phase as a function of frequency and wavenumber.

Summary of the Invention In accordance with the present invention, seismic signals representing the amplitude of seismic reflections as a function of time and distance are transformed into a section representing amplitude as a function of frequency and wavenumber. Geophysical processing operations are performed on these f-k sections. In accordance with the invention, the f-k section is filtered by weighting all samples within prescribed closed regions of frequency and wavenumber.

In accordance with a further aspect of the invention, all samples are rejected except those representing reflections from geophysical formations having a prescribed form. By properly defining the boundaries of the regions of rejected samples in the f-k transform, reflections from formations with a particular form can be filtered, or passed. When the f-k transform is converted. back to a normal seismic section, the desired formations will be displayed. For example, it is possible to filter reflections from steeply sloping formations, or from formations having zero dip.

Further in accordance with the present invention, the f-k filter has very steep sides so that dip selectivity is improved over that of the optical processor and the velocity filter of the prior art.

The foregoing and other objects, features and advantages of the invention will be better understood from the following more detailed description and appended claims.

Short Description of the Drawings Fig. 1 depicts a seismic section in its normal form of amplitude as a function of distance and time, and the f-k transform of that section; Fig. 2 depicts a seismic section and its f-k transform; Fig. 3 depicts an f-k filter of the present invention; Fig. 4 depicts a seismic section, filtering of the f-k transform and the seismic section after being filtered; Fig. 5 is a flow-sheet depicting the filtering of this invention; Fig. 6 shows the impulse response of a time domain filter for removing water bound-reflected refractions; Fig. 7 is a model seismic section; Fig. 8 shows the f-k transform of the section of Fig. 7; Fig. 9 shows an f-k filter which rejects all samples except those representing reflections of interfaces having dips of .032 seconds per trace;; Fig. 10 is the f-k transform of Fig. 7 filtered with the filter of Fig. 9; Fig. 11 is the seismic section which results when Fig. 10 is converted to an x-t array; Fig. 12 shows an f-k filter to reject all but zero dipping reflections; Fig. 13 shows an f-k filter to reject zero dipping reflections; Fig. 14 shows a model seismic section; Fig. 15 shows the f-k transform of the section of Fig. 14; Fig. 1 6 shows the f-k section of Fig. 15 filtered with the filter of Fig. 12; Fig. 17 shows the x-t transform of Fig. 16; Fig. 1 8 shows the f-k transform of Fig. 1 5 filtered with the filter of Fig. 13; Fig. 1 9 shows the seismic section after the filtering depicted in Fig. 18;; Fig. 20 is a model seismic section; Fig. 21 shows the seismic section of Fig. 20 after it has been filtered in accordance with the present invention; Fig. 22 shows the seismic section of Fig. 20 after it has been filtered with a prior art pie slice filter; Fig. 23 shows the f-k transform of Fig. 20; Figs. 24 and 25 are field seismograms; Fig. 26 shows an f-k filter for signal to noise enhancement; Fig. 26a is the f-k transform of Fig. 24; Fig. 27 shows the field record of Fig. 24 after filtering with the present invention; Fig. 28 shows the field record of Fig. 25 after it has been filtered in accordance with the present invention; Fig. 29 shows an exemplary data processing apparatus on which the invention can be practiced.

Description of the Preferred Embodiments Before describing the present invention, it is useful to consider the seismic section of Fig. 1 and its f-k transform. A seismic section represents the amplitude of seismic signals as a function of distance x along a line of exploration and time t after the shot producing the reflections. Ideally, a seismic section depicts the subsurface layering which produced the seismic reflections, the idealized interfaces 11, 12 and 13 being shown in Fig. 1. A seismic section or record is represented by arrays of digital samples.

Consider the digital samples in column 46. These represent the amplitude of seismic reflections as a function of time at the location 46 along the line of exploration. The amplitude is designated A (x, t). To be precise, the digital samples themselves are referred to as an array whereas the output plot of these samples is a seismic section. However, it is common in the geophysics art to use the word "section" to describe both the plot and the array of digital samples and that convention will be followed here. In referring to a geophysical processing operation on a seismic section, it will be understood that it is the digital samples which are being processed.

Fig. 1 also depicts an f-k transform of a conventional seismic section. Fourier transforms which convert arrays of amplitude as a function of time and distance into arrays of amplitude as a function of frequency and wavenumber are well known. The right hand side of Fig. 1 depicts an array of digital samples for each frequency and wavenumber value in the array. The digital samples are designated A (f,k).

Fig. 2 depicts some of the properties of f-k transforms that are useful in seismic processing. The line 14 on the conventional seismic section transforms into the line 1 5 in the f-k transforms. The lines 16, which are at different positions but which have the same angle, or dip, transform into a single line 1 7. The line 1 8 transforms into the line 1 9. The sinusoids 20 transform into the point 21.

I have found that filtering of f-k transforms of seismic sections can be accomplished by rejecting all samples within a prescribed closed region of frequency and wavenumber. Such a filter is depicted in Fig. 3. Fig. 3 depicts an array of digital samples representing amplitude as a function of frequency f and wavenumber k. A vertical dimension has been added to the standard f-k plot of Fig. 3 to depict amplitude. Amplitude, W (i, j), for this example, is either 1 or 0, as is conventional. In accordance with the present invention, ail samples within a prescribed closed region of frequency and wavenumber having the boundaries 22-29 are rejected. In the simplest implementation, this rejection is easily accomplished by multiplying all samples in this closed region by 0.Fig. 3 depicts this by showing all samples within the closed region having the boundaries 22-29 as being 0, whereas all other samples are 1.

The usefulness of such a filter in seismic processing is demonstrated by Fig. 4, wherein an idealized seismic section 30 is represented. The section shows the horizontal reflecting interfaces 31 and 32 and the dipping interfaces 33, 34 and 36, all having the same dip. The seismic section also depicts water-bound reflected refractions, as displayed by the lines 36-39. This is noise which should be removed from the seismic section by processing.

In the f-k transform 40 of the seismic section, the horizontal lines 31 and 32 are transformed to the single vertical line 41 and the dipping interfaces 33-35 have been transformed-to the line 42. The water-bound reflected refractions have been transformed to the lines 43 46. In accordance with the present invention, these refractions are filtered out of the seismic section by rejecting all samples within the closed region of frequency and wavenumber indicated at 47. Because of the sampling interval, it is necessary for the region 47 to encompass a broader area than that in which the lines 43-46 lie.

Filtering is accomplished by multiplying all sampes in this region by 0. Only the lines 48 and 49 remain in the filtered f-k transform of the seismic section. When this is converted back to a conventional seismic section, the interfaces 31-35 remain, but the water-bound reflected refractions have been filtered out of the section. The usefulness of the present invention can be demonstrated by considering the difficulty of removing these water-bound reflected refractions by conventional time domain filtering.

Fig. 6 depicts the impulse response of a time domain filter which would remove water-bound reflected refractions from a seismic section. Those skilled in the art will recognize that such a filter is almost impossible to realize on a time space filter. It is exceedingly complex and would be so time-consuming to execute that its implementation is virtually impossible.

As another example, consider the f-k filtering of the idealized seismic section of Fig. 7. In Fig. 7 there are reflections indicated at seven different record times designated 50-56 and there are five reflections at each line. That is, the reflections 50a-50e have a To of .1 seconds, the reflections 51a--51e have a To of .2 seconds and soon. At each time there are reflections with five different dips between At = 0 and At = .032 seconds/trace. These thirty-five reflections transform into five lines in the f-k transform of Fig. 8.The reflections 50a, 51 a, .2.... 56a of Fig. 7 transform into the vertical line 57 of Fig. 8, the reflections 50b ... 56b transform into the line 58 in Fig. 8, and the reflections 50c... 56c transform into the line 59. The reflections 50d . .. 56d transform into the line segments 60a and 60b in Fig. 8. Note that these segments are a single line which wraps around the k boundary as a result of improper spatial sampling on the seismic section. This is a common occurrence. Simiiarly,'the steepest reflections 50e ... 56e in Fig. 7 transform into a line having segments 61 a, 61b and 61 c in Fig. 8.

Fig. 9 shows an f-k filter which rejects all reflections except those having the steepest dip of .032 seconds per trace, i.e., the reflections 50e . . 56e of Fig. 7. The closed region in which samples are not rejected has boundaries 62, 63a, 63b, 63c, 64a, 64b, 64c, and 65 which are linear functions of frequency and wavenumber. By rejecting all samples outside of this region, all reflections not having a dip of .032 seconds per trace are filtered from the seismic section. Fig.10 shows the f-k transform of the seismic section which has been filtered by rejecting all samples outside of the region defined by the linear boundaries 62-65 (Fig. 9). Only the line with the segments 61 a, 61 b and 61 c remains in Fig. 10.

When this is transformed back into a conventional x-t array, the seismic section of Fig. 11 results. Only the steepest reflections 50e . . 56e remain after the f-k filtering. Note the sharpness of the results, a result not obtained with velocity or pie-slice filters. In Fig. 11, the sinusoidal noise between reflections is a result of the increased intensity in f-k space along the desired dip created by interference with the rejected events.

Fig. 12 depicts an f-k filter which will reject all but zero dipping events, i.e., it will reject all reflections except reflections 56a . .. 56e of Fig. 7. All samples outside of the region having the linear boundaries 66-69 are rejected. The boundaries 67 and 69 are constant wavenumber boundaries.

Boundary 67 is a wavenumber which is a small finite portion of the highest wavenumber +k. The highest wavenumber is related to the horizontal sampling interval which is the horizontal distance along the line of exploration between the positions at which the CDP sets or traces on a field record or with a CDP gather are obtained. That is, the highest wavenumber is k = 1/(2Ax), where Ax is the horizontal sample interval between CDP sets. As shown in Fig. 12, the constant wavenumber boundary 67 is approximately .2 of the highest wavenumber. It will be understood that this boundary can be any small finite portion of the highest wavenumber. The boundary 67 is + a/2Ax and the boundary 69 is - a/2Ax, where a is the small finite portion.The boundaries 66 and 68 are constant frequency boundaries, specifically the lowest and highest frequencies present. The lowest and highest frequencies are related to the time sampling interval. That is, f = 1/(2AT).

Figs. 14-1 7 depict an example of the operation of the filter of Fig. 12. Fig. 1 4 is a seismic section with three families of reflections: 74, 75 and 76. Each has three pairs of reflections with different dips.

The f-k transform of Fig. 14 is shown in Fig. 1 5. This demonstrates the result of spatial aliasing on the transform of the steepest dips, a folding of the transform about the Nyquist wavenumber. When this is filtered by rejecting all samples except those representing flat, zero dipping, reflections, the f-k transform of Fig. 16 results. Note that this is analogous to processing normal moveouf at primary reflection velocity. When the f-k transform of Fig. 1 6 is converted back to a normal seismic section, Fig.

17 results. Only the flat reflections remain. This example demonstrates the sensitivity of the f-k zeroing filter on events which are close together in dip. This is quite difficult to achieve in time domain filtering.

Fig. 13 shows a filter which will reject flat reflections. The filter 13 will reject all samples in the region having the linear boundaries 70-73. This has the effect of filtering out the flat reflections 50a ... 56a of Fig. 7. As is known, reflections corrected at multiple velocity will have a zero moveout per trace. Therefore, the present invention provides an effective technique for sharply discriminating against multiple reflections. Again, the boundary 71 is a small finite portion of the highest wavenumber, +a/2Ax and the boundary 73 is -a/2Ax.

When the f-k transform of Fig. 1 5 is filtered with the filter shown in Fig.13, the section of Fig. 1 8 results. All samples within the region defined by the boundaries 70-73 have been rejected. When this array is transformed back into an x-t section, Fig. 19 results. This shows the rejection of flat reflections, which can be multiple reflections. Again, this demonstrates the sensitivity of the f-k zeroing filter on events which are close together in dip.

Figs. 20-23 are useful in demonstrating the improvement of the filter of the present invention over prior art velocity filters of the type commonly referred to as "pie slice". Fig. 20 is the model seismic section and Fig. 23 shows its f-k transform. The most steeply dipping reflections are filtered out by rejecting ail samples in the closed region having the boundaries 74a-74b, 75a-75b, and 76. When such a section is filtered in this manner, the seismic section shown in Fig. 21 results. Note that the most steeply dipping reflections are not present in Fig. 21.

When such a section is filtered with prior art time domain "pie slice" filters, the effect is to reject all samples within the pie-shaped region defined by the boundaries 74a and 75a in Fig. 23. The result of such a pie-slice filter is shown in Fig. 22. Low frequency components of the most steeply dipping reflections are removed, but the reflections still appear in the section of Fig. 22 because of high frequency components. In accordance with the present invention, the reflection is completely removed by rejecting all samples representing that reflection including the aliased portion within the boundaries 74b, 75b and 76 in Fig. 23.

To prevent aliasing such as shown in Fig. 23, the horizontal sampling interval must be less than: At =.5tut where T is the shortest period in the pulse and St the move-out density AT/AX of the reflection. If this spacing is not achieved, one must filter the seismogram so that the alias frequency components are removed. All frequencies must be rejected above f = (2AxSt)-l where Ax is the actual trace spacing. The f-k zero filter of this invention permits the rejection of the whole reflection by including the aliased component in a closed region of rejected samples.

As an example of signal to noise enhancement. consider the field records shown in Figs. 24 and 25. The field section of Fig. 24 was converted into the f-k section shown in Fig. 26a and filtered with the filter shown in Fig. 26. This filter rejects all samples within the closed region defined by the boundaries 77-93. Not that in the actual implementation the boundaries such as 78, 84, 86, 88, 90 and 91 are made up of segments, each one being a constant frequency or a constant wavenumber. In this manner, all boundaries of the filter in its actual implementation are constant wavenumbers or constant frequencies.

When the field record of Fig. 24 has been filtered with the filter of Fig. 26 and converted back to an x-t section, Fig. 27 is produced. In Fig. 27, the reflecting interface 94 can be clearly seen. In the field record, Fig. 24, the corresponding reflections 94a are barely discernible to a trained geophysicist. This is a good example of the powerful filtering capability of the present invention.

Similarly, when the field section 25 is filtered by an f-k filter of the present invention, the resulting seismic section shown in Fig. 28 is produced. Again, the filtering operation greatly enhances the appearance of the iayering of the earth. Figs. 24-28 present a good example of signal to noise ratio enhancement which can be obtained by filtering in accordance with the present invention.

A flow sheet depicting one computer implemented process for carrying out the present invention is shown in Fig. 5. This processing makes use of a known Fast Fourier Transform (FFT). This Fast Fourier Transform will operate in both directions, that is, from x-t to f-k and from f-k to x-t. Therefore, both a real and imaginary section must be provided as an input. As shown in Fig. 5, the array of digital samples representing an x-t field seismogram is provided as indicated at 1 00. The imaginary input is an array of zeros, as indicated at 101. The FFT operation is indicated at 102. This converts the seismic section into an array of digital samples representing amplitude as a function of frequency and horizontal distance.

The real part of this frequency transform is indicated at 103 and the imaginary part is indicated at 104.

These sections are multiplexed at 105 to rearrange the samples. That is, all of the first samples are collected together, all of the second samples are collected together and so on. This produces the real f transform 106 and the imaginary f transform 107. Again, the FFT operation is performed as indicated at 108 to transform the arrays into a real f-k transform 109 and an imaginary f-k transform 110.

Filtering is performed by multiplying each sample of the array by a weighting function W(i, j) and W(i, j). The real part of this operation is indicated at 111 and the imaginary part is indicated at 112. W(i, j), W(i, j) can be O in all parts of the array within the closed region of frequency and wavenumber. For example, it can be 0 for all samples in the array within the boundaries 22-29 of Fig. 3. Elsewhere in the array, W(i, j), W(i, j) can be 1. The filtered sections are again applied to the Fast Fourier Transform at 11 3 to transform the section back into an x-t seismic section indicated at 114.

The processing of the present invention includes the fundamental operations of performing a Fast Fourier Transform and an f-k zeroing filter operation. Each of these operations will be better understood from the following detailed description.

Fast Fourier Transform The Fast Fourier Transform module in a working embodiment of the invention is of the Cooley Tukey type described in Cooley, J. W.; Tukey, J. W. "An Algorithm for Machine Calculation of Complex Fourier Series," Mathematical Computation, Vol. 19, 1 965 pp. 297-301. This transform is one example of a technique that can be used in seismic data processing. The following definition of terms allows this use.

The Fourier series of a two dimensional function f(t, x) is given by:

where

the two dimensional series F

?im) is complex of the form:

where

(T L)=[b (T 2 +C2(n m)]V2 which can be expressed as a pair of functions, amplitude and phase, of the variables

#T L# For the purposes of seismic data processing, we are concerned with the variables x and t and the corresponding transform variables M n km= and L T where L is the period of the x variable and T is the period for the time variable.

t, x space f-k space 0# x # L 1 1 1 2#x # 2#x Variables 2Ax # 2Ax O # f = 0 # f= - # T 2Ax Ax kS L Sampling Interval At f < T Wave Number 2#x Nyquist point Frequency 2At Moveout density Velocity Key parameter AT at V 1/#t=f/k AX Moveout density can be positive or negative, resulting in a positive or negative velocity in f-k space.

Therefore, we display f-k transforms over the range 1 2At 1 1 2Ax 2Ax In geophysical exploration an arbitrary definition of dip, or AT/Ax, has been adopted. This arbitrariness stems from the fact that seismic sections are displayed under a convention which places northerly and easterly ends of lines on the right end of seismic section displays independently of the sense of the direction in which the line was shot. The f-k transforms described in the specification depend upon the order in which the seismic traces appear on the tape on which they are stored, the first trace defining the "O" of the x-axis and subsequent traces appearing in increasing positive x direction.

With this convention, events dipping downward in positive x are said to have positive dip. Those dipping upward in positive x have negative dip.

F-K FILTERING The filtering of the f-k transforms, indicated by the steps 111 and 11 2 in Fig. 5., is carried out by an operation which rejects, or zeroes, all samples of an array within a closed region. The conceptual listing of one computer program for carrying out this operation is given below.

PARAMETER LIST, X, X, NT, TO, TL, X1 SElSDATA (FIRST, LAST, T1, T2, FILE1, FILE2) PAD TRACES (STARTNO, VALUE 1. ENDNO, VALUE2) PAD TIME (TSTARTN, TVALUE1, TENDN, TVALUE2) TRANSFORM TIME (FILE2, FILE3, FILE4, START, STOP) MULTIPLEX(FILE3, FILE4, FIRST, LAST.REAL) MULTIPLEX (FILE4, FILES, FIRST, LAST, IM) TRANSFORM SPACE (FILES, FILE6, FILE7, FILE8, START, STOP) PLOT FK (X, T, f, K, LEVELS, KEY, FILE7, FILE8) FILTER (FR, Fl, ROW, COLUMN, KEY) FILTER FK (FR, FI, FILE7, FILE8, FILES, FILE10, KEY) PLOTFK (X,T,f, K, LEVELS, KEY, FILES, FILE10) TRANSFORM K (FILE9, FILE10, FILEl 1, FlLE12, STARTK, STOPK) MULTIPLEX (FILE11, FILE12, FIRST, LAST, REAL) MULTIPLEX (FILE12, FILE14, FIRST, LAST, IM) TRANSFORM F (FILE13, FILE14, FILE1S, START, STOP) SEISDATA Takes data between trace FIRSTR and LASTR from FILE1 and loads in FILE2.

PAD TRACES Pads ENDNO and STARTNO of traces at ends of FILE1 of VALUE1 and VALUE2 usually zeros.

PAD TIME Pads time before and after TSTARTN and TENDN with values TVALUE1 and TVALUE2 respectively, usually zeros.

TRANSFORM TIME Perform Fourier transform on fine data from FILE2 and puts real results into FILE3, imaginary into FILE4.

MULTIPLEX Reorganizes frequency sequential series of FILE3 and FILES into space sequential series in FILES and FILE6.

TRANSFORM SPACE Perform Fourier transform on space sequential series of FILES 5 and 6 with real results in FILE7, imaginary in FILE8.

PLOTFK Plots the fk transform.

FILTER Constructs weighting function FR and Fl for real and imaginary series in fk space or by setting key will construct a filter to operate only the magnitude of fk transform. A second option is 1/FR + Fl.

Other options are possible.

FILTER FK Performs product of FR, Fl elements of transform on FILES 7 and 8 with results on FILES 9 and 10.

Key is used to signal option as in FILTER.

PLOTFK Plots resulted FILTER FK transform.

TRANSFORM K Performs Fourier transform on K sequentil series of FILES 9 and 10 placing results in FILTER 11 and 12.

MULTIPLEX Reorganizes space sequential series on FILTERS 13 and 14.

TRANSFORM F Performs Fourier transform of frequency sequential series on FILTER 13 and 14 with resulting time sequential series on FILE 1 5.

The result of the operation is a time space or frequency wavenumber filter operation on the input data section or record.

The foregoing is a Fortran listing of a series of subroutines, functions or modules. Each performs a series of operations in a modular form of processing.

Fig. 29 shows in one working embodiment of the invention, the filtering operations that were carried out on a Control Data Corporation computer system, model no. 175/760, having a 6600 CPU and a CYPER 175 CPU, with the following peripheral equipment, CDC 6250 9 Track Tape Transporter; CDC MAP 111 Array Processor and CDC Extended Core Storage.The specifications for the system are: Centrai Processor: 1 8 and 60 Bit Registers Peripheral Processors: 12 Bit Registers Extended Memory (ESC): 100K 60 Bit Words Central Memory: 131K 60 Bit Words (6600) 262K 60 Bit Words (C1 75) Array Processor: CDC MAP III Mass Storage: 16 Model 844-41 348 Million Words Tape Drives: 2-7 track 556/800 BPI 1 9 track 800/1600 BPI 30-9 track 1600/6250 BPI 2-21 track 356 BPI Unit Record Equipment: model 405 card readers model 415 card punch 4 - line printers The programming required to practice the invention will be apparent to those skilled in the art from the foregoing and from the users manual for the particular computer employed.

While particular embodiments have been shown and described, various modifications are within the true spirit and scope of the invention. The appended claims are, therefore, intended to cover all such modifications.

Claims (11)

1. A method of seismic exploration of the earth's formations comprising: generating seismic signals representing the amplitude of seismic reflections as a function of time and distance along a line of exploration; transforming said signals into an f-k array of digital samples representing amplitude as a function of frequency and wavenumber: operating on said f-k array to perform geophysical processing operations; and generating from the array which has been operated upon a seismic record having an enhanced representation of said formations.

2. A method recited in claim 1 wherein said step of operating on said f-k array includes filtering by rejecting all samples defined by prescribed closed regions of frequency and wavenumber.

3. A method according to claim 2 in which the rejection filtering is carried out by weighting the samples in dependence upon signal and noise.

4. A method according to claim 2 or claim 3 wherein the rejected samples are outside said closed region which has boundaries which are linear functions of frequency and wavenumber on both sides of a line having a prescribed angle to reject all samples except those representing reflections from formations having a prescribed dip.

5. A method according to claim 2 or claim 3 wherein said closed region has boundaries, one of which is a constant wavenumber above zero and another is a constant wavenumber below zero and said region of rejected samples includes all samples of approximately zero wavenumber representing multiple reflections.

6. A method according to claim 5, wherein said constant wavenumbers are approximately + a/2 Ax where a is a small finite portion of the highest wavenumber and Ax is the horizontal distance along said line of exploration between the positions at which said seismic signals are obtained.

7. A method according to claim 4 wherein one of said boundaries is a constant wavenumber greater than zero and another of said region of rejected samples includes all samples having wavenumbers greater than said one boundary and less than said other boundary whereby only reflections having zero dip are presented in said seismic record.

8. A method according to claim 2 wherein said region has linear boundaries which are segments of constant frequency and constant wavenumber.

9. A method according to claim 2 wherein filtering rejects samples in a region in which the samples represent noise whereby the signal to noise ratio of the filteres section is improved.

10. A method according to any preceding claim further comprising: retransforming the filtered array into representations of reflection times as a function of distance along a line of exploration, and wherein the step of generating a seismic record includes plotting a seismic section of said reflection times as a function of distance,

11. A method according to any preceding claim further comprising: retransforming the filtered array into representations of reflection times as a function of distance along a line of exploration, and wherein the step of generating a seismic record includes storing an array of digital samples representing a seismic section of said reflection times as a function of distance.