GB2590177A

GB2590177A - Methods and devices performing adaptive subtraction of multiples

Info

Publication number: GB2590177A
Application number: GB2016945.4A
Authority: GB
Inventors: Hugonnet Pierre; Pica Antonio
Original assignee: CGG Services SAS
Current assignee: Sercel SAS
Priority date: 2019-11-21
Filing date: 2020-10-26
Publication date: 2021-06-23
Anticipated expiration: 2040-10-26
Also published as: GB2590177B; GB202016945D0

Abstract

A seismic exploration method 600 comprising obtaining 610 seismic data recorded by receivers detecting seismic waves emerging from a subsurface formation. A low-pass filter is applied 620 to the seismic data thereby yielding filtered data, the low-pass filter having a predetermined threshold frequency of no more than 10 Hz. A primaries model valid for a bandwidth with a highest frequency exceeding the predetermined threshold frequency is constructed 630 from the filtered data. Multiples are removed 640 from the seismic data using a multiple model and the primaries model to obtain seismic data without the multiples. An image of the subsurface formation is generated 650 based on the seismic data without the multiples, wherein the image is useable to locate natural resources and/or to plan or monitor their exploitation. Other aspects relate to an apparatus for performing the method and a computer-readable recording medium for storing codes which cause a computer to perform the method. The reconstructing may be performed using a blind deconvolution algorithm or a sparseness-promoting deconvolution or inversion. The multiples may be removed using a least square adaptive subtraction or using pattern recognition techniques.

Description

Methods and Devices Performing Adaptive Subtraction of Multiples

BACKGROUND

TECHNICAL FIELD

[0001] Embodiments of the subject matter disclosed herein generally relate to methods and devices for seismic exploration, and, in particular, to generating structural images of subsurface formations from seismic data in which the primaries are protected by adaptively subtracting multiples modeled using a low-frequency-data-based model. DISCUSSION OF THE BACKGROUND [0002] Seismic surveys are an important tool used in exploration of underground formations for locating natural resources such as oil and gas, and for designing production plans (i.e., for natural resources' extraction), including drilling locations and paths. Seismic data is generated during the surveys by seismic receivers detecting seismic waves emerging from the explored formations. Besides the primary waves that travel from a source to a receiver through the explored formation while experiencing a single reflection (and a single down-to-up direction change of their vertical motion), the seismic data includes multiples that are subject to multiple reflections (and are subject to multiple direction changes of their vertical motion while traveling between the source and the receiver). Obtaining an accurate structural image from the seismic data is challenging because the multiples and the primaries overlap.

[0003] Seismic data processing workflows have either (1) used the seismic data with the multiples to image the subsurface (which may yield artifacts while obscuring less illuminated features), or (2) subtracted modeled multiples from the seismic data before imaging the subsurface (which may inadvertently alter the primaries). In marine surveys, the strongest multiples are due to the surface water layer.

[0004] Verschuur et al. presented a method in which seismic data is used to model multiple reflections On the 1992 article "Adaptive surface-related multiple elimination" by Verschuur, D. J., Berkhout, A. J., and Wapenaar, C. P. A., published in Geophysics, Vol. 57, No. 9, pp. 1166-1177, which is incorporated herewith by reference in its entirety). This method that focusses on surface multiples only uses convolutions between acquired data traces and shot point traces located at receiver positions.

[0005] It remains desirable to improve the methods and devices removing all multiples (i.e., surface and internal multiples) from seismic data to achieve accurate and reliable images of the surveyed formations.

SUMMARY

[0006] Methods and devices according to various embodiments a primaries model based on low-frequency data is employed in removal of multiples from the seismic data in order to protect the primaries.

[0007] According to an embodiment, there is a seismic exploration method including obtaining seismic data recorded by receivers detecting seismic waves emerging from a subsurface formation, and applying a low-pass filter to the seismic data thereby yielding filtered data, the low-pass filter having a predetermined threshold frequency of no more than 10 Hz. The method further includes reconstructing, from the filtered data, a primaries model valid for a bandwidth with a highest frequency exceeding the predetermined threshold frequency, removing multiples from the seismic data using a multiple model and the primaries model to obtained seismic data without the multiples, and generating an image of the subsurface formation based on the seismic data without the multiples. The image is useable to locate natural resources and/or to plan or monitor their exploitation.

[0008] According to another embodiment, there is a seismic data processing apparatus having an interface configured to obtain seismic data recorded by receivers detecting seismic waves emerging from a subsurface formation, and a data processing unit connected to the interface. The data processing unit is configured to apply a low-pass filter to the seismic data thereby yielding filtered data, the low-pass filter having a threshold frequency of no more than 10 Hz, to reconstruct, from the filtered data, a primaries model valid for a bandwidth with a highest frequency exceeding the threshold frequency, to remove multiples from the seismic data using a multiples model and the primaries model to obtain seismic data without multiples; and to generate an image of the subsurface formation based on the seismic data without the multiples.

[0009] According to yet another embodiment, there is a computer-readable recording medium non-transitorily storing executable codes which, when executed by a computer, make the computer perform a seismic exploration method. The method includes obtaining seismic data recorded by receivers detecting seismic waves emerging from a subsurface formation, and applying a low-pass filter to the seismic data thereby yielding filtered data, the low-pass filter having a predetermined threshold frequency of no more than 10 Hz. The method further includes reconstructing, from the filtered data, a primaries model valid for a bandwidth with a highest frequency exceeding the predetermined threshold frequency, removing multiples from the seismic data using a multiple model and the primaries model to obtained seismic data without the multiples, and generating an image of the subsurface formation based on the seismic data without the multiples. The image is useable to locate natural resources and/or to plan or monitor their exploitation.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate one or more embodiments and, together with the description, explain these embodiments. In the drawings: [0011] Figures 1A and 1B illustrate marine seismic data; [0012] Figures 2A and 2B illustrate filtered data; [0013] Figure 3 illustrates a velocity model; [0014] Figure 4 illustrates a trace for the velocity model in Figure 3; [0015] Figure 5 illustrates the trace in Figure 4 after being filtered; [0016] Figure 6 is a flowchart of a method according to an embodiment; [0017] Figures 7A and 7B illustrate a primaries model reconstructed using the data in Figures 2A and 2B, according to an embodiment; [0018] Figure 8 is a representation of surface and internal multiples; and [0019] Figure 9 is a schematic diagram of a computing device according to an embodiment.

DETAILED DESCRIPTION

[0020] The following description of the exemplary embodiments refers to the accompanying drawings. The same reference numbers in different drawings identify the same or similar elements. The following detailed description does not limit the invention. Reference throughout the specification to one embodiment" or "an embodiment" means that a particular feature, structure or characteristic described in connection with an embodiment is included in at least one embodiment of the subject matter disclosed. Thus, the appearance of the phrases "in one embodiment" or "in an embodiment" in various places is not necessarily referring to the same embodiment. Further, the particular features, structures or characteristics may be combined in any suitable manner in one or more embodiments.

[0021] Embodiments described hereinafter first apply a harsh low-pass filter to the seismic data. The resulting filtered data is assumed to contain only primaries (and surface multiples if they have not been removed before) and it is used to reconstruct a full band primaries model from this low-frequency data. Here, "full band" means at least the same frequency band as the seismic data prior to filtering. A model of internal multiples is then used to remove multiples from the seismic data via an adaptive subtraction or other similar processes while using the primaries model to protect primaries in the resulting seismic data (from which multiples have been subtracted or otherwise eliminated).

[0022] As explained in Verschuur's article, if multiple model mmod is available and differs from the true multiples by an unknown convolution filter, the adaptive subtraction of minim from the seismic data d consists of finding an adaption filter fm that minimizes the energy (squared L2 norm) of the subtraction: fm = argminini(Ildfra mod112). (1) [0023] The multiples In and primaries p estimated using the model mimm and the filter fm are then: = f * mmoa (2) = d -th = d - od * (Z) [0024] The primaries and multiples thus estimated are uncorrelated, i.e., their dot product is null: * a = 0 (3) [0025] Therefore, if the true primaries and multiples are correlated, they cannot be perfectly estimated (i.e., estimated primaries differ from the true primaries). If the true primaries and multiples are correlated, subtracting the estimated multiples from the seismic data alters the primaries in the remaining data.

[0026] In the article entitled "One Way for Modelling Primaries and Internal Multiples with the Two-way Wave Equation and Its Collateral Benefits" by A. Pica, published in 76th EAGE Conference and Exhibition, Extended abstracts, 2014, it was proved that if a primaries model prnad is available, and if it differs from the true primaries by a convolution filter, it can be used in the adaptive subtraction as follows: = argmin(fnbcp) 01 d fm * Mmod -fp * Pmodla (4) [0027] The estimated multiples and primaries are as in formula (2) and (2'), but the estimated primaries and multiples are no longer constrained to be uncorrelated: /3 * /33 = (Tp * Pmod) * /13,- (5) [0028] Thus, if the primaries model Pram is known, the primaries, which would be altered otherwise when subtracting estimated multiples from the seismic data, can be protected. Primaries models can be obtained from interpreted horizons, far angle stacks, interpolated well logs, or a harsh de-multiple processing. For example, primary models are obtained from interpreted horizons in the article "A strategy for effective pre-migration inter-bed multiples attenuation on land data a case study from North Kuwait," by L. Vivin et al. presented at SEG/KOC workshop "Seismic Multiples -The Challenge and the Way Forward", Kuwait, 3-5 dec. 2019 set forth a workflow of 3D pre-stack pre-migration inter-bed multiple attenuation; here, horizons picked on the non-migrated stack are back sampled on common depth point (CDP) gathers and replaced by spikes with equivalent polarity; the spiky primary model is then filtered to get a spectral bandwidth equivalent to the one of the seismic data; the primary model and two multiple models are simultaneously adapted to the input data in a least square subtraction is cross-spread domain. In another example, primary models are obtained from interpolated well logs in the 2014 article "One Way for Modelling Primaries and Internal Multiples with the Two-way Wave Equation and Its Collateral Benefits" by A. Pica published in 76th EAGE Conference and Exhibition, Extended abstracts. Both articles are incorporated herewith by reference in their entirety.

[0029] It has been observed that, for some data, a harsh low-pass filter removes a large part, if not all, of the internal multiples. Thus, Figure 1A illustrates real seismic data, the x-axis representing horizontal range of about 7.5 km, the y axis representing time in ms and the nuances of gray corresponding to amplitude. One can observe that weak primaries are obscured by sub-horizontal internal multiples. Figure 1B is the spectrum of the recorded data illustrated in Figure 1A, the source emitting waves in a range of 4-80 Hz. The gray band is generated by individual spectra of the traces while the line is the average spectrum.

[0030] Figure 2A illustrates data remaining after a harsh low-pass filter (8 Hz) has been applied to the data in Figure 1A. This harsh filtering removes most of the multiples Figure 2B is the spectra of the data in Figure 2A.

[0031] The following explanation of the multiples' disappearance in the low-frequency data is based on synthetic reflectivity and has been tested on model data. Geological formations with fine layering are characterized by fast localized variations of positive and negative reflection coefficients as illustrated in Figure 3. Figure 3 is a graph of velocity versus time (which can be converted in depth). The velocity is about 3,000 m/s from 0 to about 130 ms and then it increases at 3,200 m/s. Fast, localized variations of positive and negative reflection coefficients occur between 300 and 350 ms and around 450 ms. These fast, localized variations act as derivative filters that attenuate the low frequencies relative to the high frequencies. The internal multiples experience multiple (3, 5, 7...) reflections, each time with the above filtering effect. Consequently, almost no low frequency is left in the recorded seismic data.

[0032] Figure 4 shows amplitude versus time (i.e., a trace) for the entire frequency spectrum of data simulated for the velocity model in Figure 3 (i.e., a 15Hz Ricker wavelet, with a most of the energy in the range 0-40Hz). The horizontal scale is in number of time samples, the sample interval being dt=4ms. Close to 0 one notices the surface reflections (e.g., source-side multiples), then, when velocity changes at 130 ms, a primary P. There are primaries (P) with alternating polarities at the fast, localized variations of positive and negative reflection coefficients, and then an internal multiple (IM) at about 580 ms. Figure 5 is a series of graphs illustrating the same data after low-pass filters have been applied retaining data with frequencies less than 50 Hz, 40 Hz, 30 Hz, 20 Hz and 10 Hz, respectively. As frequency content decreases, the multiple becomes less and less visible and practically disappears when the low-pass filter retains only frequencies of less than 10 Hz.

[0033] Figure 6 is a flowchart of a method 600 according to an embodiment.

Method 600 includes obtaining seismic data acquired over a subsurface formation at 610. The seismic data may be acquired on land or in a marine environment. If seismic data is acquired in a marine environment, water-surface-related multiples (e.g., source-side multiples) may be removed prior to the next step.

[0034] Method 600 further includes applying a low-pass filter to the seismic data, thereby yielding filtered data at 620. The low-pass filter has a threshold of no more than 10 Hz. It is likely that filtered data includes only primaries, multiples having been removed by filtering.

[0035] The method then includes reconstructing a primaries model valid for a bandwidth with a highest frequency exceeding the threshold frequency, using the filtered data, at 630. In one embodiment, the bandwidth may include a bandwidth of the seismic excitations injected in the subsurface formation to acquire the seismic data. Step 630 may be implemented using the "blind deconvolution" algorithm described in the 2002 article "A mathematical framework for blind deconvolution inverse problems" by G. Candas described in a presentation at the SEG Intl Exposition and 72nd Annual Meeting, Salt Lake City, Utah, October 6-11, 2002. If d is the input data, in a convolutional model r (reflectivities), w (seimic wavelet), and n (the noise) are unknown: d = r * w n. (6) [0036] A scaled version of w and the reflectivities r are simultaneously estimated by solving the following optimization problem: (I', ft)) = ar * w112 + E211w112 (11rIlL02)- (7) [0037] No phase assumption is -r isneeded for the wavelet. The estimated reflectivities are «sparse» (super-gaussian distribution). Sparseness is obtained by using «sparseness-promoting» norms in the optimization formulation, such as the Ll norm in time domain.

[0038] The estimated reflectivities do not have to be accurate, but just «good enough» as a primaries model. That is, they can match the true primaries through an appropriate matching filter.

[0039] Figure 7A shows reflectivities estimated using blind deconvolution technique applied to data in Figure 2A. Figure 7B illustrates the spectrum of this reconstructed data.

[0040] Although the above-described implementation of step 630 employed a blind deconvolution algorithm, generating the primaries model from the filtered data may be achieved using other algorithms such as (but are not limited to): any flavor of blind deconvolution, either with similar assumptions or with more restrictive assumptions (as described, for example, in the 2016 article "Modified Sparse Multichannel Blind Deconvolution" by N. Kazemi, A. Gholami and M. D. Sacchi published in] 78th EAGE Conference and Exhibition, Conference Proceedings), any sparseness-promoting deconvolution or inversion that requires a known wavelet on input (as described, for example, in the 1979 article "Deconvolution with L1 norm" by H. L. Taylor, S. C. Banks, and J. F. McCoy, published in Geophysics, vol. 44, pp. 39-52) , a manual or automatic picking (as described in the previously mentioned 2019 article by L. Vivin et al.), iterative denoise and/or spectral whitening techniques, vector rotation techniques, independent component analysis techniques, etc. The articles cited in this paragraph are incorporated by reference in their entirety.

[0041] Returning now to method 600, multiples are removed from the seismic data using a multiples model and the primaries model, at 640. The multiples model is generated using any known method such as data-driven convolutions/correlations modelling (as described in the 1998 article "Wave equation prediction and removal of interbed multiples" by H. Jakubowicz, published in SEG Technical Program Expanded Abstracts, pp. 1527-1530), inverse scattering series (as described in the 1999 article "How can the inverse-scattering method really predict and subtract all multiples from a multidimensional earth with absolutely no subsurface information?" by A. B. Weglein, published in The Leading Edge 18, pp 132-136), wave equation modelling ( as described, for example in the 2012 article "Advanced 3-D Land Internal Multiple Modeling and Subtraction, a Wide Azimuth Oman Case Study" by N. Benjamin et al. published in GE02012, Conference Proceedings), etc. The articles cited in this paragraph are incorporated by reference in their entirety.

[0042] In one embodiment, a least-square adaptive subtraction is performed using the multiples model. Other equivalent processes may be used instead of the least-square adaptive subtraction, for example: an adaptive subtraction with an alternate norm (as described, for example, in the 2004 article Adaptive subtraction of multiples using the L1-norm" by A. Guitton and D.J. Verschuur published in Geophysical Prospecting, Vol. 52, No. 1, pp. 27-38, an adaptive subtraction in other domains than the time-space domain (e.g., the wavelet transform domain as described in the 2004 article "Curvelet-based non-linear adaptive subtraction with sparseness constraints" by F. Herrmann and P. Moghaddam published in SEG Technical Program Expanded Abstracts, 1977-1980, the curvelet transform domain as described in the 2011 article "Complex Wavelet Adaptive Multiple Subtraction with Unary Filters," by S. Ventosa, H. Rabeson, P. Ricarte and L. Duval, published in 73rd EAGE Conference and Exhibition incorporating SPE EUROPEC, Conference Proceedings, etc.), pattern recognition methods (as described in the article "Pattern recognition, spatial predictability, and subtraction of multiple events" by S. Spitz, published in "The Leading Edge", January 1999, pp. 55-58), etc. The articles cited in this paragraph are incorporated by reference in their entirety.

[0043] Then, at 650, an image of the subsurface is generated based on the seismic data without the multiples. Seismic inversion or other methods may be employed to generate such image. Here, the term "image" should not be understood narrowly as a two-dimensional grid of pixels, but as three dimensional petrophysical properties values determined for three dimensional locations or volumes. Such an image is useable to locate natural resources (e.g., oil and gas) and/or to plan or monitor their exploitation.

[0044] Although the above embodiments have been described for the internal multiple attenuation case, the same approach may also apply to the surface multiple attenuation case. As illustrated in Figure 8, a primary 810 includes one subsurface reflection, a first order surface multiple 820 experiences two subsurface reflections, a second order surface multiple 830 and a first order internal multiple 840 experience three subsurface reflections, and a 2nd order internal multiple experiences five subsurface reflections. Since an nth order surface multiple experiences (n+1) reflections in the subsurface and an internal multiple of order n experiences 2xn+1 reflections in the subsurface, the filtering effect is expected to be less pronounced on the surface multiples compared to the internal multiples. However, it is expected to be more pronounced than on the primaries, which experience a single reflection.

[0045] The above-discussed methods may be implemented in a computing device 900 as illustrated in Figure 9. Hardware, firmware, software or a combination thereof may be used to perform the various steps and operations described herein.

[0046] Exemplary computing device 900 suitable for performing the activities described in the exemplary embodiments may include a server 901. Server 901 may include a central processor (CPU) 902 coupled to a random-access memory (RAM) 804 and to a read-only memory (ROM) 906. ROM 906 may also be other types of storage media to store programs, such as programmable ROM (PROM), erasable PROM (EPROM), etc. Processor 902 may communicate with other internal and external components through input/output (I/O) circuitry 908 and bussing 910 to provide control signals and the like. Processor 902 carries out a variety of functions as are known in the art, as dictated by software and/or firmware instructions [0047] Server 901 may also include one or more data storage devices, including hard drives 912, CD-ROM drives 914 and other hardware capable of reading and/or storing information, such as DVD, etc. In one embodiment, software for carrying out the above-discussed steps may be stored and distributed on a CD-ROM or DVD 916, a USB storage device 918 or other form of media capable of portably storing information. These storage media may be inserted into, and read by, devices such as CD-ROM drive 914, disk drive 912, etc. Server 901 may be coupled to a display 920, which may be any type of known display or presentation screen, such as LCD, plasma display, cathode ray tube (CRT), etc. A user input interface 922 is provided, including one or more user interface mechanisms such as a mouse, keyboard, microphone, touchpad, touch screen, voice-recognition system, etc. [0048] Server 901 may be coupled to other devices, such as sources, detectors, etc. The server may be part of a larger network configuration as in a global area network (GAN) such as the internet 928, which allows ultimate connection to various computing devices.

[0049] According to one embodiment, I/O circuitry 908 is configured to obtain seismic data recorded by receivers detecting seismic waves emerging from a subsurface formation. Processor 902 is configured (1) to apply a low-pass filter to the seismic data thereby yielding filtered data, the low-pass filter having a threshold frequency of no more than 10 Hz, (2) to reconstruct, from the filtered data, a primaries model valid for a bandwidth with a highest frequency exceeding the threshold frequency, (3) to remove multiples from the seismic data using a multiple model and the primaries model, and (4) to generate an image of the subsurface formation based on the seismic data without the multiples.

[0050] In yet another embodiment, RAM 904 stores executable codes that, when executed, make the I/O circuitry 908 obtain seismic data recorded by receivers detecting seismic waves emerging from a subsurface formation, and processor 902 to apply a low-pass filter to the seismic data thereby yielding filtered data, the low-pass filter having a threshold frequency of no more than 10 Hz, to reconstruct, from the filtered data, a primaries model valid for a bandwidth with a highest frequency exceeding the threshold frequency, to remove multiples from the seismic data using a multiples model and the primaries model yielding seismic data without the multiples, and to generate an image of the subsurface formation based on the seismic data without the multiples.

[0051] The disclosed embodiments provide methods and apparatuses for seismic exploration in which when multiples are removed from seismic data primaries are protected because multiples model is based on a primaries model obtained from low-frequency data. It should be understood that this description is not intended to limit the invention. On the contrary, the exemplary embodiments are intended to cover alternatives, modifications and equivalents, which are included in the spirit and scope of the invention as defined by the appended claims. Further, in the detailed description of the exemplary embodiments, numerous specific details are set forth in order to provide a comprehensive understanding of the claimed invention. However, one skilled in the art would understand that various embodiments may be practiced without such specific details.

[0052] Although the features and elements of the present embodiments are described in the embodiments in particular combinations, each feature or element can be used alone without the other features and elements of the embodiments or in various combinations with or without other features and elements disclosed herein. The methods or flowcharts provided in the present application may be implemented in a computer program, software or firmware tangibly embodied in a computer-readable storage medium for execution by a general-purpose computer or a processor.

[0053] This written description uses examples of the subject matter disclosed to enable any person skilled in the art to practice the same, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the subject matter is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims.

Claims

WHAT IS CLAIMED IS: 1. A seismic exploration method (600) comprising: obtaining (610) seismic data recorded by receivers detecting seismic waves emerging from a subsurface formation; applying (620) a low-pass filter to the seismic data thereby yielding filtered data, the low-pass filter having a predetermined threshold frequency of no more than 10 Hz; reconstructing (630), from the filtered data, a primaries model valid for a bandwidth with a highest frequency exceeding the predetermined threshold frequency; removing (640) multiples from the seismic data using a multiple model and the primaries model to obtained seismic data without the multiples; and generating (650) an image of the subsurface formation based on the seismic data without the multiples, wherein the image is useable to locate natural resources and/or to plan or monitor their exploitation.
The seismic exploration method of claim 1, wherein the reconstructing is performed using a blind deconvolution algorithm.
The seismic exploration method of claim 1, wherein the reconstructing is performed using a sparseness-promoting deconvolution or inversion.
4. The seismic exploration method of claim 1, wherein the bandwidth includes a bandwidth of seismic excitations injected in the subsurface formation to acquire the seismic data.
The seismic exploration method of claim 1, wherein the removing of the multiples includes generating the multiples model.
The seismic exploration method of claim 1, wherein the multiples are removed using a least square adaptive subtraction.
7. The seismic exploration method of claim 1, wherein the multiples are removed using an adaptive subtraction performed another domain than a time domain.
The seismic exploration method of claim 1, wherein the multiples are removed using pattern recognition techniques.
The seismic exploration method of claim 1, wherein the removing of the multiples includes removal of water-surface-related multiples.
A seismic data processing apparatus (800), comprising: an interface (808) configured to obtain seismic data recorded by receivers detecting seismic waves emerging from a subsurface formation and a data processing unit (802) connected to the interface and configured to apply a low-pass filter to the seismic data thereby yielding filtered data, the low-pass filter having a threshold frequency of no more than 10 Hz; to reconstruct, from the filtered data, a primaries model valid for a bandwidth with a highest frequency exceeding the threshold frequency; to remove multiples from the seismic data using a multiples model the primaries model to obtain seismic data without multiples; and to generate an image of the subsurface formation based on the seismic data without the multiples, wherein the image is useable to locate natural resources and/or to plan or monitor their exploitation.
11. The seismic data processing apparatus of claim 10, wherein the data processing unit reconstructs the primaries model using a blind deconvolution algorithm.
12. The seismic data processing apparatus of claim 10, wherein the data processing unit reconstructs the primaries model using a sparseness-promoting deconvolution or inversion.
13. The seismic data processing apparatus of claim 10, wherein the bandwidth includes a bandwidth of seismic excitations injected in the subsurface formation to acquire the seismic data.
14. The seismic data processing apparatus of claim 10, wherein the data processing unit removes the multiples using an adaptive subtraction.
15. The seismic data processing apparatus of claim 14, wherein the adaptive subtraction is a least square subtraction.
16. The seismic data processing apparatus of claim 14, wherein the adaptive subtraction is performed another domain than a time domain.
17. The seismic data processing apparatus of claim 10, wherein the data processing unit removes the multiples using pattern recognition techniques.
18. The seismic data processing apparatus of claim 10, wherein when the data processing unit removes the multiples, water-surface-related multiples are also removed.
19. A computer-readable recording medium (804) non-transitorily storing executable codes that, when executed by a computer make the computer perform a seismic exploration method (600) comprising: obtaining (610) seismic data recorded by receivers detecting seismic waves emerging from a subsurface formation; applying (620) a low-pass filter to the seismic data thereby yielding filtered data, the low-pass filter having a predetermined threshold frequency of no more than 10 Hz; reconstructing (630), from the filtered data, a primaries model valid for a bandwidth with a highest frequency exceeding the predetermined threshold frequency; removing (640) multiples from the seismic data using a multiple model and the primaries model to obtained seismic data without the multiples; and generating (650) an image of the subsurface formation based on the seismic data without the multiples, wherein the image is useable to locate natural resources and/or to plan or monitor their exploitation.
20. The computer-readable recording medium of claim 19, wherein the reconstruction is performed using a blind deconvolution algorithm or a sparseness-promoting deconvolution or inversion.