Mixed acquisition seismic data separation method and device
By employing 3D FKK domain variable grid sparse inversion and adaptive channel compensation technology, the problem of poor separation effect of mixed seismic data was solved, achieving efficient and low-cost data separation and improving data quality and operational efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA OILFIELD SERVICES LTD
- Filing Date
- 2026-03-11
- Publication Date
- 2026-05-12
AI Technical Summary
Existing seismic data separation schemes based on sparse inversion and denoising have poor separation effects, resulting in low construction efficiency and high operating costs.
By employing a three-dimensional FKK domain variable grid sparse inversion technique combined with adaptive channel compensation technology, and through channel detection, FKK domain sparse transformation and staged sparse inversion iterative processing, the data grid block scale and sparse shrinkage threshold are dynamically adjusted to achieve efficient separation of mixed seismic data.
It improved separation efficiency, enhanced data quality, shortened the operation cycle, reduced exploration costs, and increased the efficiency of field production operations.
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Figure CN122017976A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of seismic exploration technology, specifically to a method and apparatus for separating mixed seismic data. Background Technology
[0002] With the increasing level of offshore oil exploration and development, the "two-wide-one-high" seismic acquisition technology for seabed nodes has become an inevitable trend. Seabed node acquisition typically requires high shot density to achieve high coverage and wide azimuth acquisition. Traditional sequential shot-triggered acquisition methods are inefficient and costly. Synchronous source efficient cascade acquisition is a major contributor to accelerating the large-scale application of seabed nodes. Existing application examples show that better quality can be achieved at the same cost, and lower cost can be achieved for the same quality. Data separation technology is one of the core technologies for achieving cascade acquisition, and it greatly determines the choice of field operation methods and the quality of seismic data.
[0003] Currently, the main methods for separating mixed seismic data are sparse inversion and denoising-based methods. However, these methods often result in poor separation performance. Therefore, there is an urgent need for a mixed seismic data separation method that can effectively improve the separation results. Summary of the Invention
[0004] In view of the above problems, this application is made in order to provide a method, apparatus, computing device, computer storage medium and computer program product for separating mixed seismic data to overcome or at least partially solve the above problems.
[0005] According to one aspect of the embodiments of this application, a method for separating mixed seismic data is provided, comprising: Acquire the seismic data to be separated from the mixed mining, and perform air channel detection on the seismic data to be separated from the mixed mining, wherein the seismic data to be separated from the mixed mining is synchronous source mixed mining data in the time domain; The seismic data to be separated and mixed is transformed to the FKK domain. Based on the seismic data transformed by the FKK domain corresponding to the effective channels within the preset range of each channel, the channel area is interpolated. The interpolated seismic data to be separated and mixed is then subjected to FKK inverse transformation to obtain the channel-compensated seismic data to be separated and mixed. The FKK domain sparse transformation was performed on the seismic data to be separated after the air channel compensation. Based on the FKK domain sparse transformation of the seismic data to be separated, an initial model of non-overlapping data was constructed. A phased FKK domain variable mesh sparse inversion iterative process is performed on the initial model of non-aliased data. After each iteration, the current non-aliased data model and sparse shrinkage threshold are updated until the preset stopping condition is met. Perform FKK inverse transform on the model data corresponding to the non-aliased data model that meets the stopping condition to obtain the seismic data separation results.
[0006] Furthermore, the air channel detection of the seismic data to be separated and mixed includes: For each seismic trace within the common receiver gather, amplitude statistics are performed within a preset local time window to obtain the root mean square amplitude of the corresponding seismic trace. Determine whether the root mean square amplitude is less than the preset root mean square amplitude threshold. If so, identify the seismic trace as an empty trace and record the empty trace information.
[0007] Furthermore, the process of performing air channel regional interpolation on the air channels based on the FKK domain-transformed seismic data corresponding to the effective channels within the preset range of each air channel further includes: Locate the air channels in the mixed seismic data to be separated after FKK domain transformation based on the air channel information; For any given channel, interpolation weighting coefficients are calculated based on the distances from each valid channel to the channel within the preset range of the channel. Then, channel regional interpolation is performed based on the interpolation weighting coefficients and the FKK domain transformed seismic data corresponding to each valid channel within the preset range of the channel.
[0008] Furthermore, the initial model for constructing non-aliased data based on the seismic data to be separated after sparse transformation in the FKK domain includes: The initial sparsity shrinkage threshold is calculated based on the seismic data to be separated and mixed after the FKK domain sparse transformation. An aliased data model is constructed based on the seismic data to be separated after sparse transformation in the FKK domain. A pseudo-unmixing calculation is performed on the aliased data model based on the initial sparse shrinkage threshold to obtain an initial model without aliasing.
[0009] Furthermore, a phased FKK domain variable mesh sparse inversion iterative process is performed on the initial model of the non-aliased data. After each iteration, the current non-aliased data model and the sparsity shrinkage threshold are updated until a preset stopping condition is met. This further includes: A multi-stage FKK domain sparse inversion iterative process is performed on the initial model of the non-aliased data. The iterative process is divided into multiple iterative stages based on the change threshold of the iterative residual. Each iterative stage adopts a progressively smaller grid scale to adapt to the sparse extraction of seismic signals with corresponding frequency bands and amplitude characteristics. Each iterative stage also adopts a progressively lower sparse shrinkage threshold. Each iteration updates the current non-aliased data model based on the non-aliased data model obtained in the previous iteration until the preset stopping condition is met.
[0010] Furthermore, the method also includes: calculating the objective function for this iteration after updating the current non-aliased data model; If the objective function of the current iteration is less than that of the previous iteration, then the aliasing noise estimate is updated based on the current non-aliasing data model.
[0011] Furthermore, updating the sparsity shrinkage threshold further includes: After each iteration in each stage, the sparsity shrinkage threshold is updated according to the following formula:
[0012] Where i is the current iteration number, k is the decay sparsity, and T i T is the sparse shrinkage threshold corresponding to the i-th iteration in the corresponding stage. i-1 This is the sparse shrinkage threshold corresponding to the (i-1)th iteration in the corresponding stage.
[0013] Furthermore, before performing air channel detection on the seismic data to be separated and mixed, the method also includes: The seismic data to be separated and mixed is pre-processed to suppress the background low-frequency strong amplitude surge noise, resulting in pre-processed seismic data to be separated and mixed.
[0014] According to another aspect of the embodiments of this application, a mixed-data seismic separation device is provided, comprising: The acquisition module is suitable for acquiring the mixed seismic data to be separated, wherein the mixed seismic data to be separated is synchronous source mixed data in the time domain; The detection module is suitable for performing air channel detection on the seismic data to be separated and mixed. The interpolation processing module is suitable for transforming the seismic data to be separated and mixed into the FKK domain, performing air channel regional interpolation processing on the air channels based on the FKK domain-transformed seismic data corresponding to the effective channels within the preset range of each air channel, and performing FKK inverse transformation processing on the interpolated seismic data to be separated and mixed into the FKK domain to obtain the air channel-compensated seismic data to be separated and mixed into the FKK domain. The module is suitable for performing FKK domain sparse transformation processing on the seismic data to be separated after air channel compensation, and constructing an initial model of non-overlapping data based on the seismic data to be separated after FKK domain sparse transformation. The variable mesh sparse inversion processing module is suitable for performing staged FKK domain variable mesh sparse inversion iterative processing on the initial model of non-aliased data. After each iteration, the current non-aliased data model and sparse shrinkage threshold are updated until the preset stopping condition is met. The inverse transform processing module is suitable for performing FKK inverse transform processing on the model data corresponding to the non-aliased data model that meets the stopping conditions, so as to obtain the seismic data separation results.
[0015] According to another aspect of the embodiments of this application, a computing device is provided, including: a processor, a memory, a communication interface and a communication bus, wherein the processor, the memory and the communication interface communicate with each other through the communication bus; The memory is used to store at least one executable instruction, which causes the processor to perform the operation corresponding to the above-mentioned seismic data separation method.
[0016] According to another aspect of the embodiments of this application, a computer storage medium is provided, wherein at least one executable instruction is stored in the storage medium, the executable instruction causing a processor to perform operations corresponding to the above-described mixed seismic data separation method.
[0017] According to another aspect of the embodiments of this application, a computer program product is provided, including at least one executable instruction that causes a processor to perform operations corresponding to the above-described mixed seismic data separation method.
[0018] Based on the seismic data separation method and apparatus provided in the embodiments of this application, a three-dimensional FKK domain variable grid sparse inversion technique is proposed. During the iteration process, the data grid block scale is dynamically adjusted to match the physical laws of signal extraction, which better conforms to the essence of signal extraction during inversion—first the strong axis, then the weak axis, and from low frequency to high frequency—thus achieving better separation results. An adaptive channel compensation technique is also proposed, which fills the channels in the sparse transform domain with regular interpolation, avoiding abnormal energy attenuation and effectively eliminating the whitening phenomenon in the processed data caused by variable channel gaps, while also improving the overall effect. Furthermore, the three-dimensional FKK transform domain is selected, taking into account signal coherence identification, transform reversibility, and computational efficiency, ultimately improving separation accuracy and efficiency, significantly increasing the efficiency of field operations, shortening the operation cycle, and reducing exploration costs.
[0019] The above description is merely an overview of the technical solutions of the embodiments of this application. In order to better understand the technical means of the embodiments of this application and to implement them in accordance with the contents of the specification, and to make the above and other objects, features and advantages of the embodiments of this application more obvious and understandable, specific implementation methods of the embodiments of this application are described below. Attached Figure Description
[0020] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the embodiments of this application. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 A flowchart illustrating a method for separating mixed seismic data according to an embodiment of this application is shown; Figure 2A structural block diagram of a seismic data separation apparatus according to an embodiment of this application is shown; Figure 3 A schematic diagram of the structure of a computing device according to an embodiment of this application is shown. Detailed Implementation
[0021] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
[0022] Figure 1 A flowchart illustrating a method for separating mixed seismic data according to an embodiment of this application is shown, as follows: Figure 1 As shown, the method includes the following steps: Step S101: Obtain the seismic data to be separated and mixed mining, and perform air channel detection on the seismic data to be separated and mixed mining.
[0023] Hybrid seismic data refers to the raw seismic data continuously recorded by geophones during field seismic data acquisition. This is achieved by using excitation methods with overlapping or excessively short time intervals, where multiple seismic sources (such as controlled seismic sources or air gun arrays) are excited sequentially or simultaneously at different spatial locations with random, pseudo-random, or coded time delays. This results in temporal aliasing and spatial interference of the seismic wavefields generated by each shot point. Data separation involves breaking down the individual source wavefields within this overall wavefield and restoring them to individual source signals.
[0024] Empty channels refer to seismic channels in seismic records where, due to various reasons, no valid seismic signals were recorded, or the recorded signals were completely distorted and could not be used for subsequent processing.
[0025] Read the seismic data to be separated from the field acquisition system or storage medium, and organize the data into a common receiver gather. Since there may be empty channels in the common receiver gather, which will reduce the accuracy of subsequent seismic data separation, it is necessary to perform empty channel detection on each seismic data channel. The following methods can be used to determine whether it is an empty channel: calculate the energy or average amplitude value of the data channel, set an average energy threshold or average amplitude threshold, and if the energy of the channel is lower than the average energy threshold or the average amplitude value is lower than the average amplitude threshold, it is determined to be an empty channel; or it can be determined by detecting whether the amplitude of the data channel is all zero or close to zero. If the amplitude is all zero or close to zero, it is determined to be an empty channel.
[0026] In one optional embodiment of this application, amplitude statistics within a preset local time window can be performed on each seismic trace in the common receiver gathering to obtain the root mean square amplitude of the corresponding seismic trace; it is determined whether the root mean square amplitude is less than a preset root mean square amplitude threshold, and if so, the seismic trace is identified as an empty trace and the empty trace information is recorded.
[0027] Specifically, one or more local time windows are preset based on the distribution range of the geological target strata in the work area or the main energy period of the effective reflected waves. The time window can be a fixed-length time interval; or it can be adaptively selected according to the overall energy distribution of the gather, for example, selecting a continuous time period containing the strongest reflected energy. Preferably, multiple sliding time windows are used to cover the entire recording length to comprehensively detect whether there are effective signals in each time period.
[0028] Within a selected local time window, amplitude statistics are performed on the seismic data, and the root mean square amplitude A is calculated. single The calculated root mean square amplitude is compared with the preset root mean square amplitude threshold A. averge The comparison is made by setting the root mean square amplitude threshold based on the statistical results of the root mean square amplitude of all channels within the entire working area or the current common detector gather. When A single Less than the set average threshold A averge If an empty channel exists in a common detector channel set (i.e., no valid acquisition signal), then that location is marked as an empty channel; record the empty channel information, such as detector line number, detector point number, shot line number, shot point number, coordinates, etc., to identify all empty channels, and all empty channel information is formed into the empty channel information table T_empty.
[0029] Airway detection is used to identify airways caused by missing shots or bad airways. Through airway detection, a high-quality data foundation is provided for subsequent airway regularization and separation.
[0030] In one optional embodiment of this application, before performing air channel detection on the seismic data to be separated and mixed, the method further includes: performing noise reduction preprocessing on the seismic data to be separated and mixed to suppress background low-frequency strong amplitude surge noise, thereby obtaining preprocessed seismic data to be separated and mixed.
[0031] For example, inputting the original mixed seismic data d from the seabed node synchronous source, and suppressing the background low-frequency strong amplitude surge noise through time-domain denoising, we obtain the preprocessed mixed seismic data d_pre to be separated.
[0032] Step S102: Transform the seismic data to be separated and mixed into the FKK domain. Perform air channel regional interpolation on the air channels based on the FKK domain-transformed seismic data corresponding to the effective channels within the preset range of each air channel. Perform FKK inverse transformation on the interpolated seismic data to be separated and mixed into the FKK domain to obtain the air channel-compensated seismic data to be separated and mixed into the FKK domain.
[0033] Missing shots are a common phenomenon in seismic acquisition operations. After missing shots, gaps will appear in the processing gather domain of the mixed acquisition data separation and the common receiver gather. These gaps will cause abnormal energy attenuation in the transform domain, and sparse inversion using global thresholds will be severely interfered with.
[0034] Existing methods for processing empty channels either discard the empty channel data directly (destroying the integrity of the phase axis) or fill in zero values (interfering with threshold iteration). Directly discarding empty channels in the data grid will destroy the spatial relationship of the reflection phase axis, while filling in zero-value channels will affect the thresholding iterative inversion process. Therefore, this application adopts an adaptive empty channel compensation technique. Specifically, the seismic data to be separated and mixed is first transformed to the FKK domain, and regular interpolation is performed in the FKK sparse transform domain, which preserves the spatial coherence of the signal without affecting the inversion efficiency.
[0035] Specifically, the seismic data to be separated from the mixed seismic mining is transformed from the time-space domain (tx domain) to the frequency-wavenumber domain (FKK domain) using a multidimensional Fourier transform. This transformation concentrates the seismic wavefield energy in the wavenumber domain, facilitating subsequent interpolation based on wavenumber domain characteristics. During the transformation, a Fast Fourier Transform (FFT) algorithm can be used to improve computational efficiency, and necessary boundary processing is performed on the data to avoid spectral leakage. For example, performing a row-dimensional FKK transform (forward transform operator F) on the seismic data d to be separated yields the FKK domain data D_FKK, with the formula: D_FKK=F(d).
[0036] Within the FKK domain, for each void, the surrounding valid channels are determined based on a preset spatial neighborhood. This preset neighborhood can be set according to actual acquisition parameters and geological targets; for example, a rectangular window can be formed by selecting 5 to 7 valid channels in each of two spatial directions, centered on the void. Based on the values of all valid channels within this neighborhood in the FKK domain, an interpolation algorithm is used to estimate the value of the void in the FKK domain.
[0037] After completing the FKK domain interpolation for all channels, a complete FKK domain data volume is obtained. Subsequently, a multidimensional inverse Fourier transform is performed on this data volume to transform it back into the time-space domain, thereby obtaining the channel-compensated seismic data to be separated and mixed.
[0038] The compensated seismic data to be separated has filled in the missing parts of the original gathers, making the seismic gathers complete and continuous, providing complete and stable input data for the subsequent separation and processing of the seismic data.
[0039] In one optional embodiment of this application, weighted least squares interpolation can be used to fill gaps. Specifically, gaps in the seismic data to be separated and mixed after FKK domain transformation are located based on gap information. For any gap, interpolation weight coefficients are calculated based on the distances from each valid trace to the gap within a preset range of the gap. Gap interpolation processing is then performed based on the interpolation weight coefficients and the seismic data after FKK domain transformation corresponding to each valid trace within the preset range of the gap.
[0040] Specifically, based on the empty track information determined in the preprocessing stage, the position corresponding to each empty track is precisely located in the 3D data volume after FKK transformation. For example, based on the empty track information table T_empty, the region corresponding to the empty track in D_FKK is located.
[0041] Constrained by the FKK domain energy distribution of the surrounding effective channels (typically 5-7 channels), a weighted least squares interpolation method is used to fill the empty channel. After determining the effective channel neighborhood of the empty channel, the spatial distance from each effective channel within that neighborhood to the current empty channel is calculated. The spatial distance includes the distance component along the detector line direction and the distance component perpendicular to the detector line direction, which can be calculated using Euclidean distance or Manhattan distance. Based on the calculated distances, the interpolation weight coefficients corresponding to each effective channel are further determined. The interpolation weight coefficients are inversely proportional to the distance from the effective channel to the empty channel (the closer the distance, the greater the weight). To ensure energy balance in the interpolation results, the interpolation weight coefficients of all effective channels need to be normalized so that the sum of the weights equals 1.
[0042] Finally, using the normalized interpolation weight coefficients, the values of all valid channels in the FKK domain within the neighborhood are weighted and summed to estimate the value of the current empty channel in the FKK domain. After interpolation, the complete FKK domain data D_FKK_comp is obtained, realizing empty channel compensation. The formula is: D_FKK_comp=Interp(D_FKK,T_empty,W) (where W is the interpolation weight matrix and Interp is the regularized interpolation operator).
[0043] Perform an inverse FKK transform on D_FKK_comp ( The time-domain data d_comp after air channel compensation is obtained, and the formula is: d_comp = F - ¹(D_FKK_comp).
[0044] The above processing eliminates the energy anomaly in the transform domain caused by empty channels, improves the spatial continuity of the phase axis of the reflected signal, and provides a complete gather without data faults for sparse inversion. Since sparse inversion and mixed sampling separation itself requires hundreds of iterations, while the computational cost of sparse transform interpolation performed only once is very small, it does not affect the efficiency of the entire separation process.
[0045] In one optional embodiment of this application, the denoised preprocessed data d_pre can be subjected to a row-based three-dimensional FKK transformation (positive transformation operator F) to obtain the FKK domain data D_FKK, with the formula: D_FKK=F(d_pre).
[0046] Step S103: Perform FKK domain sparse transformation on the seismic data to be separated after channel compensation, and construct an initial model of non-overlapping data based on the seismic data to be separated after FKK domain sparse transformation.
[0047] Existing solutions partially use Radon domain (irreversible transformation), FK domain (two-dimensional transformation with weak coherence identification), or curve domain (low computational efficiency). The three-dimensional FKK domain selected in this application takes into account the three major advantages of strong coherence of reflected signals, obvious incoherence of aliasing noise, completely orthogonal and reversible transformation, and mature industrial application.
[0048] Specifically, the FKK domain sparse transform is performed on the seismic data to be separated after channel compensation processing. The FKK domain sparse transform aims to utilize the structural characteristics of the seismic wavefield in the frequency-wavenumber domain to transform the seismic data into a specific sparse representation space, making the effective signal exhibit significant sparsity in this space. That is, the energy of the effective signal is concentrated only on a few large transform coefficients, while aliasing noise is relatively dispersed. Various mathematical transform bases can be used for the sparse transform, such as three-dimensional Fourier bases, curvelet transform bases, or shear wave transform bases. The specific choice can be determined based on the wavefield complexity of the seismic data and computational efficiency requirements. Then, an aliasing-free initial model is constructed based on the FKK domain sparse transform of the seismic data to be separated. For example, an aliasing data model is constructed based on the FKK domain sparse transform of the seismic data to be separated, and pseudo-demixing calculations are performed on the aliasing data model to obtain the aliasing-free initial model.
[0049] After channel compensation, the data is transformed to the optimal sparse domain (FKK domain) to construct an initial model of non-aliased data for pseudo-aliased data, providing a starting point for subsequent iterative inversion.
[0050] In one optional embodiment of this application, the initial model for non-aliased data can be determined by the following method: calculating the initial sparsity shrinkage threshold based on the seismic data to be separated after sparse transformation in the FKK domain; An aliased data model is constructed based on the seismic data to be separated after sparse transformation in the FKK domain. A pseudo-unmixing calculation is performed on the aliased data model based on the initial sparse shrinkage threshold to obtain an initial model without aliasing.
[0051] Specifically, FKK forward transformation is performed on d_comp to obtain D_FKK_final; the initial sparsity contraction threshold T0 is calculated based on the RMS amplitude (root mean square amplitude) of the seismic data to be separated after the FKK domain sparse transformation, and the formula is: T0=α×RMS(D_FKK_final) (where α is the weighting coefficient, with a value range of 0.05-0.15, balancing the error term and the sparsity constraint term).
[0052] In aliased acquisition, the aliased records of multiple sources received at a single receiver point can be represented as:
[0053] The above formula is a mixed acquisition data model, where d is the acquired mixed data, m is the non-mixed data, and Γ is the mixed matrix operator that contains the spatial location and time information of the earthquake source.
[0054] Based on the aliased data model d=Γm (where m is the unaliased data and Γ is the aliasing matrix operator containing the spatial location and temporal information of the seismic source), the initial unaliased data model m0 is obtained through pseudo-demixing calculation, with the formula: m0= F - ¹(T(F(Γ d_comp))) (where Γ (where T is the conjugate transpose of the aliasing matrix and T is the initial threshold shrinkage operator).
[0055] Step S104: Perform a phased FKK domain variable mesh sparse inversion iterative process on the initial model of non-aliased data. After each iteration, update the current non-aliased data model and the sparse shrinkage threshold until the preset stopping condition is met.
[0056] Sparse inversion cascading separation typically involves data segmentation, which yields better results and facilitates parallel computing. The volume of data acquired through efficient cascading and the computational demands of 3D sparse inversion are enormous, requiring parallel processing to meet production timeliness requirements. Furthermore, the amplitude, frequency, and signal-to-noise ratio of seismic data are spatiotemporally variable; segmenting the data to achieve independent, localized inversions yields better results than directly inverting the entire dataset. In practical applications, however, sparse inversion separation is less effective for data or localized areas with significant separation challenges, such as areas with strong amplitude phase axis intersections or strong energy dispersion in cascading shots. The process of sparse inversion cascading data separation is essentially a process of extracting mainshot (non-cascading) information. During iterative inversion, information extraction begins with low-frequency, high-amplitude information and gradually extends to high-frequency, low-amplitude information. The scale of the extracted information changes during the inversion process. Because the existing scheme uses fixed grid block inversion, it cannot take into account the extraction requirements of low-frequency strong signals and high-frequency weak signals. This leads to strong axis intersection and dispersion noise region separation distortion. In other words, using a fixed-scale data block grid cannot achieve the best inversion effect. It is difficult for technicians to choose a data grid scale that takes into account both the previous and subsequent data in production.
[0057] Therefore, this application performs a phased FKK domain variable-grid sparse inversion iterative process on the initial model of non-aliased data. In the early stage of the iterative inversion, a larger grid scale is used to extract low-frequency, high-energy, and large-scale data information. As the number of iterations increases, the grid scale gradually decreases to extract high-frequency, low-energy, and small-scale information. The variable-grid strategy makes the iterative process more compatible with the physical nature of sparse inversion aliasing and separation technology, resulting in better processing performance.
[0058] After each iteration, update the current non-aliased data model and the sparse shrinkage threshold until the preset stopping condition is met.
[0059] In one optional embodiment of this application, a multi-stage FKK domain sparse inversion iterative process can be performed on the initial model of the non-aliased data. The iterative process is divided into multiple iterative stages based on the change threshold of the iterative residual. Each iterative stage adopts a progressively smaller grid scale to adapt to the sparse extraction of seismic signals with corresponding frequency bands and amplitude characteristics. Each iterative stage also adopts a progressively lower sparse shrinkage threshold. Each iteration updates the current non-aliased data model based on the non-aliased data model obtained in the previous iteration until a preset stopping condition is met.
[0060] Specifically, the initial value of the grid scale and the total number of iterations are set, and iterative processing is performed based on the total number of iterations; Under the constraint of the initial value of the grid scale, the first stage sparse signal is extracted from the initial model of the non-aliased data based on the initial sparse shrinkage threshold. After each iteration, the current non-aliased data model and the sparse shrinkage threshold are updated, and the iteration residual is calculated. If the iterative residual drops to the first preset interval of the initial residual, the grid scale is reduced to the first preset grid scale, and the sparse shrinkage threshold is adjusted to the first preset multiple of the initial sparse shrinkage threshold. Under the constraint of the first preset grid scale, the second stage sparse signal is extracted from the non-aliased data model based on the adjusted sparse shrinkage threshold. After each iteration, the current non-aliased data model and sparse shrinkage threshold are updated, and the iterative residual is calculated. If the iterative residual drops to the second preset interval of the initial residual, the grid scale is reduced to the second preset grid scale, and the sparse shrinkage threshold is adjusted to the second preset multiple of the initial sparse shrinkage threshold. Under the constraint of the second preset grid scale, the third-stage sparse signal is extracted from the non-aliased data model based on the adjusted sparse shrinkage threshold. After each iteration, the current non-aliased data model and sparse shrinkage threshold are updated until the preset stopping condition is met. The first preset multiple is greater than the second preset multiple, and the first preset multiple and the second preset multiple are values less than 1.
[0061] For example, set the total number of iterations to niter (150 is recommended), and set the initial grid size S0 to "16×16×100" (Inline×CDP×Time direction) to extract low-frequency, high-amplitude signals.
[0062] In the initial iterations (1-50 times): Keep S0 = 16 × 16 × 100, extract strongly coherent low-frequency signals in the FKK domain through a sparse shrinkage threshold T, and update model m. i where i is the current iteration number and m i-1 For the previous model, the model update formula is: m i =F -1 (T(F(Γ d_comp-(Γ Γ-I)m i-1 Among them, m i Let F be the non-aliased data model after the i-th iteration, and let F be the three-dimensional FKK positive transform operator. -1 Here, Γ is the 3D FKK inverse transform operator (the inverse operation of F), T is the sparsity shrinkage threshold, and Γ is the aliasing matrix operator. Let Γ be the conjugate transpose of Γ (often called the "pseudo-inverse matrix" in engineering), d_comp be the time-domain seismic data to be separated after channel compensation, I be the identity matrix (a square matrix with 1s on the main diagonal and 0s elsewhere), and m be the lattice matrix. i-1 Let i be the non-aliased data model after the (i-1)th iteration (the result of the previous round), where i is the current iteration number.
[0063] Mid-cycle (51-100 iterations): When the iteration residual drops to 10%-15% of the initial residual, the grid scale is reduced to S1=8×8×60 to adapt to the extraction of medium frequency and medium amplitude signals. The above model update formula is used, and the sparse shrinkage threshold T is adjusted to T1=0.6×T0. In the later stages of iteration (101-150 times): when the iteration residual drops to 3%-5% of the initial residual, the grid scale is further reduced to S2=2×2×40, high-frequency and weak amplitude signals are extracted in a targeted manner, the sparse shrinkage threshold T is adjusted to T2=0.3×T0, and the model is continuously updated.
[0064] Each stage of grid partitioning supports parallel processing, allocating computing resources according to grid cells to solve the timeliness problem of 3D FKK inversion and large data volume, and meet the needs of industrial production.
[0065] Existing solutions partially employ the steepest descent method, which has a slow convergence speed. This application uses the Iterative Shrink Threshold Algorithm (ISTA) combined with dynamic threshold adjustment, which has a higher convergence efficiency. Furthermore, the objective function simultaneously constrains residuals and sparsity, resulting in better separation fidelity.
[0066] In one optional embodiment of this application, the method further includes: calculating the objective function for the current iteration after the current non-aliasing data model is updated; If the objective function of the current iteration is less than that of the previous iteration, then the aliasing noise estimate is updated based on the current non-aliasing data model.
[0067] Specifically, a least-squares objective function with sparse constraints is adopted, as shown in the following formula: J(m) = ||d_comp - Γm||2² + α||F(m)||0 The first term is the iterative residual (reflecting the deviation between the model's predicted value and the actual data), the second term is the FKK domain sparse constraint term (ensuring the sparse representation of the effective signal), and α is the weight coefficient (ranging from 0.01 to 0.03, balancing the weights of the two terms).
[0068] After each iteration, calculate the objective function value J(m) i If J(m) i ) <J(m i-1 (i.e., the objective function decreases), then based on the current model m i Update the aliasing noise estimate: n i =Γm i -d_comp; In one optional embodiment of this application, updating the sparsity shrinkage threshold further includes: After each iteration in each stage, the sparsity shrinkage threshold is updated according to the following formula:
[0069] Where i is the current iteration number, k is the decay sparsity, and T i T is the sparse shrinkage threshold corresponding to the i-th iteration in the corresponding stage. i-1 This is the sparse shrinkage threshold corresponding to the (i-1)th iteration in the corresponding stage.
[0070] Specifically, the sparsity contraction threshold is updated in an "exponential decay" manner: T i =T i-1 ×e^ (-k / i) (k is the attenuation coefficient, and a value of 0.5 is recommended) to ensure that the threshold is smaller in the later stages of the iteration, so that weak amplitude signals can be extracted.
[0071] The iteration stops if any of the following conditions are met: ① The number of iterations reaches niter; ② The difference of the objective function over 10 consecutive iterations |J(m) i )-J(m i-10 )|<10 -6 (Convergence accuracy threshold); ③ The ratio of the iterative residual to the RMS amplitude of the input data is less than 1%.
[0072] By iteratively updating the model and threshold, the objective function is ensured to converge, thus achieving accurate separation of effective signals and aliasing noise.
[0073] Step S105: Perform FKK inverse transform processing on the model data corresponding to the non-aliased data model that meets the stopping condition to obtain the seismic data separation result.
[0074] The non-aliased data model that meets the stopping condition is the optimal model after convergence. The separated model data is inversely transformed to the time domain, and the non-aliased effective signal, aliasing noise and separation difference are output to complete the entire separation process.
[0075] Specifically, for the converged optimal model m opt Performing the inverse FKK transform yields the time-domain alias-free effective signal m. final =F -1 (F(m opt )); The aliasing noise n is calculated based on the optimal model. final =Γm opt -d_comp, and simultaneously calculate the difference Δd = d_comp - m before and after separation. final (Used to verify whether a valid signal is damaged); Seismic data separation results include: ① Non-aliased effective signal gathers (m final); ② Aliasing noise gather (n final ); ③ Separate the difference gathers before and after separation (Δd).
[0076] The seismic data separation scheme provided in this application constitutes a logical chain of "preprocessing → channel compensation → adaptive inversion → closed-loop optimization → result output": 1. Air lane detection provides accurate positioning data for subsequent adaptive compensation, avoiding blind compensation; 2. Empty channel compensation restores data integrity and eliminates energy anomaly interference for subsequent FKK domain sparse transformation; 3. The initial model construction with non-aliased data provides a reasonable starting point for subsequent variable grid inversion. The phased grid scale adjustment and dynamic sparse shrinkage threshold update are mutually adapted (the smaller the grid, the lower the threshold, which matches the extraction of high-frequency weak signals). 4. Determine whether the stopping conditions are met to ensure optimal separation effect, and finally output high-quality data that meets the requirements of industrial applications. Each step is designed to address the shortcomings of existing solutions, and the steps are closely connected to form a complete technical closed loop.
[0077] Based on the seismic data separation method provided in the embodiments of this application, a three-dimensional FKK domain variable grid sparse inversion technique is proposed. During the iteration process, the data grid block scale is dynamically adjusted to match the physical laws of signal extraction, which better aligns with the essence of signal extraction during inversion—first the strong axis, then the weak axis, and from low frequency to high frequency—thus achieving better separation results. An adaptive channel compensation technique is also proposed, which fills the channels in the sparse transform domain with regular interpolation, avoiding abnormal energy attenuation and effectively eliminating the whitening phenomenon in the processed data caused by variable channel gaps, while simultaneously improving the overall effect. Furthermore, the three-dimensional FKK transform domain is selected, taking into account signal coherence identification, transform reversibility, and computational efficiency, ultimately improving separation accuracy and efficiency, significantly increasing the efficiency of field operations, shortening the operation cycle, and reducing exploration costs.
[0078] Figure 2 A structural block diagram of a seismic data separation apparatus according to an embodiment of this application is shown, as follows: Figure 2 As shown, the device includes: The acquisition module 201 is adapted to acquire the mixed seismic data to be separated, wherein the mixed seismic data to be separated is synchronous source mixed data in the time domain; Detection module 202 is suitable for performing air channel detection on the seismic data to be separated and mixed. The interpolation processing module 203 is adapted to transform the seismic data to be separated into the FKK domain, perform air channel regional interpolation processing on the air channels according to the seismic data of the effective channels within the preset range of each air channel, and perform FKK inverse transformation processing on the interpolated seismic data to be separated into the FKK domain to obtain the air channel compensated seismic data to be separated into the FKK domain. Module 204 is suitable for performing FKK domain sparse transformation processing on the seismic data to be separated after channel compensation, and constructing an initial model of non-overlapping data based on the seismic data to be separated after FKK domain sparse transformation. The variable mesh sparse inversion processing module 205 is suitable for performing phased FKK domain variable mesh sparse inversion iterative processing on the initial model of non-aliased data. After each iteration, the current non-aliased data model and sparse shrinkage threshold are updated until the preset stopping condition is met. The inverse transformation processing module 206 is adapted to perform FKK inverse transformation processing on the model data corresponding to the non-aliased data model that meets the stopping conditions, so as to obtain the seismic data separation result.
[0079] Optionally, the detection module is further adapted to: perform amplitude statistics within a preset local time window for each seismic trace in the common detector point gather to obtain the root mean square amplitude of the corresponding seismic trace; Determine whether the root mean square amplitude is less than the preset root mean square amplitude threshold. If so, identify the seismic trace as an empty trace and record the empty trace information.
[0080] Optionally, the interpolation processing module is further adapted to: locate the air channels in the FKK domain transformed mixed seismic data to be separated based on the air channel information; For any given channel, interpolation weighting coefficients are calculated based on the distances from each valid channel to the channel within the preset range of the channel. Then, channel regional interpolation is performed based on the interpolation weighting coefficients and the FKK domain transformed seismic data corresponding to each valid channel within the preset range of the channel.
[0081] Optionally, the building module is further adapted to: calculate the initial sparsity shrinkage threshold based on the seismic data to be separated and mixed after the FKK domain sparse transformation; An aliased data model is constructed based on the seismic data to be separated after sparse transformation in the FKK domain. A pseudo-unmixing calculation is performed on the aliased data model based on the initial sparse shrinkage threshold to obtain an initial model without aliasing.
[0082] Optionally, the variable grid sparse inversion processing module is further adapted to: perform multi-stage FKK domain sparse inversion iterative processing on the initial model of non-aliased data; the iterative process is divided into multiple iterative stages according to the change threshold of the iterative residual, each iterative stage adopts a progressively smaller grid scale to adapt to the sparse extraction of seismic signals with corresponding frequency bands and amplitude characteristics, and each iterative stage adopts a progressively lower sparse shrinkage threshold; each iteration updates the current non-aliased data model based on the non-aliased data model obtained in the previous iteration until the preset stopping condition is met.
[0083] Optionally, the variable mesh sparse inversion processing module is also suitable for: calculating the objective function of the current iteration after the current non-aliased data model is updated; If the objective function of the current iteration is less than that of the previous iteration, then the aliasing noise estimate is updated based on the current non-aliasing data model.
[0084] Optionally, the variable mesh sparse inversion processing module is further adapted to: After each iteration in each stage, the sparsity shrinkage threshold is updated according to the following formula:
[0085] Where i is the current iteration number, k is the decay sparsity, and T i T is the sparse shrinkage threshold corresponding to the i-th iteration in the corresponding stage. i-1 This is the sparse shrinkage threshold corresponding to the (i-1)th iteration in the corresponding stage.
[0086] Optionally, the device further includes a preprocessing module, adapted to perform denoising preprocessing on the seismic data to be separated and mixed to suppress background low-frequency strong amplitude surge noise, so as to obtain preprocessed seismic data to be separated and mixed.
[0087] The descriptions of the above modules refer to the corresponding descriptions in the method embodiments, and will not be repeated here.
[0088] Based on the seismic data separation device provided in the embodiments of this application, a three-dimensional FKK domain variable grid sparse inversion technique is proposed. During the iteration process, the data grid block scale is dynamically adjusted to match the physical laws of signal extraction, which is more in line with the essence of signal extraction from low frequency to high frequency during inversion, namely, extracting strong axes first and then weak axes. This results in better separation performance. An adaptive channel compensation technique is also proposed, which fills the channels in the sparse transform domain with regular interpolation to avoid abnormal energy attenuation, effectively eliminate the whitening phenomenon of processed data caused by variable channel missing, and improve the performance. At the same time, the three-dimensional FKK transform domain is selected to take into account signal coherence identification, transform reversibility, and computational efficiency, ultimately improving the separation accuracy and efficiency, significantly improving the efficiency of field production operations, shortening the operation cycle, and reducing exploration costs.
[0089] This application provides a non-volatile computer storage medium storing at least one executable instruction or computer program that enables a processor to perform the operation corresponding to the mixed seismic data separation method in any of the above method embodiments.
[0090] This application provides a computer program product, which includes at least one executable instruction or computer program that enables a processor to perform the operation corresponding to the mixed seismic data separation method in any of the above method embodiments.
[0091] Figure 3The diagram shows a structural schematic of an embodiment of the computing device of this application. The specific embodiments of this application do not limit the specific implementation of the computing device.
[0092] like Figure 3 As shown, the computing device may include: a processor 302, a communications interface 304, a memory 306, and a communications bus 308.
[0093] The processor 302, communication interface 304, and memory 306 communicate with each other via communication bus 308. Communication interface 304 is used to communicate with other network elements, such as clients or other servers. The processor 302 executes program 310, specifically performing the relevant steps in the above-described embodiment of the mixed-seismic data separation method for computing devices.
[0094] Specifically, program 310 may include program code that includes computer operation instructions.
[0095] Processor 302 may be a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application. The computing device includes one or more processors, which may be processors of the same type, such as one or more CPUs; or processors of different types, such as one or more CPUs and one or more ASICs.
[0096] Memory 306 is used to store program 310. Memory 306 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.
[0097] Specifically, program 310 can be used to cause processor 302 to execute the mixed seismic data separation method in any of the above method embodiments. The specific implementation of each step in program 310 can be found in the corresponding descriptions of the steps and units in the above mixed seismic data separation embodiments, and will not be repeated here. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the devices and modules described above can be referred to the corresponding process descriptions in the foregoing method embodiments, and will not be repeated here.
[0098] The algorithms and displays provided herein are not inherently related to any particular computer, virtual system, or other device. Various general-purpose systems can also be used in conjunction with the teachings herein. The required structure for constructing such systems is apparent from the above description. Furthermore, the embodiments of this application are not directed to any particular programming language. It should be understood that the contents of the embodiments of this application described herein can be implemented using various programming languages, and the above description of specific languages is for the purpose of disclosing the best implementation of the embodiments of this application.
[0099] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of this application may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.
[0100] Similarly, it should be understood that, in order to simplify this disclosure and aid in understanding one or more of the various inventive aspects, in the foregoing description of exemplary embodiments of the present application, various features of the present application embodiments are sometimes grouped together into a single embodiment, figure, or description thereof. However, this approach to disclosure should not be construed as reflecting an intention that the claimed embodiments of the present application require more features than expressly recited in each claim. Rather, as reflected in the following claims, inventive aspects lie in fewer than all features of a single foregoing disclosed embodiment. Therefore, the claims following the detailed description are hereby expressly incorporated into that detailed description, wherein each claim itself is a separate embodiment of the present application.
[0101] Those skilled in the art will understand that modules in the device of the embodiments can be adaptively changed and placed in one or more devices different from that embodiment. Modules, units, or components in the embodiments can be combined into a single module, unit, or component, and further, they can be divided into multiple sub-modules, sub-units, or sub-components. Except where at least some of such features and / or processes or units are mutually exclusive, any combination can be used to combine all features disclosed in this specification (including the accompanying claims, abstract, and drawings) and all processes or units of any method or device so disclosed. Unless expressly stated otherwise, each feature disclosed in this specification (including the accompanying claims, abstract, and drawings) may be replaced by an alternative feature that serves the same, equivalent, or similar purpose.
[0102] Furthermore, those skilled in the art will understand that although some embodiments described herein include certain features but not others included in other embodiments, combinations of features from different embodiments are meant to be within the scope of the embodiments of this application and form different embodiments. For example, in the following claims, any one of the claimed embodiments can be used in any combination.
[0103] The various component embodiments of this application can be implemented in hardware, or as software modules running on one or more processors, or a combination thereof. Those skilled in the art will understand that microprocessors or digital signal processors (DSPs) can be used in practice to implement some or all of the functions of some or all of the components according to the embodiments of this application. The embodiments of this application can also be implemented as device or apparatus programs (e.g., computer programs and computer program products) for performing part or all of the methods described herein. Such programs implementing the embodiments of this application can be stored on a computer-readable medium, or can be in the form of one or more signals. Such signals can be downloaded from an Internet website, provided on a carrier signal, or provided in any other form.
[0104] It should be noted that the above embodiments are illustrative of the embodiments of this application and not limiting of the embodiments of this application, and those skilled in the art can devise alternative embodiments without departing from the scope of the appended claims. In the claims, any reference signs placed between parentheses should not be construed as limiting the claims. The word "comprising" does not exclude the presence of elements or steps not listed in the claims. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. Embodiments of this application can be implemented by means of hardware comprising several different elements and by means of a suitably programmed computer. In the unit claims enumerating several means, several of these means may be embodied by the same item of hardware. The use of the words first, second, and third, etc., does not indicate any order. These words can be interpreted as names.
Claims
1. A method for separating mixed seismic data, comprising: Acquire the seismic data to be separated and mixed, and perform air channel detection on the seismic data to be separated and mixed, wherein the seismic data to be separated and mixed is synchronous source mixed data in the time domain; The seismic data to be separated and mixed is transformed to the FKK domain. Based on the seismic data transformed by the FKK domain corresponding to the effective channels within the preset range of each channel, the channel is subjected to channel area interpolation. The interpolated seismic data to be separated and mixed is subjected to FKK inverse transformation to obtain the channel-compensated seismic data to be separated and mixed. The FKK domain sparse transformation was performed on the seismic data to be separated after the air channel compensation. Based on the FKK domain sparse transformation of the seismic data to be separated, an initial model of non-overlapping data was constructed. A phased FKK domain variable mesh sparse inversion iterative process is performed on the initial model of the non-aliased data. After each iteration, the current non-aliased data model and the sparse shrinkage threshold are updated until the preset stopping condition is met. Perform FKK inverse transform on the model data corresponding to the non-aliased data model that meets the stopping condition to obtain the seismic data separation results.
2. The method according to claim 1, wherein, The air channel detection of the seismic data to be separated and mixed further includes: For each seismic trace within the common receiver gather, amplitude statistics are performed within a preset local time window to obtain the root mean square amplitude of the corresponding seismic trace. Determine whether the root mean square amplitude is less than a preset root mean square amplitude threshold. If so, identify the seismic trace as an empty trace and record the empty trace information.
3. The method according to claim 2, wherein, The step of performing channel region interpolation processing on the channels based on the FKK domain transformed seismic data corresponding to the effective channels within a preset range of each channel further includes: Locate the air channels in the mixed seismic data to be separated after FKK domain transformation based on the air channel information; For any given channel, interpolation weighting coefficients are calculated based on the distances from each valid channel within the preset range of the channel to the channel. Then, channel regional interpolation processing is performed based on the interpolation weighting coefficients and the FKK domain transformed seismic data corresponding to each valid channel within the preset range of the channel.
4. The method according to any one of claims 1-3, wherein, The step of constructing an initial model for non-aliased data based on the seismic data to be separated after sparse transformation in the FKK domain further includes: The initial sparsity shrinkage threshold is calculated based on the seismic data to be separated and mixed after the FKK domain sparse transformation. An aliased data model is constructed based on the seismic data to be separated after sparse transformation in the FKK domain. A pseudo-demixing calculation is performed on the aliased data model based on the initial sparse shrinkage threshold to obtain an initial model without aliasing.
5. The method according to any one of claims 1-3, wherein, The step of performing a phased FKK domain variable mesh sparse inversion iterative process on the initial model of the non-aliased data, and updating the current non-aliased data model and sparse shrinkage threshold after each iteration until a preset stopping condition is met, further includes: The initial model of the non-aliased data is subjected to multi-stage FKK domain sparse inversion iterative processing. The iterative process is divided into multiple iterative stages based on the change threshold of the iterative residual. Each iterative stage adopts a progressively smaller grid scale to adapt to the sparse extraction of seismic signals with corresponding frequency bands and amplitude characteristics. Each iterative stage also adopts a progressively lower sparse shrinkage threshold. Each iteration updates the current non-aliased data model based on the non-aliased data model obtained in the previous iteration until a preset stopping condition is met.
6. The method according to claim 5, wherein, The method further includes: calculating the objective function for this iteration after updating the current non-aliased data model; If the objective function of the current iteration is less than that of the previous iteration, then the aliasing noise estimate is updated based on the current non-aliasing data model.
7. The method according to any one of claims 1-3, wherein, The updated sparse shrinkage threshold further includes: After each iteration in each stage, the sparsity shrinkage threshold is updated according to the following formula: Where i is the current iteration number, k is the decay sparsity, and T i T is the sparse shrinkage threshold corresponding to the i-th iteration in the corresponding stage. i-1 This is the sparse shrinkage threshold corresponding to the (i-1)th iteration in the corresponding stage.
8. The method according to any one of claims 1-3, wherein, Before performing air channel detection on the seismic data to be separated and mixed, the method further includes: The seismic data to be separated and mixed is subjected to denoising preprocessing to suppress background low-frequency strong amplitude surge noise, resulting in preprocessed seismic data to be separated and mixed.
9. A seismic data separation device for mixed seismic data, comprising: The acquisition module is adapted to acquire the mixed seismic data to be separated, wherein the mixed seismic data to be separated is synchronous source mixed data in the time domain; The detection module is adapted to perform air channel detection on the seismic data to be separated and mixed. The interpolation processing module is adapted to transform the seismic data to be separated and mixed into the FKK domain, perform air channel regional interpolation processing on the air channel based on the seismic data after FKK domain transformation corresponding to the effective channel within the preset range of each air channel, and perform FKK inverse transformation processing on the interpolated seismic data to be separated and mixed into the FKK domain to obtain the air channel compensated seismic data to be separated and mixed into the FKK domain. The module is suitable for performing FKK domain sparse transformation processing on the seismic data to be separated after air channel compensation, and constructing an initial model of non-overlapping data based on the seismic data to be separated after FKK domain sparse transformation. The variable mesh sparse inversion processing module is suitable for performing a phased FKK domain variable mesh sparse inversion iterative processing on the initial model of the non-aliased data. After each iteration, the current non-aliased data model and the sparse shrinkage threshold are updated until the preset stopping condition is met. The inverse transform processing module is suitable for performing FKK inverse transform processing on the model data corresponding to the non-aliased data model that meets the stopping conditions, so as to obtain the seismic data separation results.
10. A computing device, comprising: The processor, memory, communication interface, and communication bus are provided, wherein the processor, memory, and communication interface communicate with each other via the communication bus. The memory is used to store at least one executable instruction, which causes the processor to perform the operation corresponding to the seismic data separation method as described in any one of claims 1-8.
11. A computer storage medium storing at least one executable instruction that causes a processor to perform an operation corresponding to the seismic data separation method according to any one of claims 1-8.
12. A computer program product comprising at least one executable instruction that causes a processor to perform an operation corresponding to the seismic data separation method of any one of claims 1-8.