Multiple - wave Adaptive Subtraction Method Based on Multi - window Joint Optimization

Abstract

The present invention provides a multiple-wave adaptive subtraction method based on multi-window joint optimization, comprising: Step 1, windowing the original data and the predicted multiple waves and shuffling the arrangement order of the windows; Step 2, grouping the original data and the predicted multiple-wave data according to the number of window matches; Step 3, inputting multiple original data windows and multiple predicted multiple-wave windows, and constructing a convolution matrix of the predicted multiple waves and a vector of the original data; Step 4, constructing a mathematical model and an optimization problem for multiple-wave adaptive subtraction; Step 5, using an improved fast iterative shrinkage threshold algorithm to solve the matching filter for multiple-wave adaptive subtraction; Step 6, estimating the primary wave. The multiple-wave adaptive subtraction method based on multi-window joint optimization can better protect the primary wave and effectively remove the residual multiple waves by using the prediction information of multiple data windows for adaptive subtraction simultaneously.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic data processing for oil and gas exploration, and particularly to a multiple wave adaptive subtraction method based on multi-window joint optimization. Background Art

[0002] At present, multiple wave suppression is one of the most prominent problems in seismic data processing for oil and gas exploration. Multiple waves are actually a kind of false interference signals, and their existence will interfere with the correct identification of primary waves. The quality of multiple wave suppression determines the quality of seismic data imaging and inversion results. Therefore, the research on multiple wave suppression has always been an important link that cannot be ignored in seismic data processing.

[0003] The predictive subtraction method based on the wave equation includes two steps. First, the multiple waves are estimated by simulating the actual wave field or inverting the seismic data, and then the predicted multiple waves are adaptively subtracted from the original seismic data. Adaptive subtraction is the core step of this method for suppressing multiple waves. The adaptive subtraction method of multiple waves based on the matched filter uses the matched filter to match the original data and the predicted multiple waves, and directly subtracts the matched multiple waves from the original seismic data. Among them, the key problem is to design a better matched filter to eliminate the complex differences between the predicted multiple waves and the real multiple waves. The traditional adaptive subtraction based on the matched filter divides the original data and the predicted multiple waves into windows, and fits the predicted multiple waves with the original data window by window to suppress the multiple waves. However, in the actual seismic data acquisition process, there are factors such as wavelet change, feather angle drift, lateral line dip, and limited offset, which result in complex amplitude, time, and spatial differences between the predicted multiple waves and the real multiple waves. The filter obtained by optimizing a single window cannot effectively characterize the complex differences between the predicted multiple waves and the real multiple waves, and there will be primary wave damage and multiple wave residues in the result of adaptive subtraction. Therefore, making full use of the prediction information of multiple windows to optimize the filter is of great significance for protecting the primary wave and removing the residual multiple waves.

[0004] In the Chinese patent application with the application number: CN201810971326.7, a multiple - wave adaptive subtraction method and device are involved. The method includes: constructing a feature vector and a label value respectively using the predicted multiple waves in a two - dimensional data window and the original seismic data in the two - dimensional data window, and generating training data according to the feature vector and the label value; taking the training data as input, and estimating a support vector regression function through the support vector regression method; inputting the feature vector into the support vector regression function to obtain the estimated multiple waves in the two - dimensional data window; subtracting the estimated multiple waves from the original seismic data to obtain the primary - wave estimation result in the two - dimensional data window; and obtaining the estimated primary waves of the original seismic data according to the primary - wave estimation results in all two - dimensional data windows of the original seismic data. By reducing the multiple - wave adaptive subtraction to a support vector regression problem, it is possible to better balance the protection of primary waves and the separation of multiple waves.

[0005] In the Chinese patent application with the application number: CN202010013146.5, a multiple - wave adaptive subtraction method based on prediction feature extraction is involved. The multiple - wave adaptive subtraction method based on prediction feature extraction includes: Step 1, setting the initial values of variables; Step 2, constructing a convolutional neural network; Step 3, training the convolutional neural network; Step 4, using the trained convolutional neural network to extract the predicted multiple - wave features; Step 5, constructing a mathematical model and an optimization problem for multiple - wave adaptive subtraction using the original data and the predicted multiple - wave features; Step 6, solving the matching filter for multiple - wave adaptive subtraction; Step 7, estimating the primary waves. The method of using the predicted multiple - wave features for multiple - wave adaptive subtraction in this invention can better balance the protection of primary waves and the separation of multiple waves, and effectively reduce the residual multiple waves while protecting the primary waves.

[0006] In the Chinese patent application with the application number: CN202010013892.4, a multiple - wave adaptive subtraction algorithm based on filter morphology detection is involved, including the following steps: S1, windowing the data; S2, performing one - dimensional cross - correlation in the time direction between the predicted multiple waves and the original data to estimate the time misalignment Δt between the time - shifted operator predicted multiple waves and the true multiple waves; S3, estimating the filter morphology; S4, estimating the optimal matching filter constrained by the filter morphology; S5, obtaining the primary waves using the obtained results; S6, merging the data of different windows to obtain the complete primary - wave data. The invention uses the multiple - wave adaptive subtraction algorithm based on filter morphology detection to obtain a more accurate multiple - wave estimation result, with a better effect of separating primary waves and multiple waves, and can more effectively remove the multiple - wave signal while better protecting the primary - wave signal.

[0007] All of the above prior arts are quite different from the present invention and fail to solve the technical problems we want to address. Therefore, we have invented a new multiple-wave adaptive subtraction method based on multi-window joint optimization. Summary of the Invention

[0008] The objective of the present invention is to provide a multiple-wave adaptive subtraction method that uses the prediction information of multiple data windows for adaptive subtraction, which can better protect the primary wave, namely, the multiple-wave adaptive subtraction method based on multi-window joint optimization.

[0009] The objective of the present invention can be achieved by the following technical measures: The multiple-wave adaptive subtraction method based on multi-window joint optimization, which includes:

[0010] Step 1: Window the original data and predicted multiple waves, and shuffle the order of the windows.

[0011] Step 2: Group the original data and predicted multiple-wave data according to the number of window matches.

[0012] Step 3: Input multiple original data windows and multiple predicted multiple-wave windows, and construct the convolution matrix of the predicted multiple waves and the vector of the original data.

[0013] Step 4: Construct the mathematical model and optimization problem for multiple-wave adaptive subtraction.

[0014] Step 5: Use the improved fast iterative shrinkage threshold algorithm to solve the matching filter for multiple-wave adaptive subtraction.

[0015] Step 6: Estimate the primary wave.

[0016] The objective of the present invention can also be achieved by the following technical measures:

[0017] The multiple-wave adaptive subtraction method based on multi-window joint optimization further includes, before Step 1, setting the initial values of variables. The initial value variables to be set include the time length T of the 2D data window for adaptive subtraction, the spatial length R of the 2D data window, the time length p of the 2D matching filter, the spatial length q of the 2D matching filter, the number N of windows for simultaneous optimization, the primary wave threshold s, the damping factor α, and the maximum number of iterations M. [[ID=*********]] [[ID=*********]]

[0018] [[ID=*********]]In Step 1, window the original data and predicted multiple-wave data, generate a set of random numbers according to the number of windows, and then shuffle the order of the original data and predicted multiple-wave windows according to the random numbers. [[ID=*********]] [[ID=*********]]

[0019] [[ID=*********]]In Step 2, match the original data and predicted multiple-wave data in groups according to the number of window matches N. Each time, match the data of N windows until all windows are processed. [[ID=*********]]

[0020] In step 3, according to the number of window matches N, N original data windows and N predicted multiple data windows are collected respectively; vectors d are constructed for the original data of each window i (i = 1, 2,..., N), and then according to the predicted multiple data, the 2D data window time length T, the 2D data window spatial length R, the time length p of the 2D matching filter, and the spatial length q of the 2D matching filter, a convolution matrix H is constructed for each predicted multiple window i (i = 1, 2,..., N).

[0021] In step 4, a mathematical model p for adaptive subtraction is constructed i = d i - H i x (i = 1, 2,..., N), where p i (i = 1, 2,..., N) represents the vector constructed from the primary wave of each window, x represents the 2D matching filter, and an optimization problem is constructed where represents solving the unknown x by minimizing the objective function, ||m||1 represents the L1 norm of vector m, ||m||2 represents the L2 norm of vector m, and α is a weighting factor

[0022] In step 5, the improved fast iterative shrinkage threshold algorithm is used to process all 2D window data groups of the seismic trace gather

[0023] Specifically, it includes

[0024] e1. Calculate the inverse matrix and the initial estimate of the filter Estimate the primary wave p i (1) = d i (1) - H i (1) x (1) (i = 1, 2,..., N), and set the iteration number m = 1. Where, H represents the convolution matrix of the predicted multiple, N represents the number of window matches, α is the weighting factor, I is the identity matrix, and d is the vector constructed from the original data

[0025] e2. Calculate the primary wave shrinkage threshold result where the distance operator S α is

[0026] S α {p} (j,k) =(|p (j,k) |- s × max(|p|)) + × sgn(p (j,k)),

[0027] where \(j = 1, 2, \cdots, T\), \(k = 1, 2, \cdots, R\), \(0 \lt s \lt 1\), \(p\) (j,k) represents estimating the element with subscript \((j, k)\) in the primary wave vector \(p\). where \(m\) is the number of iterations and \(N\) is the number of window matches;

[0028] e3. Calculate the shrinkage threshold result of primary wave update where t (1) \(= 1\), \(m\) is the number of iterations;

[0029] e4. Calculate the filter where \(H\) represents the convolution matrix for predicting multiple waves, \(N\) is the number of window matches, and \(d\) represents the vector constructed from the original data;

[0030] e5. Estimate the primary wave where \(d\) represents the vector constructed from the original data, \(N\) is the number of window matches, and \(H\) represents the convolution matrix for predicting multiple waves;

[0031] e6. Let \(m = m + 1\). If \(m \leq M\), return to step e2; if \(m \gt M\), output the estimated primary wave in \(N\) 2D data windows.

[0032] In step 6, determine whether all 2D window data in the original data have been processed; if not, return to step 5; if all have been processed, first weight the primary wave estimation results in each 2D window using a 2D Gaussian window and fuse them into a data volume Then fuse the 2D Gaussian windows into a data volume in the same way The final primary wave estimation result is expressed as: where \( / \) represents element-by-element division operation.

[0033] The predictive subtraction method based on the wave equation is a widely used multiple suppression method in seismic exploration. There are differences in amplitude, time, and space between the predicted multiples and the real multiples. A matching filter needs to be designed to minimize the differences between the predicted multiples and the real multiples. Then, the matched multiples are adaptively subtracted from the original data to obtain the final primary wave. The present invention utilizes the predicted multiple information of multiple windows, and uses a matching filter to simultaneously fit the predicted multiples and the original data within multiple windows, and adaptively subtract the multiples in multiple windows at the same time. Compared with the filter obtained by optimizing a single window in the traditional method, the filter obtained by jointly optimizing multiple windows in the present invention can better characterize the complex differences between the predicted multiples and the real multiples. Therefore, the multiple adaptive subtraction method based on multi-window joint optimization in the present invention can effectively balance primary wave protection and multiple suppression. Compared with the traditional adaptive subtraction method that matches through a single data window, the method of the present invention that adaptively subtracts using the predicted information of multiple data windows at the same time can better protect the primary wave and effectively remove residual multiples. Description of the Drawings

[0034] Figure 1 It is a flowchart of a specific embodiment of the multiple adaptive subtraction method based on multi-window joint optimization of the present invention;

[0035] Figure 2 It is a common shot gather diagram of the original data and the predicted multiples in a specific embodiment of the present invention;

[0036] Figure 3 It is a common shot gather diagram of the primary wave estimation results of the multiple adaptive subtraction method based on single-window matching and multi-window joint optimization in a specific embodiment of the present invention;

[0037] Figure 4 It is a common shot gather diagram of the removed multiples of the multiple adaptive subtraction method based on single-window matching and multi-window joint optimization in a specific embodiment of the present invention;

[0038] Figure 5 It is a schematic diagram of the primary wave estimation result and the removed multiple result of the model data with 140 window matches in a specific example of the present invention;

[0039] Figure 6 It is a common offset gather diagram of the original data and the predicted multiples in a specific embodiment of the present invention;

[0040] Figure 7 It is a common offset gather diagram of the primary wave estimation results of the multiple adaptive subtraction method based on single-window matching and multi-window joint optimization in a specific embodiment of the present invention;

[0041] Figure 8 The common offset gather map of the multiple waves removed by the multiple wave adaptive subtraction method based on single window matching and multi-window joint optimization in a specific embodiment of the present invention. Detailed implementation manners

[0042] It should be noted that the following detailed description is exemplary and is intended to provide further illustration of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the technical field to which the present invention belongs.

[0043] It should be noted that the terms used herein are only for describing specific implementation manners and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular forms are also intended to include the plural forms. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they specify the presence of features, steps, operations, and / or combinations thereof.

[0044] As Figure 1 shown, Figure 1 The flowchart of the multiple wave adaptive subtraction method based on multi-window joint optimization of the present invention. The multiple wave adaptive subtraction method based on multi-window joint optimization includes the following steps:

[0045] (1) Set the initial values of variables;

[0046] (2) Window the original data and predicted multiples, and shuffle the order of the windows;

[0047] (3) Group the original data and predicted multiple data according to the number of window matches;

[0048] (4) Input multiple original data windows and multiple predicted multiple windows, and construct the convolution matrix of the predicted multiples and the vector of the original data;

[0049] (5) Construct the mathematical model and optimization problem of multiple wave adaptive subtraction;

[0050] (6) Use the improved fast iterative shrinkage threshold algorithm to solve the matching filter of multiple wave adaptive subtraction;

[0051] (7) Estimate the primary wave.

[0052] The following are several specific embodiments of applying the present invention.

[0053] Embodiment 1

[0054] In a specific embodiment 1 of applying the present invention, the multiple wave adaptive subtraction method based on multi-window joint optimization includes the following steps:

[0055] a. Set the initial values of the variables. The variables for which the initial values need to be set include the time length T of the 2D data window for adaptive subtraction, the spatial length R of the 2D data window, the time length p of the 2D matching filter, the spatial length q of the 2D matching filter, the number N of windows for simultaneous optimization, the primary wave threshold s, the damping factor α, and the maximum number of iterations M.

[0056] b. Window the original data and the predicted multiple wave data. Generate a set of random numbers according to the number of windows, and then shuffle the window order of the original data and the predicted multiple wave data based on the random numbers. Group the original data and the predicted multiple wave data for matching according to the number N of window matches. Each time, match the data of N windows until all windows are processed.

[0057] c. According to the number N of window matches, input N original data windows and N predicted multiple wave data windows respectively. Construct a vector d for the original data of each window i (i = 1, 2,..., N), and then construct a convolution matrix H for each predicted multiple wave window according to the predicted multiple wave data and the parameters T and R of the 2D data window, and the parameters p and q of the 2D matching filter i (i = 1, 2,..., N);

[0058] d. Construct the mathematical model for adaptive subtraction p i = d i - H i x (i = 1, 2,..., N), where p i (i = 1, 2,..., N) represents the vector constructed by the primary wave of each window, x represents the 2D matching filter, and construct the optimization problem where represents solving the unknown x by minimizing the objective function, ||m||1 represents the L1 norm of the vector m, and ||m||2 represents the L_{2} norm of the vector m;

[0059] e. Use the improved fast iterative shrinkage threshold algorithm to process all the 2D window data groups of the seismic trace gather;

[0060] Specifically include:

[0061] e1. Calculate the inverse matrix and the initial estimate of the filter Estimate the primary wave p i (1) = d i (1) - H i (1) x (1)(i = 1, 2, ..., N), and set the number of iterations m = 1. Where H represents the convolution matrix for predicting multiple waves, N represents the number of window matches, α is the weighting factor, I is the identity matrix, and d is the vector constructed from the original data;

[0062] e2. Calculate the result of the primary wave shrinkage threshold Where the distance operator S α is:

[0063] S α {p} (j,k) =(|p (j,k) |-s × max(|p|)) + × sgn(p (j,k) ),

[0064] where j = 1, 2, ..., T, k = 1, 2, ..., R, 0 < s < 1, p (j,k) represents the element with subscript (j, k) in the estimated primary wave vector p, where m is the number of iterations and N is the number of window matches;

[0065] e3. Calculate the updated result of the primary wave shrinkage threshold where t (1) =1, and m is the number of iterations.

[0066] e4. Calculate the filter where H represents the convolution matrix for predicting multiple waves, N is the number of window matches, and d represents the vector constructed from the original data.

[0067] e5. Estimate the primary wave where d represents the vector constructed from the original data, N is the number of window matches, and H represents the convolution matrix for predicting multiple waves.

[0068] e6. Let m = m + 1. If m ≤ M, return to step e2; if m > M, output the estimated primary wave in N 2D data windows.

[0069] f. Determine whether all 2D window data in the original data have been processed; if not, return to step e; if all have been processed, first weight the estimated primary wave results in each 2D window using a 2D Gaussian window and fuse them into a data volume Then fuse the 2D Gaussian windows into a data volume in the same way The final estimated primary wave result is expressed as: where / represents element-by-element division operation.

[0070] Example 2

[0071] In a specific Embodiment 2 of applying the present invention, the processing results of the model data are first given. Figure 2 a is the common shot gather map of the original data. Figure 2 b is the common shot gather map of the predicted multiple waves. Figure 3 a is the common shot gather map of the primary wave estimation result of the multiple wave adaptive subtraction method based on single window matching. Figure 3 b is the common shot gather map of the primary wave estimation result of the multiple wave adaptive subtraction based on multi-window joint optimization. Figure 4 a is the common shot gather map of the multiple waves removed by the multiple wave adaptive subtraction method based on single window matching. Figure 4 b is the common shot gather map of the multiple waves removed by the multiple wave adaptive subtraction method based on multi-window joint optimization. Figure 3 a and Figure 3 As shown by the black arrows in b, compared with the traditional single window matching method, the multi-window joint optimization method adopted by the present invention can better remove the residual multiple waves in the primary wave estimation result. Figure 4 a and Figure 4 As shown by the white arrows in b, the multi-window joint optimization method adopted by the present invention can better protect the primary wave. In addition, from the perspective of quantitative analysis, the signal-to-noise ratio of the estimated primary wave by the multiple wave adaptive subtraction method based on single window matching is 13.36 dB, while the signal-to-noise ratio of the estimated primary wave by using the method of the present invention is 20.45 dB, an increase of 7.09 dB.

[0072] Embodiment 3

[0073] In the processing results of the model data of the present invention, the number of window matchings adopted is 280. In order to analyze the influence of the number of window matchings in the present invention on the separation effect of the primary wave and the multiple waves, further experiments were conducted on the model data. The number of window matchings was selected as 140, and other parameters (data window size, filter length, primary wave threshold, damping factor, maximum number of iterations) were the same as the corresponding parameter values in Figure 3 b. Figure 5 a is the primary wave estimation result with the number of window matchings being 140, Figure 5 b is the result of removing the multiple waves with the number of window matchings being 140. In addition, when the number of window matchings is 140, the signal-to-noise ratio of the estimated primary wave is 20.11 dB.

[0074] Embodiment 4

[0075] Then the processing results of the actual data are given. Figure 6 a is the common offset gather map of the original data. Figure 6 b is the common offset gather map of the predicted multiple waves. Figure 7 a is the common offset gather map of the primary wave estimation result of the multiple wave adaptive subtraction method based on single window matching.Figure 7 b is the common offset gather map of the primary wave estimation result of multiple wave adaptive subtraction based on multi-window joint optimization. Figure 8 a is the common offset gather map of the multiple waves removed by the multiple wave adaptive subtraction method based on single-window matching. Figure 8 b is the common offset gather map of the multiple waves removed by the multiple wave adaptive subtraction method based on multi-window joint optimization. Figure 7 a and Figure 7 The circled areas in a and b indicate that, compared with the traditional single-window matching method, the multi-window joint optimization method adopted by the present invention can better remove the residual multiple waves in the primary wave estimation result. The Trace Number on the horizontal axis represents the trace number of the seismic gather, and the Time (ms) on the vertical axis represents the time (milliseconds).

[0076] Finally, it should be noted that the above are only the preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0077] Except for the technical features described in the specification, the rest are the known technologies of those skilled in the art.

Claims

1. Multiple - wave adaptive subtraction method based on multi - window joint optimization, characterized in that The multiple - wave adaptive subtraction method based on multi - window joint optimization includes the following steps: Step 1: Window the original data and predicted multiple waves, and shuffle the arrangement order of the windows; Step 2: Group the original data and predicted multiple - wave data according to the number of window matches; Step 3: Input multiple original - data windows and multiple predicted - multiple - wave windows, and construct the convolution matrix of the predicted multiple waves and the vector of the original data; Step 4: Construct the mathematical model and optimization problem of multiple - wave adaptive subtraction; Step 5: Use the improved fast iterative shrinkage threshold algorithm to solve the matching filter for multiple - wave adaptive subtraction; Step 6: Estimate the primary wave.

2. The multiple-wave adaptive subtraction method based on multi-window joint optimization according to claim 1, wherein, The multiple - wave adaptive subtraction method based on multi - window joint optimization also includes, before Step 1, setting the initial values of variables. The initial - value variables to be set include the time length T of the 2D data window for adaptive subtraction, the spatial length R of the 2D data window, the time length p of the 2D matching filter, the spatial length q of the 2D matching filter, the number N of window matches for simultaneous optimization, the primary - wave threshold s, the damping factor α, and the maximum number of iterations M.

3. The multiple-wave adaptive subtraction method based on multi-window joint optimization according to claim 1, wherein In Step 1, window the original data and predicted multiple - wave data, generate a set of random numbers according to the number of windows, and then shuffle the order of the original - data and predicted - multiple - wave windows according to the random numbers.

4. The multiple wave adaptive subtraction method based on multi-window joint optimization according to claim 1, wherein In Step 2, match and group the original data and predicted multiple - wave data according to the number N of window matches. Each time, match the data of N windows until all windows are processed.

5. The multiple wave adaptive subtraction method based on multi-window joint optimization according to claim 1, wherein In step 3, according to the number of window matches N, N original data windows and N predicted multiple data windows are collected respectively; vectors d are constructed for the original data of each window, i = 1, 2, …, N; then, according to the predicted multiple data, the time length T of the 2D data window, the spatial length R of the 2D data window, the time length p of the 2D matching filter, and the spatial length q of the 2D matching filter, a convolution matrix H is constructed for each predicted multiple window, i = 1, 2, …, N. i , i = 1, 2, …, N; then according to the predicted multiple data, the time length T of the 2D data window, the spatial length R of the 2D data window, the time length p of the 2D matching filter, and the spatial length q of the 2D matching filter, a convolution matrix H is constructed for each predicted multiple window i , i = 1, 2, …, N.

6. The multiple wave adaptive subtraction method based on multi-window joint optimization according to claim 5, wherein In step 4, construct the mathematical model p for adaptive subtraction i = d i - H i x, i = 1, 2, …, N; where p i represents the vector constructed from the primary wave of each window, x represents the 2D matched filter, and construct the optimization problem where means to solve the unknown x by minimizing the objective function, ||m||1 represents the L1 norm of vector m, ||m||2 represents the L2 norm of vector m, and α is the weighting factor.

7. The adaptive multiple subtraction method based on multi-window joint optimization according to claim 6, wherein In Step 5, use the improved fast iterative shrinkage threshold algorithm to process all grouped 2D window data of the seismic trace gather; Specifically, it includes: e1. Calculate the inverse matrix and the initial estimate of the filter Estimate the primary wave p i (1) = d i (1) - H i (1) x (1) , i = 1, 2,..., N; and set the number of iterations m = 1; where H represents the convolution matrix for predicting the multiple waves, N represents the number of window matches, α is the weighting factor, I is the identity matrix, and d is the vector constructed from the original data; e2. Calculate the result of the primary wave contraction threshold where the distance operator S α is as follows: S α {p} (j,k) =(|p (j,k) |-s×max(|p|)) + ×sgn(p (j,k) ), where \(j = 1,2,\cdots,T\), \(k = 1,2,\cdots,R\), \(0\lt s\lt1\), \(p\) (j,k) represents estimating the element with subscript \((j,k)\) in the wave vector \(p\) for one time, where \(m\) is the number of iterations and \(N\) is the number of window matches; e3. Calculate the shrinkage - threshold result of the updated primary wave Among them t (1) = 1, m is the number of iterations; e4. Calculate the filter Where H represents the convolution matrix for predicting multiple waves, N is the number of window matches, and d represents the vector constructed from the original data; e5. Estimate primary wave where d represents the vector constructed from the original data, N is the number of window matches, and H represents the convolution matrix for predicting multiple waves; e6. Let m = m + 1. If m ≤ M, return to Step e2; if m > M, output the estimated primary wave in N 2D data windows.

8. The multiple wave adaptive subtraction method based on multi-window joint optimization according to claim 1, wherein In step 6, it is judged whether all the 2D window data in the original data have been processed; if not, return to step 5; if all have been processed, first, the primary wave estimation results in each 2D window are weighted using a 2D Gaussian window and fused into a data volume Then, the 2D Gaussian windows are fused into a data volume in the same way The final primary wave estimation result is expressed as: where, / represents the element-by-element division operation

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