Marchenko imaging near-offset missing seismic data reconstruction method and device

Abstract

The invention relates to the technical field of seismic data processing, in particular to a Marchenko imaging-oriented dual-norm constraint near-offset missing seismic data reconstruction method and device. The method comprises the following steps: obtaining original data, and carrying out Radon reconstruction on the original data to obtain data after Radon reconstruction; calculating a residual error between the Radon domain reconstruction data and the original data to obtain empty channel data; constructing a sparse reconstruction framework based on an lq1-lq2 norm to obtain a final objective function; and by utilizing a block coordinate descent method, substituting the data reconstructed based on the Radon and the empty channel data into the final objective function for solving so as to obtain a final reconstruction result. According to the method, a conventional single-norm sparse reconstruction method based on an l1 norm is improved into a double-norm constraint framework based on an lq1-lq2 norm, Radon reconstruction and Shearlet domain reconstruction are combined, compared with a traditional reconstruction method, the improved method has the advantages that the reconstruction effect of near large offset missing is obviously improved, and the reconstruction efficiency is greatly improved. And meanwhile, the requirement on the sampling rate of the input data is also reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic data processing, and in particular to a method and device for reconstructing near-offset missing seismic data with double-norm constraint in Marchenko imaging. Background Art

[0002] As an imaging method that can effectively eliminate the interference of interlayer multiple waves, Marchenko imaging has received extensive attention in the international exploration geophysics community in recent years. This method can combine the input seismic data with a macroscopic velocity model to accurately suppress the interlayer multiple waves existing in the data without damaging the effective signals, effectively solving the problem of interlayer multiple wave interference that has plagued the industry for many years. With the improvement of the requirements for seismic exploration imaging accuracy, this method is receiving more and more attention and may become the future development direction. There is a basic assumption in the Marchenko imaging method, that is, the input data must be densely sampled. However, in actual situations, the problem of undersampling of seismic data is widespread, which will lead to a large amount of aliasing in the Marchenko imaging results and even make the iterative process non-convergent. Therefore, the problem of undersampling of seismic data is an obstacle that must be overcome. The undersampling problem is caused by obstacles such as mountains and rivers during the data acquisition process, resulting in the inability to lay out survey lines, making the collected data incomplete. At the same time, mechanical failures or human factors during the acquisition process will also lead to the appearance of waste shots and bad traces in the seismic data.

[0003] Data reconstruction is the most common and widely used method to solve this problem. However, conventional data reconstruction methods, such as norm-constrained sparse reconstruction, are often affected by interference such as noise, and the quality of the reconstructed data is poor. It should be particularly noted that the existing data reconstruction methods often have poor reconstruction effects for the large-offset missing near the offset, and the Marchenko method has more stringent requirements for the data density near the near-offset. Therefore, the existing data reconstruction methods cannot meet the needs of actual processing work, and will seriously interfere with the subsequent processing and interpretation processes. Summary of the Invention

[0004] In order to solve the above technical problems existing in the prior art, the present invention provides a method and device for reconstructing near-offset missing seismic data with double-norm constraint for Marchenko imaging. Compared with conventional data reconstruction methods, the proposed method has fewer requirements for data, and the processing results, especially for near-offset missing, have better reconstruction results, thus meeting the requirements of the Marchenko imaging method for densely sampled data.

[0005] To achieve the above object, the embodiments of the present invention provide the following technical solutions:

[0006] In a first aspect, in an embodiment provided by the present invention, a double-norm constraint near-offset missing seismic data reconstruction method for Marchenko imaging is provided. The method includes the following steps:

[0007] Obtain the original data, and perform Radon reconstruction on the original data (a method of reconstructing VSP data into virtual SSP data through Radon transform. This method combines Radon transform with cross-correlation seismic interferometry and convolution seismic interferometry, and reconstructs VSP data into virtual SSP data through the virtual source method in the Radon domain. At the same time, using the characteristic of suppressing random noise by the Radon transform method, the signal-to-noise ratio of the virtual SSP shot gather record can be improved), so as to obtain the data after Radon reconstruction;

[0008] Calculate the residual between the Radon-domain reconstructed data and the original data to obtain the empty trace data;

[0009] Construct a sparse reconstruction framework based on the l q1 -l q2 norm to obtain the final objective function;

[0010] Use the block coordinate descent method to substitute the data after Radon reconstruction and the empty trace data into the above final objective function for solution, so as to obtain the final reconstruction result.

[0011] As a further solution of the present invention, the formula for the trace data is as follows:

[0012] x B =y - x R .

[0013] In the formula, y represents the original data, and x R represents the data after Radon reconstruction, and x B represents the empty trace data.

[0014] As a further solution of the present invention, the constructing a sparse reconstruction framework based on the l q1 -l q2 norm to obtain the final objective function includes:

[0015] Construct an initial objective function for conventional unconstrained optimization;

[0016] Introduce a double-norm sparse reconstruction framework based on the l q1 -l q2 norm and optimize the initial objective function to obtain an intermediate objective function;

[0017] Introduce the Shearlet transform (a signal transformation method based on multi-scale analysis and multi-directional analysis) to the intermediate objective function. It decomposes the signal into Shearlet functions of different scales and directions. By linearly combining these functions, the original signal can be restored. The Shearlet function is an extension based on the wavelet function and has the characteristics of multi-scale and multi-direction. Each Shearlet function is described by a scale parameter and a direction parameter. The scale parameter determines the size of the Shearlet function, and the direction parameter determines the direction of the Shearlet function. The key to the Shearlet transform lies in constructing the Shearlet system, which consists of a group of Shearlet functions, and each function represents the local characteristics of a certain scale and direction. By performing the inner product operation between the original signal and the Shearlet system, the components of the signal at different scales and directions can be obtained) to obtain the final objective function.

[0018] As a further solution of the present invention, the calculation formula of the initial objective function is:

[0019]

[0020] where A represents the linear transformation process, that is, there is a linear relationship between y and x, J(x) is the penalty term, λ is the Lagrange multiplier, The superscript of represents the quantity estimated by the optimization algorithm.

[0021] As a further solution of the present invention, the calculation formula of the intermediate objective function is:

[0022]

[0023] where β is a penalty parameter, represents the calculation of the l q norm, that is In the reconstruction problem, A2 is the identity matrix, that is, A2 = I, l q1 and l q2 are the norms selected by us for constraint. q1 and q2 represent the types of norms selected. In the optimization problem, the selection range is 0-2, and different values have different constraint effects. In this method, we use the shearlet transform to reconstruct the original data, that is, A1 = S T That is to say, in this method, A1 represents the forward and inverse shearlet transforms.

[0024] As a further solution of the present invention, the calculation formula of the final objective function is:

[0025]

[0026] where ST For synthesizing the Shearlet operator (an operator used in image processing and computer vision. It is an operator based on the Shearlet transform and is used for multi-scale and multi-directional analysis and representation of images. The Shearlet operator can capture important features such as edges and textures in images, so it is widely used in tasks such as image segmentation, object detection, and image enhancement).

[0027] As a further aspect of the present invention, using the block coordinate descent method (BCD, Block Coordinate Descent), substituting the data after Radon reconstruction and the null trace data into the above final objective function for solution to obtain the final reconstruction result, which includes the following steps:

[0028] Set

[0029] Use the block coordinate descent method to solve the final objective function;

[0030] When the iteration satisfies the pre-set number of iterations, output the reconstructed result

[0031] As a further aspect of the present invention, using the block coordinate descent method (BCD) to solve the final objective function, and its iterative update formula is:

[0032]

[0033]

[0034] As a further aspect of the present invention, when the iteration satisfies the pre-set number of iterations, that is, after k = N, jump out and output the reconstructed result

[0035] In a second aspect, in another embodiment provided by the present invention, a double-norm constrained near-offset missing seismic data reconstruction device for Marchenko imaging is provided, and the device includes: a reconstruction processing module, a null trace data calculation module, an objective function construction module, and a reconstruction calculation module.

[0036] The reconstruction processing module is used to obtain the original data and perform Radon reconstruction on the original data to obtain the data after Radon reconstruction.

[0037] The null trace data calculation module is used to calculate the residual between the Radon domain reconstructed data and the original data to obtain the null trace data.

[0038] The objective function construction module is used to construct based on l q1 -l q2The sparse reconstruction framework of the norm to obtain the final objective function.

[0039] The reconstruction calculation module is used to substitute the data reconstructed based on Radon and the null trace data into the above final objective function for solution by using the block coordinate descent method to obtain the final reconstruction result.

[0040] The technical solution provided by the present invention has the following beneficial effects:

[0041] The present invention provides a method and device for reconstructing near-offset missing seismic data with double-norm constraints for Marchenko imaging. Through the technical solution of this method, the original data is acquired, and the original data is subjected to Radon reconstruction to obtain the data after Radon reconstruction; the residual between the reconstructed data in the Radon domain and the original data is calculated to obtain the null trace data; a sparse reconstruction framework based on the l q1 -l q2 norm is constructed to obtain the final objective function; the method of block coordinate descent is used to substitute the data reconstructed based on Radon and the null trace data into the above final objective function for solution to obtain the final reconstruction result.

[0042] The present invention improves the conventional single-norm sparse reconstruction method based on the l1 norm to a double-norm constraint framework based on the l q1 -l q2 norm. By combining Radon reconstruction and Shearlet domain reconstruction, the improved method has significantly improved the reconstruction effect compared with the traditional reconstruction method, especially for near-offset large-offset missing, and at the same time reduces the requirement for the sampling rate of the input data and improves the ability to resist noise interference, has robustness, and is more suitable for data preprocessing of methods such as Marchenko imaging that have strict requirements for the sampling rate of input data, especially near the offset.

[0043] These aspects or other aspects of the present invention will be more clearly understood in the following description of the embodiments. It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other embodiments can be obtained based on these drawings without creative efforts.

[0045] Figure 1Flow chart of the double - norm - constrained near - offset missing seismic data reconstruction method for Marchenko imaging according to an embodiment of the present invention.

[0046] Figure 2 It is a near - offset missing seismic record graph.

[0047] Figure 3 It is Figure 2 The conventional single - norm reconstruction effect diagram using the existing technology.

[0048] Figure 4 It is Figure 2 The reconstruction effect diagram obtained by using the double - norm - constrained near - offset missing seismic data reconstruction method for Marchenko imaging of the present invention.

[0049] Figure 5 It is the cross - section diagram with poor conventional reconstruction effect using the existing technology.

[0050] Figure 6 It is the cross - section diagram with poor reconstruction effect obtained by using the double - norm - constrained near - offset missing seismic data reconstruction method for Marchenko imaging of the present invention.

[0051] Figure 7 It is the imaging result graph of the missing data.

[0052] Figure 8 It is the imaging effect diagram after reconstruction obtained by using the double - norm - constrained near - offset missing seismic data reconstruction method for Marchenko imaging of the present invention.

[0053] Figure 9 It is the imaging effect diagram of the densely sampled data.

[0054] Figure 10 It is the cross - section diagram of the difference between the reconstruction result obtained by using the double - norm - constrained near - offset missing seismic data reconstruction method for Marchenko imaging of the present invention and the densely sampled data.

[0055] Figure 11 Structure diagram of the double - norm - constrained near - offset missing seismic data reconstruction device for Marchenko imaging according to an embodiment of the present invention.

[0056] In the figure: Reconstruction processing module - 100, empty - trace data calculation module - 200, objective - function construction module - 300, reconstruction calculation module - 400. Detailed implementation manner

[0057] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part rather than all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0058] The flowcharts shown in the accompanying drawings are only illustrative, not necessarily including all contents and operations / steps, nor necessarily executed in the described order. For example, some operations / steps can be decomposed, combined or partially merged, so the actual execution order may be changed according to the actual situation.

[0059] It should be understood that the terms used in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the specification of the present invention and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an" and "the" are intended to include the plural forms.

[0060] Specifically, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0061] Please refer to Figures 1-10 , Figure 1 which is a flowchart of a dual-norm constraint near-offset missing seismic data reconstruction method for Marchenko imaging provided by an embodiment of the present invention. As shown in Figure 1 , the dual-norm constraint near-offset missing seismic data reconstruction method for Marchenko imaging includes steps S10 to S40.

[0062] S10. Obtain the original data, and perform Radon reconstruction on the original data to obtain the data after Radon reconstruction.

[0063] Among them, the original data can be represented as y, and the data after Radon reconstruction is represented as x. R .

[0064] It should be noted that in S10, this process is to perform a Radon forward transform on the original data y to obtain its Radon domain form, that is, m = Ry, where R represents the Radon forward transform, and then the transformed data is constrained by the least squares method. The formula for this process is expressed as:

[0065] min||y - Rm|| 2

[0066] This objective function can be solved by the Gauss - Newton method, and finally the Radon inverse transform is performed on the constrained data to obtain the spatio - temporal domain data x after Radon reconstruction. R , that is, x R = R -1 y, where R -1 represents the Radon inverse transform.

[0067] It should be noted that the original data y is spatio - temporal domain data.

[0068] S20. Calculate the residual between the Radon domain reconstructed data and the original data to obtain the empty - channel data.

[0069] It should be noted that the empty - channel data is denoted as x B .

[0070] In the embodiment of the present invention, for step S20, its calculation formula is as follows:

[0071] x B = y - x R .

[0072] S30. Construct a sparse reconstruction framework based on the l q1 - l q2 norm to obtain the final objective function.

[0073] The step S30 of constructing a sparse reconstruction framework based on the l q1 - l q2 norm to obtain the final objective function includes:

[0074] S301. Construct the initial objective function of conventional unconstrained optimization.

[0075] It should be noted that conventional sparse reconstruction usually uses a single norm to constrain the reconstruction process, that is, based on the data that can be linearly represented by y = Ax, and its corresponding initial objective function of unconstrained optimization is:

[0076]

[0077] where A represents the linear transformation process, that is, there is a linear relationship between y and x, J(x) is the penalty term (in machine learning and statistics, the penalty term is usually used to prevent overfitting by adding an additional term to the loss function. This additional term penalizes the complexity of the model, thus encouraging the model to choose a simpler solution), the equation solves the optimization equation by minimizing the penalty term and the observed data and the model data, λ is the Lagrange multiplier, The superscript of represents the quantity estimated by the optimization algorithm.

[0078] S302. Introduce the double-norm sparse reconstruction framework based on the l q1 -l q2 norm and optimize the initial objective function to obtain the intermediate objective function.

[0079] It should be noted that introducing the double-norm sparse reconstruction framework based on the l q1 -l q2 norm and optimizing the objective function, based on the l q1 -l q2 norm double-norm constraint framework, which assumes that the input data can be expressed as y = A1x1 + A2x2. Compared with the conventional single-norm constraint, a new noise term A2x2 is added. In the missing reconstruction problem, it represents the seismic missing trace, and its corresponding intermediate objective function is expressed as:

[0080]

[0081] where β is a penalty parameter, denotes the calculation of the l q norm, that is A2 is the identity matrix, that is A2 = I, and l q1 and l q2 are the norms we selected for constraint. q1 and q2 represent the types of norms selected. In the optimization problem, the selection range is 0 - 2, and different values have different constraint effects. In this method, we use the shearlet transform to reconstruct the original data. That is to say, in this method, A1 represents the forward and inverse shearlet transforms.

[0082] S303. Introduce the Shearlet transform to the intermediate objective function to obtain the final objective function.

[0083] It should be noted that introducing the Shearlet transform into the above optimized intermediate objective function, that is A1 = S T , therefore, the final objective function is expressed as:

[0084]

[0085] where S T is the synthesis Shearlet operator.

[0086] It should be noted that the Shearlet transform is a multi-scale analysis method. It can decompose the signal into wavelets of different scales and directions, so as to better describe the local characteristics of the signal. The principle of the Shearlet transform is based on polynomial interpolation and shear operations, and it can effectively process non-stationary signals and non-local signals.

[0087] S40. Use the block coordinate descent method (BCD) to substitute the data after Radon reconstruction and the null trace data into the above final objective function for solution to obtain the final reconstruction result.

[0088] It should be noted that the reconstruction result is expressed as

[0089] Among them, in S40, using the block coordinate descent method (BCD), based on the data x R and the null trace data x B are substituted into the above final objective function for solution to obtain the final reconstruction result including the following steps:

[0090] S401. Set

[0091] S402. Use the block coordinate descent method (BCD) to solve the objective function.

[0092] Among them, in S402, using the block coordinate descent method (BCD) to solve the final objective function, its iterative update formula is:

[0093]

[0094]

[0095] S403. When the iteration meets the preset number of iterations, output the reconstructed result

[0096] In the embodiment of the present invention, in S403, when the iteration meets the preset number of iterations, that is, after k = N, jump out and output the reconstructed result

[0097] Combined with Figures 2-4 comparisons, Figure 5 and Figure 6 comparisons and Figures 7-10 comparisons, it can be clearly seen that after reconstruction by the method described in the above embodiments, the anti-interference ability of data processing is effectively enhanced, a better reconstruction effect is obtained, and the requirements of the Marchenko imaging method for densely sampled data are met.

[0098] The present invention aims at the undersampling problem commonly existing in seismic data, and improves the conventional single-norm sparse reconstruction method based on the l1 norm to be based on l q1 -l q2The dual-norm constraint framework of the norm combines Radon reconstruction with Shearlet domain reconstruction. The improved method has significantly improved the reconstruction effect of the traditional reconstruction method, especially the reconstruction effect of the near-offset large offset missing. At the same time, it also reduces the requirements on the input data sampling rate and improves the ability to resist noise interference. It is robust and more suitable for data preprocessing such as Marchenko imaging, which has strict requirements on the input data sampling rate, especially the near-offset sampling rate.

[0099] It should be understood that, although described in a certain order, these steps are not necessarily performed in sequence in the above order. Unless there is clear explanation in this article, the execution of these steps does not have strict order restriction, and these steps can be performed in other orders. Moreover, a part of the steps of the present embodiment may include a plurality of steps or a plurality of stages, and these steps or stages are not necessarily performed at the same time, but can be performed at different times, and the execution order of these steps or stages is not necessarily performed in sequence, but can be performed in turn or alternately with at least a part of the steps or stages in other steps or other steps.

[0100] In one embodiment, see Figure 11 As shown, in an embodiment of the present invention, a dual-norm constrained near-missing seismic data reconstruction device for Marchenko imaging is also provided, which includes a reconstruction processing module 100, an empty channel data calculation module 200, an objective function construction module 300 and a reconstruction calculation module 400.

[0101] The reconstruction processing module 100 is used to obtain original data, and perform Radon reconstruction on the original data to obtain Radon reconstructed data.

[0102] The empty channel data calculation module 200 is used to calculate the residual between the Radon domain reconstructed data and the original data to obtain the empty channel data.

[0103] The objective function building module 300 is used to build a q1 -l q2 The sparse reconstruction framework of the norm is used to obtain the final objective function.

[0104] The reconstruction calculation module 400 is used to substitute the data reconstructed based on Radon and the empty track data into the above-mentioned final objective function by using the block coordinate descent method to solve it, so as to obtain the final reconstruction result.

[0105] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, storage, database, or other medium used in the embodiments provided by the present invention can include at least one of non-volatile and volatile memories.

[0106] It should be understood that, as used herein, unless the context clearly supports the exception, the singular form "a" is also intended to include the plural form. It should also be understood that the "and / or" used herein refers to any and all possible combinations of one or more of the associated listed items. The serial numbers of the disclosed embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0107] Those of ordinary skill in the art should understand that the discussion of any of the above embodiments is only exemplary and is not intended to imply that the scope (including the claims) of the disclosure of the embodiments of the present invention is limited to these examples; under the concept of the embodiments of the present invention, the technical features in the above embodiments or different embodiments can also be combined, and there are many other variations in different aspects of the embodiments of the present invention as above, which are not provided in detail for the sake of brevity. Therefore, any omission, modification, equivalent replacement, improvement, etc. made within the spirit and principle of the embodiments of the present invention shall be included in the protection scope of the embodiments of the present invention.

Claims

1. A method for reconstructing near-offset missing seismic data in Marchenko imaging, characterized in that, The method includes: Obtaining original data, performing Radon reconstruction on the original data to obtain the data after Radon reconstruction; Calculating the residual between the data reconstructed in the Radon domain and the original data to obtain the empty trace data; Construct a sparse reconstruction framework based on l q1 -l q2 norm to obtain the final objective function; Using the block coordinate descent method to substitute the data after Radon reconstruction and the empty trace data into the above final objective function for solution to obtain the final reconstruction result.

2. The method for reconstructing near-offset missing seismic data by Marchenko imaging according to claim 1, characterized in that, The formula for the empty trace data is as follows: x B = y - x R where y represents the original data, and x R represents the data after Radon reconstruction, and x B represents the empty channel data.

3. The method for reconstructing near-offset missing seismic data by Marchenko imaging according to claim 2, characterized in that, The construction is based on l q1 -l q2 norm-based sparse reconstruction framework to obtain the final objective function, including: Constructing an initial objective function for conventional unconstrained optimization; Introduce a double-norm sparse reconstruction framework based on the l q1 -l q2 norm and optimize the initial objective function to obtain an intermediate objective function; Introducing the Shearlet transform to the intermediate objective function to obtain the final objective function.

4. The method for reconstructing near-offset missing seismic data by Marchenko imaging according to claim 3, wherein The formula for the initial objective function is: where \(J(x)\) is the penalty term and \(\lambda\) is the Lagrange multiplier, and the superscript indicates the quantity estimated by the optimization algorithm.

5. The method for reconstructing near-offset missing seismic data by Marchenko imaging according to claim 4, characterized in that, The formula for the intermediate objective function is: where β is a penalty parameter, denotes the calculation of the l q norm, that is A2 is an identity matrix.

6. The method for reconstructing near-offset missing seismic data by Marchenko imaging according to claim 5, wherein The formula for the final objective function is: Among them, S T is for synthesizing the Shearlet operator.

7. The near-offset missing seismic data reconstruction method for Marchenko imaging according to claim 2, characterized in that, The method of using the block coordinate descent method to substitute the data after Radon reconstruction and the empty trace data into the above final objective function for solution to obtain the final reconstruction result includes the following steps: Set Using the block coordinate descent method to solve the final objective function; When the iteration meets the preset number of iterations, output the result after reconstruction 8. The method for reconstructing near-offset missing seismic data by Marchenko imaging according to claim 7, wherein, The iterative update formula for using the block coordinate descent method to solve the final objective function is:

9. The method for reconstructing near-offset missing seismic data by Marchenko imaging according to claim 8, characterized in that, When the iteration satisfies the preset number of iterations, that is, after k = N, it jumps out and outputs the result after reconstruction 10. A near-offset missing seismic data reconstruction device for Marchenko imaging, characterized in that, The device includes: a reconstruction processing module, an empty trace data calculation module, an objective function construction module, and a reconstruction calculation module; The reconstruction processing module is used to obtain original data and perform Radon reconstruction on the original data to obtain the data after Radon reconstruction; The empty trace data calculation module is used to calculate the residual between the data reconstructed in the Radon domain and the original data to obtain the empty trace data; The target function construction module is used to construct a sparse reconstruction framework based on the l q1 -l q2 norm to obtain the final target function; The reconstruction calculation module is used to use the block coordinate descent method to substitute the data after Radon reconstruction and the empty trace data into the above final objective function for solution to obtain the final reconstruction result.

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