COMPUTING PROGRAM PRODUCT AND METHOD FOR PROSPECTING AND ELIMINATING SURFACE-RELATED MULTIPLES IN THE BEAM DOMAIN WITH DEGHOST OPERATOR

Abstract

A computing program product and method for prospecting and eliminating surface-related multiples in the beam domain with deghost operator, are disclosed. The method and system are based on the compress-sensing theory, which decompose the common shot data into sparse shot beams, then convolve the sparse beams instead of dense traces, to construct the surface related multiples. Those constructed multiples can be either subtracted from the data domain or the image domain, and surface-related-multiple-free images, can thereafter be generated to help illuminate and interpret the targets.

Claims

1. A computing program product, embodied in a computing system device with a non-transitory computer readable device, that stores instructions for performing by a device, a method that prospects and eliminates a surface-related multiple, in beam-domain, employing a beam-domain deghost operator. The instructions comprising: retrieving a set of image gathers, preconditioned to preserve signal amplitude information at various angles of source and receiver points of incidence locations, having several common beam centers, over a survey region; executing a computer program product for pre-processing the retrieved set of common image gathers, having several common beam centers, over a survey region; executing a computer program product for decomposing the retrieved set of common image gathers, having several common beam centers, over a survey region; arranging the pre-processed and decomposed set of image gathers by their source and receiver points of incidence locations with common beam centers, over a survey region over the survey region; repeating the arranging step for each common beam center of the pre-processed and decomposed set of common image gathers; deghosting the arranged common beam centers of each source and receiver points of incidence location; applying a beam-domain deghost operator to the deghosted common beam centers at each source point of incidence location; applying a beam-domain deghost operator to the deghosted of common beam centers at each receiver point of incidence location; splitting the set of image gathers at all source points of incidence locations, with the applied beam-domain deghost operator into primary-beams and ghost beams over each common beam center; splitting the set of image gathers at all receiver points of incidence locations, with the applied beam-domain deghost operator into primary-beams and ghost beams over each common beam center; executing a computer program product for convolving the set of image gathers at all source and receiver points of incidence locations having the applied beam-domain deghost operator; executing a computer program product for summing the convolved set of image gathers at all source and receiver points of incidence locations; generating surface-related, interbed multiples in data and image domains, for each summed set of image gathers at all receiver points of incidence locations; executing a computer program product for subtracting the generated surface-related, interbed multiples in data and images domain employing a least-square subtraction or curvelet subtraction; and storing a final generated surface-related, interbed multiples in data and images domain with subtracted multiples from the executed computer program product, to a memory resource.

2. The computer program product of claim 1, wherein the non-transitory computer readable device further stores a computer program comprising program code instructions which can be loaded in a programmable device to cause said programmable device to implement the instructions according to claim 1, when said program is executed by a processor of said device, coupled through a communication bus to a memory resource.

3. The computing program product, embodied in a non-transitory computer readable device of claim 1, wherein the instruction of executing a computer program product for pre-processing the retrieved set of common image gathers further comprises: a) sorting the retrieved set of image gathers, into common-source domain gathers and common-receiver domain gathers; b) deconvolving the common-source domain gather and common-receiver domain gathers; c) deghosting the deconvolved common-source domain gather and common-receiver domain gathers; and d) regularizing and interpolating the deghosted common-source domain gather and common-receiver domain gathers.

4. The computing program product, embodied in a non-transitory computer readable device of claim 1, wherein the instruction of executing a computer program product for decomposing the retrieved set of common image gathers further comprises: a) filtering the retrieved a set of image gathers; b) clipping the filtered set of image gathers; c) shaping a set of wavelets from the clipped image gathers; d) forming common beam centers, over the survey region; e) computing semblance analysis for each formed common beam centers, over the survey region; and f) storing sparse seismic elements from the computed semblance analysis to a memory resource.

5. The computing program product, embodied in a non-transitory computer readable device of claim 1, wherein the instruction of applying a beam-domain deghost operator to the deghosted common beam centers at each source point of incidence location further comprises the expression: $D_{X_g}^P\left(L,p^s,\omega \right)=\frac{D_{X_g}\left(L,p^s,\omega \right)}{\left(\exp \left[2{\mathrm{iz}}_s\omega \sqrt{\frac{1}{v^2}-{\left(p^s\right)}^2}\right]-1\right)}$

6. The computing program product, embodied in a non-transitory computer readable device of claim 1, wherein the instruction of applying a beam-domain deghost operator to the deghosted of common beam centers at each receiver point of incidence location further comprises the expression: $D_{X_g}^P\left(L,p^g,\omega \right)=\frac{D_{X_g}\left(L,p^g,\omega \right)}{\left(\exp \left[2{\mathrm{iz}}_s\omega \sqrt{\frac{1}{v^2}-{\left(p^s\right)}^2}\right]-1\right)}$

7. The computing program product, embodied in a non-transitory computer readable device of claim 1, wherein the instruction of executing a computer program product for convolving the set of image gathers at all source points of incidence locations having the applied beam-domain deghost operator; further comprises the expression: $m\left(s,s^{\prime }=g^{\prime },t\right)=\underset{L,p,\tau }{.Math.}\left\{D_{X_s}^P\left(L,s,p^g,\tau \right)*D_{X_{s^{\prime }}}^G\left(L,s^{\prime },-p^g,t-\tau \right)+D_{X_s}^G\left(L,s,p^g,\tau \right)*D_{X_{s^{\prime }}}^P\left(L,s^{\prime },-p^g,t-\tau \right)\right\}$

8. The computing program product, embodied in a non-transitory computer readable device of claim 1, wherein the instruction of executing a computer program product for convolving the set of image gathers at all receiver points of incidence locations having the applied beam-domain deghost operator; further comprises the expression: $m\left(g,g^{\prime }=s^{\prime },t\right)=\underset{L,p,\tau }{.Math.}\left\{D_{X_g}^P\left(L,g,p^s,\tau \right)*D_{X_{g^{\prime }}}^G\left(L,g^{\prime },-p^s,t-\tau \right)+D_{X_g}^G\left(L,g,p^s,\tau \right)*D_{X_{g^{\prime }}}^P\left(L,g^{\prime },-p^s,t-\tau \right)\right\}$

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The teachings of the present invention can be readily understood by considering the following detailed description in conjunction with the accompanying drawings.

[0050] FIG. 1, is a schematic diagram showing a cross-sectional view of a survey region with a well location, source locations, receiver locations, and elements, according to an embodiment of the present disclosure;

[0051] FIG. 2, illustrates a flow chart of the method and instructions to be used in a computer program product embodied in a non-transitory computer readable device, that stores instructions for performing by a device a method that prospects and eliminates a surface-related multiple, in beam-domain, employing a beam-domain deghost operator, according to an embodiment of the present disclosure;

[0052] FIG. 3, illustrates a flow chart of the sub-routine of executing a computer program product for pre-processing the retrieved set of common image gathers; according to an embodiment of the present disclosure;

[0053] FIG. 4, illustrates a flow chart of the sub-routine of executing a computer program product for decomposing the retrieved set of common image gathers; according to an embodiment of the present disclosure;

[0054] FIG. 5, is an illustration showing the survey region in a 2D model domain as the computer program product is executing the method that prospects and eliminates a surface-related multiple, in beam-domain, employing a beam-domain deghost operator, according to an embodiment of the present disclosure; and

[0055] FIG. 6, is an electric diagram, in block form of the computing program product embodied, that stores instructions for implementation by a device a method that prospects and eliminates a surface-related multiple, in beam-domain, employing a beam-domain deghost operator, according to an embodiment of the present disclosure.

DETAILED DESCRIPTION OF THE INVENTION

[0056] Reference will now be made in detail, to several embodiments of the present disclosures, examples of which, are illustrated in the accompanying figures. It is noted that wherever practicable similar or like reference symbols may be used in the figures and may indicate similar or like functionality. The figures depict embodiments of the present disclosure, for purposes of illustration only. One skilled in the art will readily recognize from the following description that alternative embodiments of the structures, systems, and methods illustrated therein may be employed without departing from the principles of the disclosure described herein.

[0057] The subject matter regarded as the invention is particularly pointed out and distinctly claimed in the concluding portion of the specification. The invention, however, both as to organization and method of operation, together with objects, features, and advantages thereof, may best be understood by reference to the following detailed description when read with the accompanying drawings.

[0058] Because the illustrated embodiments of the present invention may for the most part, be implemented using electronic components and circuits known to those skilled in the art, details will not be explained in any greater extent than that considered necessary as illustrated above, for the understanding and appreciation of the underlying concepts of the present invention and in order not to obfuscate or distract from the teachings of the present invention.

[0059] Any reference in the specification to a method should be applied mutatis mutandis to a system capable of executing the method and should be applied mutatis mutandis to a computer program product that stores instructions that once executed by a system result in the execution of the method.

[0060] Additionally, the flowcharts and block diagrams in the Figures (“FIG.”) illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the Figures. For examples, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowcharts illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified hardware functions or acts, or combinations of special purpose hardware and computer instructions.

[0061] Any reference in the specification to a computer program product should be applied mutatis mutandis to a system capable of executing the instructions stored in the computer program product and should be applied mutatis mutandis to method that may be executed by a system that reads the instructions stored in the non-transitory computer readable medium.

[0062] As used herein, “and/or” placed between a first entity and a second entity means one of (1) the first entity, (2) the second entity, and (3) the first entity and the second entity. Multiple elements listed with “and/or” should be construed in the same fashion, i.e., “one or more” of the elements so conjoined.

[0063] There may be provided a system, a computer program product and a method for dissipation of an electrical charge stored in a region of an object. The region of the object may be any part of the object. The region may have any shape and/or any size.

[0064] The object may be a part of the system. Alternatively, the object may be a substrate or any other item that may be reviewed by the system, inspected by the system and/or measured by the system.

[0065] As previously mentioned, exploration seismology aims at revealing the accurate location and amplitude of a target hydro carbonate within the subsurface from the prestack seismic data acquired at the earth surface. In presence of the multiples, this becomes a challenging task because the introduced errors and artifacts will significantly harm the migration, reflection tomography and velocity estimation process. To date, traditional or more advanced SRME method have treated the data with 3D sampling issues as the first-order factor instead and uses the 5D type regularization methods (or less accurate shot and cable interpolation/extrapolations) in order to reduce the multiple prediction sampling errors. Even with the obvious advantages of each of the existing SRME methods, few or none applications of data-based beam processing in the beam domain, have been mentioned in the art for the data-based, surface-related multiple or interbed multiple removal.

[0066] Therefore, embodiments of the present invention are based on the compress-sensing theory, wherein a beam method can decompose the dense data into sparse seismic elements and then save them for future seismic processing. The sparse beam elements are then described by their most relevant attributes including location, dips and wavelets, and capable of representing those complex and dense prestack dataset for following tomography and migration processing. Furthermore, embodiments of the present invention simplify the seismic processing in the sparse beam domain, which in turns reduces the time and computational-consuming seismic processing, to an acceptable turnaround time. Additionally, embodiments of the present invention introduce an additional beam-domain deghost operator into the beam-domain SRME flow, and thereby demonstrating its superiority over 2D/3D synthetic, and real datasets.

[0067] Turning over to FIG. 1, it represents a typical survey region 101, over a land-based region, showing different types of earth formation, 109, 110, 111, in which an embodiment of the present invention is useful. Persons of ordinary skill in the art, will recognize that seismic survey regions produce detailed images of local geology in order to determine the location and size of possible hydrocarbon (oil and gas) reservoirs, and therefore a well location 105. Nevertheless, as observed in FIG. 1, when using MWD downhole systems 108 during directional drilling, in order to reach the well or reservoir 105, the MWD downhole system 108 must deviate from a vertical downward trajectory, to a trajectory that is kept within prescribed limits of azimuth and inclination to reach a well or reservoir 105. This degree of deviation is given by a myriad of situations, but most likely due to populated or obstructed areas.

[0068] In these survey regions 101, sound waves bounce off underground rock formations during blasts at various points of incidence, sources, or shots 104, and the waves that reflect back to the surface are captured by seismic data recording or receiving sensors, 103, transmitted by data transmission systems 602, wirelessly, from said sensors, 103, then stored for later processing, and analysis by the computing program product, embodied in a non-transitory computer readable device, that stores instructions for performing by a device, a method that prospects and eliminates a surface-related multiple, in beam-domain, employing a beam-domain deghost operator.

[0069] In particular, persons having ordinary skill in the art will soon realize that the present example shows a common midpoint-style gather, wherein seismic data traces are sorted by surface geometry to approximate a single reflection point in the earth. In this example, data from several shots and receivers may be combined into a single image gather or used individually depending upon the type of analysis to be performed. Although the present example may illustrate a flat reflector and a respective image gather class, other types or classes of image gathers known in the art maybe used, and its selection may depend upon the presence of various earth conditions or events. As shown on FIG. 1, the reflections captured by the multiple seismic data recording sensors 103, each of which will be placed at different location offsets from each other, and the well 105. Because all points of incidences or shots 104, and all seismic data recording sensors 103 are placed at different offsets, the survey seismic data or traces, also known in the art as gathers, will be recorded at various angles of incidence represented by reflections to (downward transmission rays) 106 and from (upward transmission reflection) 107 the reservoir 105. Well location 105, in this example, is illustrated with an existing drilled well attached to a wellbore, 102, along which multiple measurements are obtained using techniques known in the art. This wellbore 102, is used to obtain well log data, that includes P-wave velocity, S-wave velocity, Density, among others. Other sensors, not depicted in FIG. 1, are placed within the survey region to also capture horizons data information required for interpreters and persons of ordinary skilled in the art to perform various geophysical analysis. In the present example, the gathers will be sorted from field records in order to examine the dependence of amplitude, signal-to -noise, move-out, frequency content, phase, and other seismic attributes, on incidence angles, offset measurements, azimuth, and other geometric attributes that are important for data processing and imaging and known by persons having ordinary skills in the art.

[0070] A receiving system or sensor as used herein, typically includes at least hardware capable of executing machine readable instructions, as well as the software for executing acts (typically machine-readable instructions) that produce a desired result. In addition, a retrieving system may include hybrids of hardware and software, as well as computer sub-systems.

[0071] Turning over to FIG. 2, 201 illustrates a flow chart of the method and instructions to be used in a computer program product embodied in a non-transitory computer readable device, that stores instructions for performing by a device a method that prospects and eliminates a surface-related multiple, in beam-domain, employing a beam-domain deghost operator. The method and instructions to be used in a computer program product embodied in a non-transitory computer readable device, that stores instructions for performing by a device a method that prospects and eliminates a surface-related multiple, in beam-domain, employing a beam-domain deghost operator, 201, begins by retrieving at 202 certain information from a survey region 101. In particular, the method starts when the non-transitory computer readable device, 605, of the computing program product embodied in a computing system device 601, receives a message hook from the telemetry system 602 that it has started retrieving data at 202 from a plurality of receiver sensors 103 located over a defined survey region 101, containing a set of image gather 203 from the survey region. Nevertheless, a person having ordinary skills in the art, will soon realize that the retrieved data 203 may also be acquired in a variety of other ways, like from an external database already containing said data, from a variety of seismic surface or subsurface seismic tomography surveys, as well as from the memory resource 603, of the computing program product embodied in a computing system device 601.

[0072] Once said set of image gathers 203 has been retrieved, the non-transitory computer readable device, 605 will message the memory resource 603, of the computing program product embodied in a computing system device 601, to begin executing at 204 a multi-thread two-part sub-routine, which is illustrated by FIG. 3 and FIG. 4. In particular, 301 illustrates how the sub-routine executes the computer program product for pre-processing the retrieved set of common image gathers. This is initiated by the non-transitory computer readable device, 605 executing a sorting command 302, over the set of image gathers into common shot/receiver gather and adapted to the input multiples by a least-square matching or curvelet matching method. Upon successfully executing the sorting command, the non-transitory computer readable device, 605 will begin deconvolving 303 in order to remove the embedded wavelets from the original input data (D.sub.X.sub.g(L, g, p.sup.s, τ)) 203, either in the data domain or the image domain. It is important to note, that even when the input data (D.sub.x.sub.g(L, g, p.sup.s, τ)) 203, is not preprocessed with source designature, or not preprocessed with source-side and receiver-side ghost removed in the 3D data-domain, the simple or traditional SRME flow in the time/beam domain would still be able to use a least-square matching filter or curvelet method to compensate the ghost effects at the convolution point together with source wavelet effects. Yet, those effects will create second-order errors when comparing to the 3D field data sampling issues which are not observed by the present invention due to the execution of step 204.

[0073] After the deconvolution has been executed by the non-transitory computer readable device, 605 it will begin the process 304 of conventional deghosting both sides (source and receiver) in order to prevent crosstalk between ghosts or between primaries while predicting the multiples by convolving the primaries with ghosts. Thereafter, the non-transitory computer readable device 605, will regularized using a combination of Fourier's theory and estimation methods to locate frequency on the irregular grid of the survey region 101 in order to obtain a constant grid of source and receiver locations. followed by an interpolation of missing near offsets and missing intermediate offsets.

[0074] Depending upon the computing program's utilization of the computing system device 601 the non-transitory computer readable device 605, will determine whether the subroutines within 204 will be performed in parallel or in sequence with a typical resource (CPU, GPU, and memory) utilization of less than 70%. Accordingly, the non-transitory computer readable device 605, will begin executing the computer program product for decomposing the retrieved set of common image gathers, having several common beam centers 401. This step begins with a structure-oriented filtering at 402, of the image gathers 203 in order to remove any undesired prestack seismic phenomena, while preserving amplitude of the 203 gathers. Said filtering 402 is not only executed along the offset, but also azimuth, inline, and crossline directions along the structural dip found in the survey region 101. Thereafter, the non-transitory computer readable device 605, will clip the filtered set of image gathers at 403 to the exact value of the image, in order to allow for more precision of the retrieved set of image gathers 203, as well as increase compatibility with other applications. One the set of image gathers 203, have been clipped the non-transitory computer readable device 605, will begin shaping wavelets at 404 from clipped gathers to form beams at 405. The wavelet shaping that occurs at 404 is a localized transform in both time and frequency domains and is advantageous to the method of the present invention as it is used to extract information from a signal that is not possible to unravel with a Fourier or even windowed Fourier transform. Additionally, beam forming step 405 will take the form of multi-arrival Kirchhoff-beam migration in order to make the image cleaner for post-processing. Once the beam is formed, the non-transitory computer readable device 605, will determine its composition in the form of a regular or irregular beam. If the beam is regularly formed, then the non-transitory computer readable device 605, will perform a Fast Fourier Transform (FFT), and the calculate the Inverse FFT. On the other hand, if the beam formed is irregular, then the non-transitory computer readable device 605, will execute the following algorithm:

[00001]$\begin{array}{cc}{D}_{X_c}\left(X,p^{\prime },\omega \right)=\left|\frac{\omega }{{\omega }_x}\right|\int \int \frac{{\mathrm{dx}}^{\prime }{\mathrm{dy}}^{\prime }}{4{\pi }^2}{D}_{X_c}\left(r^{\prime },\omega \right)\exp \left[{\mathrm{i\omega p}}^{\prime }.Math.\left(r^{\prime }-X\right)-\left|\frac{\omega }{{\omega }_x}\right|\frac{|r^{\prime }-X{|}^2}{2{\omega }_x^2}\right]& \left(1\right)\end{array}$

[0075] Upon successfully forming the beams of step 405, the non-transitory computer readable device 605, will begin computing semblance 406, in order to further refine the land acquisition input data. The use of this technique along makes it possible to greatly increase the resolution of the data despite the presence of background noise. Furthermore, those skilled in the art will soon recognize that the new data received following the computation of semblance 406 will be easier to interpret when trying to deduce the underground structure of an area. Weighted semblance can also be used by the non-transitory program computer readable memory storage device, 605, upon selection by a user of the computer program product, using the computer system device 606, through either the keyboard 609 or the mouse 610. This will help increase the resolution of traditional semblance and thereby make the traditional semblance analysis capable of providing more complicated seismic data. In the present embodiment, the computation of semblance utilizes the following algorithm:

[00002]$\begin{array}{cc}{D}_{X_c}\left(X,p^{\prime },\omega \right)=\left|\frac{\omega }{{\omega }_x}\right|\int \int \frac{{\mathrm{dx}}^{\prime }{\mathrm{dy}}^{\prime }}{4{\pi }^2}{D}_{X_c}\left(r^{\prime },\omega \right)e^{\left[{\mathrm{i\omega p}}^{\prime }.Math.\left(r^{\prime }-X\right)-\left|\frac{\omega }{{\omega }_x}\right|\frac{|r^{\prime }-X{|}^2}{2{\omega }_x^2}\right]};& \left(2\right)\end{array}$

[0076] Once the semblance has been computed at 406, the non-transitory program computer readable memory storage device 603, signals the computer system device 606, to display on monitor 608 the shot and receiver events, as well as each wavelet. The person having ordinary skills in the art, operating the computer system device 606, will soon realize from observing the display monitor 608, which events and wavelets are relevant from each semblance, and select them by using a combination of keyboard 609 and mouse 609 from the computer system device 606. Upon selection, the person of ordinary skills operating the computer system device 606, will be presented with a graphical user interface in monitor 608 asking to confirm selection. If a selection is confirmed, then the computer system device 606 messages the non-transitory program computer readable device, 603 via the communication bus 604, to store at 407, the sparse seismic elements which will typically include selected event(s) and wavelet(s) for each semblance. If the selection is not confirmed, the non-transitory program computer readable device 605, presents the events and wavelets through the computer system's 606 monitor 608 again for selection. Once the selected event(s) and wavelet(s) is/are stored at 407, the system exits sub-routine and finalizes the execution of the computer program product for pre-processing and decomposing the retrieved set of common image gathers, having several common beam centers, 204.

[0077] The memory resource 603, will send a signal over the communication bus 604, for the non-transitory computer readable device 605 to begin arranging or fixing at 205 the pre-processed and decomposed set of image gathers by their respective source and receiver location. The non-transitory computer readable device 605 will loop or repeat at 206 the processes of arranging until all set of image gather have been arranged by their source and receivers with common beam centers. Nonetheless, before moving on to the next step, the non-transitory computer readable device 605 will present someone skilled in the art operating the computer system device 606 through display monitor 608, with a graphical user interface to determine whether the non-transitory computer readable device 605 has satisfactorily completed step 206. Upon confirmation, the computer system device 606 messages the non-transitory program computer readable device, 603 via the communication bus 604, to begin deghosting at 207, the receiver-side/shot-side for common shot/receiver data, respectively.

[0078] At step 207, the non-transitory computer readable device, 605 will verify that all sub-routines executed at step 204 were successfully performed and begin deghosting at 207 applying the deghost operator to both sides (receiver and source) at 208. In particular, the beam-domain deghost that occurs at 207 for the source-side on decomposed common-shot Tau-P data D.sub.X.sub.S (L, p.sup.g, ω) (with source-side ghost already removed in the preprocessing step 204) will be implemented according to the following algorithm:

[00003]$\begin{array}{cc}{D}_{X_s}^P\left(L,p^g,\omega \right)=\frac{D_{X_s}\left(L,p^g,\omega \right)}{\left(\sin \left[z_g\omega \sqrt{\frac{1}{v^2}-{\left(p^g\right)}^2}\right]\right)}& \left(3\right)\end{array}$

[0079] Where (3) has p.sup.s and p.sup.g as the initial source-receiver ray slowness vector of the beams respectively; z.sub.s and z.sub.g as source-receiver depth respectively; and v as the velocity of the water column. D.sub.X.sub.s.sup.P (L, p.sup.g, ω) is then the ghost-compensated primaries Tau-P data for common shot X.sub.s, thereby (3) causing ghost side-lobes to collapse, whilst retaining the original phase of the wavelet. On the other hand, the beam-domain deghost for the receiver-side on a decomposed common-shot Tau-P data will be implemented according to the following algorithm equation that removes the receiver ghosts and retains the kinematics leaving a primary event at its actual arrival time:

[00004]$\begin{array}{cc}{D}_{X_s}^P\left(L,p^g,\omega \right)=\frac{D_{X_s}\left(L,p^g,\omega \right)}{\left(\exp \left[2{\mathrm{iz}}_g\omega \sqrt{\frac{1}{v^2}-{\left(p^g\right)}^2}\right]-1\right)}& \left(4\right)\end{array}$

[0080] As such, these beam-domain deg hosting algorithms executed at 207 by the non-transitory computer readable device, 605 are more accurate than a traditional data-domain 3D deghost as they are not performed as an inversion and computationally less-intensive and faster. These algorithms (3) and (4) take into account the source and receiver depth/ghost effects at the convolution point away from the free sea surface, so it can prevent cross-talks between ghosts or cross-talks between primaries, while predicting the multiples by convolving the beam primaries with beam ghosts. After algorithms (3) and (4) are executed, the decomposed common-shot Tau-P data D.sub.X.sub.s (L, p.sup.g, ω) is then split into beam primaries D.sub.X.sub.s (L, p.sup.g, ω) and beam ghosts D.sub.X.sub.s.sup.G (L, .sub.p.sup.g, ω) at 209 by the non-transitory computer readable device, 605.

[0081] With the beams split into primaries and ghost, the non-transitory computer readable device, 605 begins executing the steps of convolving and then summing the beam ghosts with beam primaries, at 210 and 211 respectively. Once the beam ghosts and the beam primaries have been summed together by the non-transitory computer readable device, 605, it generates at 212 the predicted surface-related/interbed multiples for common shot using algorithm (5) and algorithm (6) for the receiver data.

[00005]$\begin{array}{cc}m\left(s,s^{\prime }=g^{\prime },t\right)=\underset{L,p,\tau }{.Math.}\left\{D_{X_s}^P\left(L,s,p^g,\tau \right)*D_{X_{s^{\prime }}}^G\left(L,s^{\prime },-p^g,t-\tau \right)+D_{X_s}^G\left(L,s,p^g,\tau \right)*D_{X_{s^{\prime }}}^P\left(L,s^{\prime },-p^g,t-\tau \right)\right\}& \left(5\right)\\ m\left(g,g^{\prime }=s^{\prime },t\right)=\underset{L,p,\tau }{.Math.}\left\{D_{X_g}^P\left(L,g,p^s,\tau \right)*D_{X_{g^{\prime }}}^G\left(L,g^{\prime },-p^s,t-\tau \right)+D_{X_g}^G\left(L,g,p^s,\tau \right)*D_{X_{g^{\prime }}}^P\left(L,g^{\prime },-p^s,t-\tau \right)\right\}& \left(6\right)\end{array}$

[0082] 7Where from the above algorithms, m(s, g′, t) is one predicted multiple trace with source at s and receiver at g′, or m(g, s′,t) is the predicted multiple at source s′ and receiver g. Then the predicted multiple trace m(s, g′, t) or are sorted into common shot/receiver gather, and adapted to the input multiples by a least-square matching or curvelet matching method, finally it will be subtracted and removed from the original input data either in the data domain or the image domain. Note that for algorithm (5), if the source-side ghost is not removed in the 3D data-domain deghost preprocessing, the beam domain source-side deghost can also be implemented in the common receiver beam migration stage on predict primary data d.sub.X.sub.s(s, g′, t)-m(s, g′, t) which can be sorted into common-receiver domain. Nonetheless, these prediction multiples in algorithm (5) and (6), take into account the source and receiver depth/ghost effects at the convolution point away from the free sea surface, so it can prevent cross-talk between ghosts or between primaries while predicting the multiples by convolving the primaries with ghosts.

[0083] Thereafter, and after the non-transitory computer readable device 605, has generated the surface-related interbed multiples, it being executing at 213 the subtraction of the surface-related/interbed multiples in the data domain or in the image domain using least-square subtraction or curvelet subtraction. This will trigger, the non-transitory computer readable device 605 to signal the memory resource 603 to begin storing the added and eliminated a surface-related interbed multiples, in beam-domain, employing a beam-domain deghost operator. Furthermore, the non-transitory computer readable device 605 will signal the computer system device 606, to display on 608 a message to the user of the computing program product embodied in a computing system device 601, to decide whether to also store said generated the added and eliminated a surface-related interbed multiples, in beam-domain, employing a beam-domain deghost operator, to a different memory resource memory resource, such as an external memory device, to print the results to the printing device 611, or both.

[0084] FIG. 5, is an illustration showing the survey region 101, as a result of performing the array of operations and instructions for performing the method that prospects and eliminates a surface-related multiple, in beam-domain, employing a beam-domain deghost operator, 201 of FIG. 2. In particular, to achieve said results, FIG. 5 is shown divided by a primary beam represented by 502 and a ghost beam represented by 505. To sort them out and produce a useful outcome that can be utilized in the field by those skilled in the art, embodiments of the present disclosure process algorithms within method 201 represented by FIG. 2.

[0085] As it is shown on 502, the primary beam is represented by the input common shot data at a source point of incidence or shot, s represented by 104 and receiver at g, represented by 103 after it has been preprocessed with source-side deghost by a data domain 3D deghost algorithm. At 502, source s 104 produces a downward beam 106, which reflects off reservoir 105, while receiver g captures its upward reflection represented by 107. These are then decomposed in the common shot domain [D.sub.X.sub.s(r′, ω)], into common shot into Tau-P-domain sparse beams according to expression:

[00006]$\begin{array}{cc}{D}_{X_s}\left(L,p^g,\omega \right)=\left|\frac{\omega }{{\omega }_x}\right|\int \int \frac{{\mathrm{dx}}^{\prime }{\mathrm{dy}}^{\prime }}{4{\pi }^2}{D}_{X_s}\left(r^{\prime },\omega \right)\exp \left[\mathrm{i\omega }{p}^g.Math.\left(r^{\prime }-L\right)-\left|\frac{\omega }{{\omega }_x}\right|\frac{|r^{\prime }-L{|}^2}{2{\omega }_x^2}\right];& \left(7\right)\end{array}$

[0086] These, are then stacked according to expression:

I.sub.X.sub.s (r)=−C.sub.0Σ.sub.x ∫dω∫∫dp.sub.x.sup.gdp.sub.y.sup.gU.sub.x(r; L, p; ω)* D.sub.X.sub.s(L, p.sup.g, ω)   (8);

[0087] Here the function D.sub.X.sub.s(L, p.sup.g, ω) is the decomposed Tau-P data from common shot data (with source-side ghost already removed in the preprocessing), L is the common shot beam center L(L.sub.x, L.sub.y), p.sup.g is the slowness vector (p.sub.x.sup.g, p.sub.y.sup.g) at the receiver point r′(g.sub.x, g.sub.y), r′ is the trace location r′ (g.sub.x, g.sub.y), r is the image point r(x, y, z); D.sub.X.sub.s(r′, ω) is the recorded wavefield at common shot X.sub.s; U.sub.x(r; L, p; ω) is the migration operator which expand as:

[00007]$\begin{array}{cc}{U}_X\left(r;L,p;\omega \right)=\frac{-i\omega }{2\pi }\int \int \frac{d{p}_y^{r}d{p}_x^r}{p_z^s}{u}_{GB}^{*}\left(r;s,p^s;\omega \right)*u_{GB}^{*}\left(r;g,p^g;\omega \right);& \left(9\right)\end{array}$

[0088] Here u*.sub.GB(r; s, p.sup.s; ω) and u*.sub.GB(r; g, p.sup.g; ω) are the source beams and receiver beams respectively which can then be split into ghost beams 505, by the receiver-side beam domain deghost operator represented by 506. The computing program product 201, then executes the convolution instructions from the method that prospects and eliminates a surface-related multiple, in beam-domain, employing a beam-domain deghost operator; which convolves the top ghost beams (source at s represented by 104 and receiver at g represented by 103) with the bottom primary beams (source at s′ represented by 507 and receiver at g represented by 104) at the same convolution receiver point g, 103, that will generate a predict multiple beam with beam path s to g and g to s′, thereby forming a ghost*primary, wherein g, 103, actually becomes the beam center L. Thereafter the computing program product 201, will executes the summation instruction from the method that prospects and eliminates a surface-related multiple, in beam-domain, employing a beam-domain deghost operator; to the top predict beam (with beam path s to g to s′ and a form of ghost*primary) with another predict beam path from s to g to s′, as represented by beams 106, 107, 506, and 508 thereby forming a primary*ghost. The computing program product 201 will then sum over the convolution receiver point g/L with the slowness p to generate one predict surface-related multiple trace m(s,s′) with source at s and receiver at s′.

[0089] As it pertains to FIG. 6, the computing program product embodied in a computing system device 601 is shown comprising a telemetry system 602, a memory resource for storing data 603, a communication bus 604, a non-transitory computer readable device 605, and a computer system device 606. The computing program product embodied in a computing system device 601, illustrates a functional block diagram used to perform an array of operations and instruction for performing by a device, a method that prospects and eliminates a surface-related multiple, in beam-domain, employing a beam-domain deghost operator, 201 of FIG. 2.

[0090] The memory resource 603 may include any of various forms of memory media and memory access devices. For example, memory devices 603 may include semiconductor RAM and ROM devices as well as mass storage devices such as CD-ROM drives, magnetic disk drives, and magnetic tape drives.

[0091] The computer system device, 606, acts as a user interface the non-transitory program computer readable device, 605; to input, set, select, and perform the operations of acquiring, storing, splitting, computing, generating, retrieving, superimposing, re-sizing, locating, indexing, modelling, calculating, and repeating, (collectively the message hook procedures). Said computer system device, 606, is connected to (wired and/or wirelessly) through a communication device 604 to the telemetry system 602, to the memory resource 603, and to the non-transitory computer readable device 605. The computer system device, 606, further includes other devices like a central processing unit (CPU), 607, a display or monitor, 608, a keyboard, 609, a mouse, 610, and a printer, 611. One or more users may supply input to the computing program product embodied in a computing system device 601 through the set of input devices of the computing system 606 like 609 or 610. Nevertheless, a person having ordinary skills in the art will soon realize that input devices may also include devices such as digitizing pads, track balls, light pens, data gloves, eye orientation sensors, head orientation sensors, etc. The set of display devices 608 and 611 may also include devices such as projectors, head-mounted displays, plotters, etc.

[0092] In one embodiment of computing program product embodied in a computing system device 601 may include one or more communication devices (communications bus) 604, like network interface cards for interfacing with a computer network. For example, seismic data gathered at a remote site may be transmitted to the computing program product embodied in a computing system device 601 using a telemetry system 602, through a computer network. The computing program product embodied in a computing system device 601 may receive seismic data, coordinates, elements, source and receiver information from an external computer network using the communication's bus 604 network interface card. In other embodiments, the computing program product embodied in a computing system device 601 may include a plurality of computers and/or other components coupled over a computer network, where storage and/or computation implementing embodiments of the present may be distributed over the computers (and/or components) as desired.

[0093] The computing program product embodied in a computing system device, 601, has firmware, a kernel and a software providing for the connection and interoperability of the multiple connected devices, like the telemetry system 602, the memory resources for storing data, 603, the communication bus 604, the non-transitory computer readable device, 605, and the computer system device, 606. The computing program product embodied in a computing system device, 601, includes an operating system, a set of message hook procedures, and a system application.

[0094] Furthermore, because performance and computation costs are always an important issue, the computing program product embodied in a computing system device, 601, uses the non-transitory computer readable device, 605 to ensure that the steps of the method 201 will not be bottlenecked by the computing system (601) I/O, or any other network communications. In fact, file-distribution systems like Apache Hadoop in combination with proper data-compressions, as well as smart file caching according to the data will ensure that the operations or instructions performed by the computer program product for performing by a device, a method that prospects and eliminates a surface-related multiple, in beam-domain, employing a beam-domain deghost operator, 201, as shown on of FIG. 2; are only limited by the memory/cache speed and CPU/GPU computing power, and nothing else.

[0095] The operating system embedded within the computing program product embodied in a computing system device 601, may be a Microsoft “WINDOWS” operating system, OS/2 from IBM Corporation, UNIX, LINUX, Sun Microsystems, or Apple operating systems, as well as myriad embedded application operating systems, such as are available from Wind River, Inc.

[0096] The message hook procedures of computing program product embodied in a computing system device 601 may, for example, represent an operation or command of the memory resources, 603, the computer system device, 606, the non-transitory computer readable device, 605, which may be currently executing a certain step process or subroutine from the method that prospects and eliminates a surface-related multiple, in beam-domain, employing a beam-domain deghost operator, 201, as shown on of FIG. 2.

[0097] The set of message hook procedures may be first initiated by: (i) an input from a user, which will typically be a person having ordinary skills in the art, like the entering of user-defined values or parameters; (ii) the manipulation of the computer system device, 606; (iii) the processing of operations in the non-transitory computer readable memory device, 605; or (iv) automatically once certain data has been stored or retrieved by either the memory resources, 603, or the non-transitory computer readable memory device, 605. Based on any of these inputs, processes or manipulation events, the memory resource, 603, the non-transitory computer readable memory device, 605, or the computer system device, 606; generate a data packet that is passed using the communication bus, 604, which are indicative of the event that has occurred as well as the event that needs to occur. When either the memory resource, 603, the non-transitory computer readable device, 605, or the computer system device, 606, receive the data packet, they convert it into a message based on the event, and executes the required operations or instruction of 201. This is achieved when the operating system examines the message hook list and determines if any message hook procedures have registered themselves with the operating system before. If at least one message hook procedure has registered itself with the operating system, the operating system passes the message via the communication bus 604 to the registered message hook procedure that appears first on the list. The called message hook executes and returns a value to either the memory resource, 603, the non-transitory computer readable memory device, 605, or the computer system device, 606, instructing them, to pass the message to the next registered message hook, and either the memory resource, 603, the non-transitory computer readable memory device, 605, or the computer system device, 606. The computing program product embodied in a computing system device 601, continues executing the operations until all registered message hooks have passed, which indicates the completion of the operations or instruction 201, by the generation and storing a final generated surface-related, interbed multiples in data and images domain with subtracted multiples from the executed computer program product, to the memory resource, 603.

[0098] The non-transitory computer readable device, 605, is configured to read and execute program instructions, e.g., program instructions provided on a memory medium such as a set of one or more CD-ROMs and loaded into semiconductor memory at execution time. The non-transitory computer readable device, 605 may be coupled wired or wireless to memory resource 603 through the communication bus 604 (or through a collection of busses). In response to the program instructions, the non-transitory computer readable memory device, 605 may operate on data stored in one or more memory resource 603. The non-transitory computer readable memory device, 605 may include one or more programmable processors (e.g., microprocessors).

[0099] A “computer program product or computing system device” includes the direct act that causes generating, as well as any indirect act that facilitates generation. Indirect acts include providing software to a user, maintaining a website through which a user is enabled to affect a display, hyperlinking to such a website, or cooperating or partnering with an entity who performs such direct or indirect acts. Thus, a user may operate alone or in cooperation with a third-party vendor to enable the reference signal to be generated on a display device. A display device may be included as an output device, and shall be suitable for displaying the required information, such as without limitation a CRT monitor, an LCD monitor, a plasma device, a flat panel device, or printer. The display device may include a device which has been calibrated through the use of any conventional software intended to be used in evaluating, correcting, and/or improving display results (e.g., a color monitor that has been adjusted using monitor calibration software). Rather than (or in addition to) displaying the reference image on a display device, a method, consistent with the invention, may include providing a reference image to a subject.

[0100] Software includes any machine code stored in any memory medium, such as RAM or ROM, and machine code stored on other devices (such as non-transitory computer readable media like external hard drives, or flash memory, for example). Software may include source or object code, encompassing any set of instructions capable of being executed in a client machine, server machine, remote desktop, or terminal.

[0101] Combinations of software and hardware could also be used for providing enhanced functionality and performance for certain embodiments of the disclosed invention. One example is to directly manufacture software functions into a silicon chip. Accordingly, it should be understood that combinations of hardware and software are also included within the definition of a retrieving system and are thus envisioned by the invention as possible equivalent structures and equivalent methods.

[0102] Data structures are defined organizations of data that may enable an embodiment of the invention. For example, a data structure may provide an organization of data, or an organization of executable code. Data signals could be carried across non-transitory transmission mediums and stored and transported across various data structures, and, thus, may be used to transport an embodiment of the invention.

[0103] According to the preferred embodiment of the present invention, certain hardware, and software descriptions were detailed, merely as example embodiments and are not to limit the structure of implementation of the disclosed embodiments. For example, although many internal, and external components have been described, those with ordinary skills in the art will appreciate that such components and their interconnection are well known. Additionally, certain aspects of the disclosed invention may be embodied in software that is executed using one or more, receiving systems, computers systems devices, or non-transitory computer readable memory devices. Program aspects of the technology may be thought of as “products” or “articles of manufacture” typically in the form of executable code and/or associated data that is carried on, or embodied in, a type of machine readable medium. Tangible non-transitory “storage” type media and devices include any or all memory or other storage for the computers, process or the like, or associated modules thereof such as various semiconductor memories, tape drives, disk drives, optical or magnetic disks, and the like which may provide storage at any time for the software programming.

[0104] It is to be noted that, as used herein the term “survey region” refers to an area or volume of geologic interest, and may be associated with the geometry, attitude and arrangement of the area or volume at any measurement scale. A region may have characteristics such as folding, faulting, cooling, unloading, and/or fracturing that has occurred therein.

[0105] Also, the term “executing” encompasses a wide variety of actions, including calculating, determining, processing, deriving, investigation, look ups (e.g. looking up in a table, a database or another data structure), ascertaining and the like. It may also include receiving (e.g. receiving information), accessing (e.g. accessing data in a memory) and the like. “Executing” may include computing, resolving, selecting, choosing, establishing, and the like.

[0106] Acquiring certain data may include creating or distributing the referenced data to the subject by physical, telephonic, or electronic delivery, providing access over a network to the referenced data, or creating or distributing software to the subject configured to run on the subject's workstation or computer including the reference image. In one example, acquiring of a referenced data or information could involve enabling the subject to obtain the referenced data or information in hard copy form via a printer. For example, information, software, and/or instructions could be transmitted (e.g., electronically or physically via a data storage device or hard copy) and/or otherwise made available (e.g., via a network) in order to facilitate the subject using a printer to print a hard copy form of reference image. In such an example, the printer may be a printer which has been calibrated through the use of any conventional software intended to be used in evaluating, correcting, and/or improving printing results (e.g., a color printer that has been adjusted using color correction software).

[0107] Furthermore, modules, features, attributes, methodologies, and other aspects can be implemented as software, hardware, firmware or any combination thereof. Wherever a component of the invention is implemented as software, the component can be implemented as a standalone program, as part of a larger program, as a plurality of separate programs, as a statically or dynamically linked library, as a kernel loadable module, as a device driver, and/or in every and any other way known now or in the future to those of skill in the art of computer programming. Additionally, the invention is not limited to implementation in any specific operating system or environment.

[0108] While in the foregoing specification this disclosure has been described in relation to certain preferred embodiments thereof, and many details have been set forth for purpose of illustration, the invention is not to be unduly limited to the foregoing which has been set forth for illustrative purposes. On the contrary, a wide variety of modifications and alternative embodiments will be apparent to a person skilled in the art, without departing from the true scope of the invention, as defined in the claims set forth below. Additionally, it should be appreciated that structural features or method steps shown or described in any one embodiment herein can be used in other embodiments as well.

TABLE-US-00001 Symbols Table Symbol Brief Definition Symbol Brief Definition D.sub.X.sub.c (X, p′, ω) Frequency domain D.sub.X.sub.s.sup.P (L, p.sup.g, ω) Primary beams for decomposed Tau-P frequency domain data from common decomposed Tau-P data spread X.sub.c data, at Beam from common shot X.sub.s center X and slowness data, at Beam center L p′ and receiver slowness p.sup.g x Arbitrary point location τ Intercept time in tau-p domain t Time g and g′ Receiver location ω Harmonic waves of D.sub.X.sub.s′.sup.G Ghost beams for frequency frequency domain decomposed Tau-P data from common shot X.sub.s′ data D.sub.X.sub.c (r', ω) Recorded frequency m(g, g′ = s′, t) Time domain multiple domain common spread trace with source at g′ = X.sub.c wavefield at r′ s′ and receiver at g α P-wave velocity p.sup.s Slowness vector at source s T Travel Time D.sub.X.sub.g.sup.P and D.sub.X.sub.g′.sup.P Primary beams for frequency domain decomposed Tau-P data from common receiver X.sub.g and X.sub.g′ ν and ν' Velocity I.sub.X.sub.s (r) Common shot X.sub.s migration image at image point r x Location z.sub.g Receiver depth p.sub.x.sup.g x component of slowness vector p.sup.g at receiver location g X Common spread beam p.sub.y.sup.g y component of slowness center vector p.sup.g at receiver location g p′ Slowness vector U.sub.X Common spread migration operator r′ Trace location p.sup.g Slowness vector at receiver g location X.sub.c Common Spread point p.sub.z.sup.s z component of slowness vector p.sup.s at source location s D.sub.X.sub.c (X, p′, ω) Frequency domain D.sub.X.sub.s.sup.P (L, p.sup.g , ω) Primary beams for decomposed Tau-P frequency domain data from common decomposed Tau-P data spread X.sub.c data, at Beam from common shot X.sub.s center X and slowness data, at Beam center L p′ and receiver slowness p.sup.g x Arbitrary point location τ Intercept time in tau-p domain t Time g and g′ Receiver location ω Harmonic waves of D.sub.X.sub.s′.sup.G Ghost beams for frequency frequency domain decomposed Tau-P data from common shot X.sub.s′ data D.sub.X.sub.c (r′, ω) Recorded frequency m(g, g′ = s′, t) Time domain multiple domain common spread trace with source at g′ = X.sub.c wavefield at r′ s′ and receiver at g α P-wave velocity p.sup.s Slowness vector at source s T Travel Time D.sub.X.sub.g.sup.P and D.sub.X.sub.g′.sup.P Primary beams for frequency domain decomposed Tau-P data from common receiver X.sub.g and X.sub.g′ ν and ν′ Velocity I.sub.X.sub.s (r) Common shot X.sub.s migration image at image point r x Location