A method, system, medium and device for low-rank constrained reconstruction of five-dimensional seismic data

Abstract

The present invention discloses a method, system, medium and equipment for low-rank constrained reconstruction of five-dimensional seismic data, which comprises a data tensor, a sampling tensor, weight parameters of optimization terms and regularization terms, and the TR rank R1, ..., R1 of the matrix decomposed by the mode-{n, l} method along the direction. N Input seismic data to reconstruct the model and initialize the parameter Y 0 , #imgabs0# as the initial value; expand the low-rank reconstruction data tensor of the current step, cross-optimize the variables using the sampling block coordinate descent method during iteration, and use random sampling to improve computational efficiency. The low-rank reconstruction data is decomposed by mode-{n,l}#imgabs1#, and the optimal decomposition matrix #imgabs2# is calculated. The training sample #imgabs3# is reconstructed using the tensor to obtain the next step #imgabs4#. Repeat these steps until the predetermined stopping criterion is met, obtaining the low-rank reconstruction result of the real data. All frequency components are combined and restored to the original data format, achieving five-dimensional seismic data reconstruction. This method has good reconstruction effect, reduces computing resource consumption, and has broad industrial application prospects.

Description

Technical Field

[0001] The present invention belongs to the field of signal processing technology, and in particular relates to a method, system, medium and equipment for low-rank constrained reconstruction of five-dimensional seismic data. Background Art

[0002] Due to certain obstacles in seismic data acquisition, such as irregular surface conditions and equipment limitations, seismic data are often sampled irregularly along spatial coordinates. Missing traces in seismic records can negatively impact subsequent processing, imaging, and methods involving multi-channel deconvolution, velocity analysis, full waveform inversion, simultaneous source separation, and fault detection. Therefore, seismic data reconstruction is an ongoing and significant problem, attracting widespread attention from both academia and industry.

[0003] In recent years, tensor decomposition theory based on tensor networks has received increasing attention and has shown extraordinary promise in processing high-order tensors, especially tensors of order three and above. Among them, Tensor Train (TT) decomposition is the most representative, with high data compression capability and computational efficiency, and has been intensively studied in many tasks. SVD, alternating least squares, and gradient descent algorithms are usually used to calculate the potential core tensor of TT decomposition to exploit its low-rank structure. As a generalization of TT, TR decomposition decomposes a tensor into several periodically contracted third-order tensors. In addition to the main properties of TT, TR has enhanced compressibility and cyclically movable tensor cores. Earthquake reconstruction has great potential, and despite the existence of many optimization algorithms, explicit TT decomposition and TR decomposition remain difficult to solve for large-scale applications due to high computational cost.

[0004] The existing KSVD method is based on sparse coding, assuming that the data to be processed can be linearly represented by a finite number of atoms. Unlike methods that use fixed basic atoms, KSVD learns atoms from the data to be processed that can effectively represent the signal. These atoms reflect the characteristics of the data itself. The seismic data reconstruction problem is constructed as an optimization problem. A tracking algorithm is used to iteratively update the sparse representation of the data, and then the atoms are weighted to recover the data. However, the following disadvantages exist:

[0005] (1) Since the KSVD method needs to learn atomic representations from the current data, if the current data contains too many missing seismic traces, it will be difficult to process effectively.

[0006] (2) When using the KSVD method to process high-dimensional data, the computational complexity becomes unbearable. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to address the deficiencies in the above-mentioned prior art and provide a method, system, medium and equipment for low-rank constrained reconstruction of five-dimensional seismic data. The method is based on five-dimensional seismic data, fully utilizes the correlation between high-dimensional data, obtains sufficient redundant information for recovering lost seismic traces, and uses random sampling in the optimization process to improve computational efficiency, thereby solving the technical problem of low seismic trace interpolation efficiency.

[0008] The present invention adopts the following technical solutions:

[0009] A low-rank constrained reconstruction method for five-dimensional seismic data comprises the following steps:

[0010] S1. Convert the seismic data reconstruction problem into a low-rank constrained optimization problem and build a seismic data reconstruction model;

[0011] S2. Read the original 5D seismic data, divide the 5D seismic data with missing traces into different frequencies, and construct 4D seismic data.

[0012] S3, the 4-dimensional seismic data obtained in step S2 Input the seismic data reconstruction model constructed in step S1, set the regularization parameter u and the decomposition tensor rank R1, ..., R N , initialize the parameters of the seismic data reconstruction model and obtain the initial decomposition matrix Y 0 and the initial low-rank reconstructed data tensor S4. Obtain the initial decomposition matrix Y for step S3. 0 and the initial low-rank reconstructed data tensor Iterate and use the sketch method and block coordinate descent method to calculate the low-rank reconstructed data tensor obtained in the previous step of the kth iteration Several components obtained by TR decomposition Decomposition matrix Decomposition Matrix Tensor reconstruction Obtain the low-rank reconstruction data tensor for the next step

[0013] S5, repeat step S4 using the iterative optimization method, and As real data The low-rank reconstruction results are used to restore all frequency components to the original data format, realizing five-dimensional seismic data reconstruction.

[0014] Specifically, in step S1, the seismic data reconstruction model is specifically as follows:

[0015]

[0016] in, is the seismic data to be solved, represents the sampling matrix, is a tensor mode-{n,l} expansion, with a predefined rank R n , Z {n,l} Decomposition matrix, N is a tensor The dimension size of ||·|| F Represents the calculation of the Frobenius norm of a matrix.

[0017] Specifically, in step S2, the 4D seismic data D obs for:

[0018]

[0019] Among them, ⊙ represents the Hadamard product, represents the sampling matrix, is the seismic data to be solved.

[0020] Furthermore, the sampling matrix Element p i1i2i4i3 The following conditions must be met:

[0021]

[0022] in, 4D seismic data The element with index i1i2i3i4 in .

[0023] Specifically, in step S4, the low-rank reconstruction data tensor for:

[0024]

[0025] in, is the unit tensor, α is the proportional coefficient between the reconstructed tensor and the observed data, is the sampling matrix.

[0026] Furthermore, in the k+1th iteration, the matrix is decomposed for:

[0027]

[0028] Decomposition Matrix for

[0029]

[0030] in, for The conjugate transpose of It is 4D seismic data.

[0031] Specifically, in step S5, an iterative optimization method is used to interpolate seismic data. When the number of iterations is less than 300 and the relative error of data reconstruction is less than 10 -4 The iterative process terminates when .

[0032] In a second aspect, an embodiment of the present invention provides a low-rank constrained reconstruction system for five-dimensional seismic data, characterized by comprising:

[0033] The conversion module converts the seismic data reconstruction problem into a low-rank constrained optimization problem and constructs a seismic data reconstruction model;

[0034] Data module, reads the original 5D seismic data, divides the 5D seismic data with missing traces into different frequencies, and constructs 4D seismic data

[0035] Initial module, the 4D seismic data obtained by the data module In the seismic data reconstruction model constructed by the input conversion module, the regularization parameter u and the decomposition tensor rank R1,…,R N , initialize the parameters of the seismic data reconstruction model and obtain the initial decomposition matrix Y 0 and the initial low-rank reconstructed data tensor

[0036] Calculation module, obtain the initial decomposition matrix Y for the initial module 0 and the initial low-rank reconstructed data tensor Iterate and use the sketch method and block coordinate descent method to calculate the low-rank reconstructed data tensor obtained in the previous step of the kth iteration Several components obtained by TR decomposition Decomposition matrix Decomposition Matrix Tensor reconstruction Obtain the low-rank reconstruction data tensor for the next step

[0037] After the reconstruction module and the calculation module meet the iteration stop condition, the As real data The low-rank reconstruction results are used to restore all frequency components to the original data format, realizing five-dimensional seismic data reconstruction.

[0038] In a third aspect, a computer device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned method for low-rank constrained reconstruction of five-dimensional seismic data when executing the computer program.

[0039] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, comprising a computer program, which, when executed by a processor, implements the steps of the above-mentioned method for low-rank constrained reconstruction of five-dimensional seismic data.

[0040] Compared with the prior art, the present invention has at least the following beneficial effects:

[0041] This patent describes a low-rank constrained reconstruction method for five-dimensional seismic data. The proposed PMF-TRH algorithm enables faster reconstruction without sacrificing quality. Furthermore, the reconstruction process is accelerated using sketch technology. The proposed method not only successfully recovers missing seismic traces from extremely incomplete data but also significantly improves the quality of both pre-stack and post-stack data, providing greater flexibility for practical implementation.

[0042] Furthermore, in order to supplement the missing seismic traces and obtain complete data On the one hand, requirements The rank is as small as possible, and the recovered data is required to be The sampling results are as close as possible to the observed data. Based on the above conditions, a seismic data reconstruction model based on minimizing tensor rank is constructed.

[0043] Furthermore, in the actual seismic data acquisition process, there is often a problem of data missing. Decomposing the five-dimensional seismic data into four-dimensional seismic data according to frequency It can be regarded as the result of ideal data sampling with no missing gathers.

[0044] Furthermore, considering the low-rank nature of the data, the reconstruction of seismic data can be expressed as a low-rank tensor filling problem, using the fourth-order tensor To represent earthquake data at a specific frequency point, use express Data of a specific point, where i1, i2, i3, i4 correspond to the spatial coordinates x, y, and h respectively x and h y , construct 4D seismic data D that meets the processing requirements obs .

[0045] Furthermore, the mode-{n,l} tensor decomposition method can capture the previous Mode and the following The optimization problem can be converted into several convex subproblems to be solved. For each X n ,Y n and Fix two of them and optimize the other one to reduce general iterative operations. In addition, the random sampling method is used to accelerate the operation while ensuring the reconstruction effect. The random sampling algorithm is recorded as sketch.

[0046] Furthermore, the block coordinate descent algorithm is used to optimize X and Y respectively to obtain the real data The optimization result of the block coordinate descent algorithm can avoid the problem of finding the minimum value based on multiple variables, and the cross-iteration optimization method is used to gradually obtain the convergence result.

[0047] Furthermore, it was found in the experiment that when the number of iterations is greater than 300, the optimization result of the model will hardly change. In addition, when the relative error of data reconstruction is less than 10 -4 At this point, the iteration process is terminated to obtain the final result.

[0048] It can be understood that the beneficial effects of the second to fourth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0049] In summary, the present invention minimizes the TR rank, implicitly utilizes the low-rank structure, and performs parallel low-rank matrix decomposition on different tensor expansions, which greatly reduces the computational cost compared with traditional methods. At the same time, a randomized algorithm sketch is further applied to accelerate seismic data reconstruction.

[0050] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Schematic diagram of mode-{n,l} tensor decomposition;

[0052] Figure 2 The reconstructed images of synthetic noise-free seismic data, where (a) is synthetic noise-free seismic data and (b) is synthetic noise-free seismic data with a loss rate of 90%;

[0053] Figure 3 Figure 2 is the result of synthetic seismic data restoration, where (a) is the result obtained by the PSMF method, (b) is the result obtained by the PSMF-sketch method, (c) is the result obtained by the PMF-TRH method, and (d)-(f) are the errors between the restoration results of various methods in (a)-(c) and the original data;

[0054] Figure 4Figure 1 is a synthetic seismic data diagram with a signal-to-noise ratio of 1 dB, where (a) is synthetic noisy seismic data and (b) is synthetic noisy seismic data with a loss rate of 90%;

[0055] Figure 5 Figure 2 is the restoration result of synthetic noisy seismic data, where (a) is the result obtained by the PSMF method, (b) is the result obtained by the PSMF-sketch method, (c) is the result obtained by the PMF-TRH method, and (d)-(f) are the errors between the restoration results of various methods in (a)-(c) and the original data respectively;

[0056] Figure 6 are actual 5D seismic data with fixed CMP x and offset; the result in (a) is the earthquake with missing seismic traces before reconstruction, including 6 azimuths; the result in (b) corresponds to the reconstruction result of the data in (a);

[0057] Figure 7 are actual five-dimensional seismic data with fixed offset and azimuth; the result in (a) is the earthquake with missing seismic traces before reconstruction, and the result in (b) corresponds to the reconstruction result of the data in (a).

[0058] Figure 8 are post-stack five-dimensional seismic data; (a) is the post-stack data before seismic trace interpolation, and (b) is the post-stack data after seismic trace interpolation.

[0059] Figure 9 It is a flowchart of the present invention. DETAILED DESCRIPTION

[0060] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0061] In the description of the present invention, it is to be understood that the terms “include” and “comprise” indicate the presence of the described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0062] It should also be understood that the terms used in the present specification are only for the purpose of describing particular embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0063] It should be further understood that the term "and / or" as used in the present specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items. For example, A and / or B may represent: A alone, A and B simultaneously, or B alone. In addition, the character " / " herein generally indicates that the associated items are in an "or" relationship.

[0064] It should be understood that although the terms "first," "second," and "third" may be used to describe preset ranges in embodiments of the present invention, these preset ranges should not be limited to these terms. These terms are merely used to distinguish one preset range from another. For example, without departing from the scope of embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0065] The word "if," as used herein, may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting," depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to the determination" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)," depending on the context.

[0066] The accompanying drawings illustrate various schematic diagrams of structures according to embodiments disclosed herein. These figures are not drawn to scale; for clarity, some details are exaggerated and some details may be omitted. The shapes of the various regions and layers shown in the figures, as well as their relative sizes and positional relationships, are merely exemplary and may deviate in practice due to manufacturing tolerances or technical limitations. Those skilled in the art may design regions / layers with different shapes, sizes, and relative positions as needed.

[0067] The present invention provides a low-rank constrained reconstruction method for five-dimensional seismic data. The complete seismic data satisfies the low-rank property. However, missing traces or seismic signals contaminated by noise will increase the rank of the original data. Therefore, the low-rank property of the tensor core is used to complete the missing seismic traces through iterative optimization. TR decomposition has enhanced compressibility and a cyclically movable tensor core. Since the explicit use of TR decomposition requires a large amount of computation, the present invention implicitly utilizes the relationship between the rank of TR decomposition and parallel matrix decomposition to utilize its low-rank information, and uses the low-rank prior of tensor decomposition to reconstruct the seismic data of the missing traces, thereby completing the recovery of the missing seismic trace data.

[0068] See also Figure 8The present invention provides a low-rank constrained reconstruction method for five-dimensional seismic data, which uses the low-rank prior of tensor decomposition to reconstruct the seismic data of missing traces and complete the recovery of the missing seismic trace data. The specific steps are as follows:

[0069] S1. Convert the seismic data reconstruction problem into a low-rank constrained optimization problem and build a seismic data reconstruction model;

[0070] The reconstruction of seismic data is converted into an optimization problem under low-rank constraints. The rank obtained after tensor decomposition is used to simplify the solution of the optimization problem, and then the solution that satisfies the low-rank constraint is obtained through cross-iteration optimization.

[0071] The seismic data reconstruction model based on minimizing tensor rank is as follows:

[0072]

[0073] in, is the seismic data to be solved, For is the low-rank constraint, and u is the regularization weight parameter.

[0074] After using matrix decomposition to express low-rank constraints, the resulting seismic data reconstruction model is as follows:

[0075]

[0076] in, is the seismic data to be solved, represents the sampling matrix, is a tensor mode-{n,l} expansion, with a predefined rank R n , Z {n,l} Decomposition matrix, N is a tensor The dimension size of ||·|| F Represents the calculation of the Frobenius norm of a matrix.

[0077] The nth component Z obtained by mode-{n,l} tensor decomposition [n] for:

[0078]

[0079] S2. Read the original 5D seismic data, divide the 5D seismic data with missing traces according to different frequencies, and construct 4D seismic data D that meets the processing requirements. obs ;

[0080] Considering the low-rank characteristics of the data, the reconstruction of seismic data can be expressed as a low-rank tensor filling problem.obs (ω,x,y,hx,hy) represents five-dimensional seismic data, x,y represents the spatial coordinates of the common midpoint of the inline line and the cross line; hx;hy represents the offset distance of the main survey line and the connecting survey line, and the data lost during acquisition is supplemented with 0. Use the fourth-order tensor D obs To represent earthquake data at a specific frequency point, use Indicates D obs Data of a specific point, where i1, i2, i3, i4 correspond to the spatial coordinates x, y, and h respectively x and h y .

[0081] The ideal data corresponding to the seismic data with missing traces is a low-rank tensor Z. The actual observed data is expressed as follows:

[0082]

[0083] Among them, ⊙ represents the Hadamard product, Represents the sampling matrix, sampling matrix Chinese elements The following conditions must be met:

[0084]

[0085] in, for The element with index i1i2i3i4 in .

[0086] S3. Input the data to be processed into the seismic data reconstruction model, and use the mode-{n,l} tensor decomposition method to represent the TR rank. The ranks of the decomposed tensors are set to R1, R2, ···R N-1 ,R N . Sampling Tensor The weight parameter μ of the regularization term is input into the reconstruction model. Initialize the initial decomposition matrix Y 0 and the initial low-rank reconstructed data tensor

[0087] Carrying the contents of a tensor in several matrices is called tensor expansion or tensor matrixization. The most commonly used tensor is mode-{n,l} expansion A variant of the mode-{n,l} expansion is expressed as The mode-{n,l} tensor decomposition of χ is a cyclic tensor expansion method, expressed as

[0088] Low-rank tensor ring (TR) component decomposition using a chain of 3D tensor cores The data is represented by the cyclic multilinear product of , where the size of the i-th tensor core is R i-1 ×I i ×R i+1 , each element of χ under TR decomposition is expressed as:

[0089]

[0090] Among them, Tr(·) represents the matrix trace operation, using rank TR (χ) mark {R1, R2, ···R N-1 ,R N}, represents TR Rank.

[0091] In practice, by constraining X ＜n＞ Instead of solving the TR rank minimization problem, the mode-{n,l} tensor decomposition method can maintain the low rank property of the tensor. The present invention uses the mode-{n,l} tensor decomposition method to represent the TR rank. For the tensor Z, the nth mode obtained by decomposition is in At the same time, the rank of each decomposed pattern needs to be set, which are R1, R2, ···R N-1 ,R N , and initialize the initial decomposition matrix Y according to the size of each pattern rank set by the input data kernel 0 and the initial low-rank reconstructed data tensor Prepare for the next iteration.

[0092] S4. Obtain the initial decomposition matrix Y for step S3. 0 and the initial low-rank reconstructed data tensor Iterate and use the sketch method and block coordinate descent method to calculate the low-rank reconstructed data tensor obtained in the previous step of the kth iteration Several components obtained by TR decomposition Decomposition matrix Decomposition Matrix Tensor reconstruction Obtain the low-rank reconstruction data tensor for the next step

[0093] The mode-{n,l} tensor decomposition method can capture the previous Mode and the following The optimization problem can be converted into several convex subproblems to be solved. For each X n ,Y n and Fixing two of them and then optimizing the other one, the present invention adopts a block coordinate descent algorithm to iteratively update different variables.

[0094] X n ,Y n The corresponding convex subproblem can be calculated as follows:

[0095]

[0096]

[0097] In the kth iteration, the decomposition matrix is obtained using the sketch technique. for:

[0098]

[0099] Using sketch technology from Random sampling:

[0100]

[0101] get for

[0102]

[0103] The sub-problems corresponding to the optimization are as follows:

[0104]

[0105] By taking the derivative of the above formula, we can get:

[0106]

[0107] in,

[0108] The above process is recorded as PMF-TR. In addition, in the mode-{n,l} tensor decomposition, This reduces the number of typical iterations, a method we refer to as PMF-TRH. Furthermore, we use random sampling to accelerate the computation while ensuring the reconstruction quality, a random sampling algorithm we refer to as sketch.

[0109] S5. Repeat step S4 until the iteration stop condition is met and output the result of seismic data reconstruction. All frequency components are processed to obtain corresponding results, which are then combined and restored to the original data format to achieve five-dimensional seismic data reconstruction.

[0110] The block coordinate descent algorithm is used to interpolate seismic data. Each variable is gradually optimized by cross iteration. The number of iteration stops set by the present invention is 300. In addition, if the relative error of data reconstruction is less than 10 when the number of iterations is less than 300, -4 The iterative process will terminate when .

[0111] In another embodiment of the present invention, a low-rank constrained reconstruction system for five-dimensional seismic data based on Tensor Ring Rank is provided. The system can be used to implement the above-mentioned low-rank constrained reconstruction method for five-dimensional seismic data based on Tensor Ring Rank. Specifically, the five-dimensional seismic data reconstruction system based on Tensor Ring Rank includes a conversion module, a data module, an initial module, a calculation module and a reconstruction module.

[0112] Among them, the conversion module transforms the seismic data reconstruction problem into a low-rank constrained optimization problem and constructs a seismic data reconstruction model;

[0113] Data module, reads the original 5D seismic data, divides the 5D seismic data with missing traces into different frequencies, and constructs 4D seismic data

[0114] Initial module, the 4D seismic data obtained by the data module In the seismic data reconstruction model constructed by the input conversion module, the regularization parameter u and the decomposition tensor rank R1,…,R N , initialize the parameters of the seismic data reconstruction model and obtain the initial decomposition matrix Y 0 and the initial low-rank reconstructed data tensor

[0115] Calculation module, obtain the initial decomposition matrix Y for the initial module 0 and the initial low-rank reconstructed data tensor Iterate and use the sketch method and block coordinate descent method to calculate the low-rank reconstructed data tensor obtained in the previous step of the kth iteration Several components obtained by TR decomposition Decomposition matrix Decomposition Matrix Tensor reconstruction Obtain the low-rank reconstruction data tensor for the next step

[0116] After the reconstruction module and the calculation module meet the iteration stop condition, the As real data The low-rank reconstruction results are used to restore all frequency components to the original data format, realizing five-dimensional seismic data reconstruction.

[0117] In another embodiment of the present invention, a terminal device is provided, which includes a processor and a memory, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, which is suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to implement the corresponding method flow or corresponding function; the processor described in the embodiment of the present invention can be used for the operation of the low-rank constrained reconstruction method of five-dimensional seismic data, including:

[0118] The seismic data reconstruction problem is transformed into a low-rank constrained optimization problem, and a seismic data reconstruction model is constructed; the original five-dimensional seismic data is read, and the five-dimensional seismic data with missing traces is divided into different frequencies to construct a four-dimensional seismic data. 4D seismic data In the seismic data reconstruction model, the regularization parameter u and the decomposition tensor rank R1, ..., R are set. N , initialize the parameters of the seismic data reconstruction model and obtain the initial decomposition matrix Y 0 and the initial low-rank reconstructed data tensor For the initial decomposition matrix Y 0 and the initial low-rank reconstructed data tensor Iterate and use the sketch method and block coordinate descent method to calculate the low-rank reconstructed data tensor obtained in the previous step of the kth iteration Several components obtained by TR decomposition Decomposition matrix Decomposition Matrix Tensor reconstruction Obtain the low-rank reconstruction data tensor for the next step After the iteration stop condition is met, the As real data The low-rank reconstruction results are used to restore all frequency components to the original data format, realizing five-dimensional seismic data reconstruction.

[0119] In another embodiment of the present invention, the present invention further provides a storage medium, specifically a computer-readable storage medium (Memory), which is a memory device in a terminal device for storing programs and data. It can be understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and, of course, the extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space. These instructions can be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory or a non-volatile memory (Non-Volatile Memory), such as at least one disk memory.

[0120] The processor may load and execute one or more instructions stored in a computer-readable storage medium to implement the corresponding steps of the method for low-rank constrained reconstruction of five-dimensional seismic data in the above embodiment; the processor may load and execute the following steps:

[0121] The seismic data reconstruction problem is transformed into a low-rank constrained optimization problem, and a seismic data reconstruction model is constructed; the original five-dimensional seismic data is read, and the five-dimensional seismic data with missing traces is divided into different frequencies to construct a four-dimensional seismic data. 4D seismic data In the seismic data reconstruction model, the regularization parameter u and the decomposition tensor rank R1, ..., R are set. N , initialize the parameters of the seismic data reconstruction model and obtain the initial decomposition matrix Y 0 and the initial low-rank reconstructed data tensor For the initial decomposition matrix Y 0 and the initial low-rank reconstructed data tensor Iterate and use the sketch method and block coordinate descent method to calculate the low-rank reconstructed data tensor obtained in the previous step of the kth iteration Several components obtained by TR decomposition Decomposition matrix Decomposition Matrix Tensor reconstruction Obtain the low-rank reconstruction data tensor for the next step After the iteration stop condition is met, the As real data The low-rank reconstruction results are used to restore all frequency components to the original data format, realizing five-dimensional seismic data reconstruction.

[0122] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0123] See also Figure 2 ,in, Figure 2 (a) shows the synthetic seismic data without noise interference, with 20 channels and 256 sampling points. Figure 2 (b) shows the data with 90% missing traces, which are processed using the PMF method, PMF-sketch method, PMF-TT method, PMF-TT-sketch method, PSMF method, PSMF-sketch method, and PMF-TRH method, respectively.

[0124] See also Figure 3 ,in, Figure 3 (a) shows the result of seismic data interpolation using the above method for synthetic seismic data with a data missing rate of 90%. Figure 3 (b) shows the errors between various restoration methods and the original lossless seismic data. It can be seen that the PSM-TRH method achieves good results.

[0125] See also Figure 4 ,in, Figure 4 (a) shows the synthesized seismic data with a signal-to-noise ratio of 1 dB, a total of 20 channels, and 256 sampling points. Figure 4 (b) shows the data with 90% missing traces, which are processed using the PMF method, PMF-sketch method, PMF-TT method, PMF-TT-sketch method, PSMF method, PSMF-sketch method, and PMF-TRH method, respectively.

[0126] See also Figure 5 ,in, Figure 5 (a) shows the result of seismic data interpolation using the above method for synthetic noisy seismic data with a data missing rate of 90%. Figure 5(b) shows the error between various restoration methods and the original lossless seismic data. The comparison shows that the sampling sketch method can significantly improve processing efficiency and also has better reconstruction performance.

[0127] See also Figure 6 As shown, Figure 6 The seismic profile of the original data in (a) is incomplete and contains considerable noise, which poses a significant challenge to successful reconstruction. By applying the PMF-TR-sketch method, all lost traces are fully recovered, as shown in Figure 6 (b) shows that these reflections are clearer than those observed before reconstruction. In addition, the continuity of the seismic events is satisfactory because there is no obvious error between the original and reconstructed traces.

[0128] See also Figure 7 As shown, in Figure 7 In (a), large gaps in incomplete observations complicate reconstruction. Figure 7 (b) provides the results obtained by the PMF-TR-sketch method. It is clear that most of the missing data are accurately reconstructed, resulting in a more coherent spatial representation of the seismic waveform.

[0129] See also Figure 8 , Figure 8 (a) shows the stacked data cube before interpolation. From this figure, we can see that the Q value of the original stacked data is very low, resulting in many reflections being blocked by noise. The reconstructed stacked cube is as follows Figure 8 (b) Comparing the two stacking results, PMFTR-sketch effectively eliminates prestack random noise and significantly increases signal energy. This result confirms the effectiveness of the PMF-TR-sketch method in recovering noisy and irregularly sampled seismic data.

[0130] In summary, the present invention provides a method, system, medium and equipment for low-rank constrained reconstruction of five-dimensional seismic data, which can effectively reconstruct seismic data with lost seismic traces. At the same time, the acceleration method proposed in this patent can improve the efficiency of seismic data reconstruction without reducing the effect.

[0131] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0132] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0133] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0134] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0135] The above content is only for explaining the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A low-rank constrained reconstruction method for five-dimensional seismic data, characterized in that: The following steps are involved: S1. Convert the seismic data reconstruction problem into a low-rank constrained optimization problem and build a seismic data reconstruction model; S2. Read the original 5D seismic data, divide the 5D seismic data with missing traces into different frequencies, and construct 4D seismic data. S3, the 4-dimensional seismic data obtained in step S2 Input the seismic data reconstruction model constructed in step S1, set the regularization parameter u and the decomposition tensor rank R1, ..., R N , initialize the parameters of the seismic data reconstruction model and obtain the initial decomposition matrix Y 0 and the initial low-rank reconstructed data tensor S4. Obtain the initial decomposition matrix Y for step S3. 0 and the initial low-rank reconstructed data tensor Iterate and use the sketch method and block coordinate descent method to calculate the low-rank reconstructed data tensor obtained in the previous step of the kth iteration Several components obtained by TR decomposition Decomposition matrix Decomposition Matrix Tensor reconstruction Obtain the low-rank reconstruction data tensor for the next step S5, repeat step S4 using the iterative optimization method, and As real data The low-rank reconstruction results are used to restore all frequency components to the original data format, realizing five-dimensional seismic data reconstruction.

2. The low-rank constrained reconstruction method for five-dimensional seismic data according to claim 1, characterized in that: In step S1, the seismic data reconstruction model is specifically as follows: in, is the seismic data to be solved, represents the sampling matrix, is a tensor mode-{n,l} expansion, with a predefined rank R n , Z {n,l} Decomposition matrix, N is a tensor The dimension size of ||·|| F Represents the calculation of the Frobenius norm of a matrix.

3. The low-rank constrained reconstruction method for five-dimensional seismic data according to claim 1, characterized in that: In step S2, 4D seismic data for: Among them, ⊙ represents the Hadamard product, represents the sampling matrix, is the seismic data to be solved.

4. The low-rank constrained reconstruction method for five-dimensional seismic data according to claim 3, characterized in that: Sampling Matrix Element p i1i2i4i3 The following conditions must be met: in, 4D seismic data The element with index i1i2i3i4 in .

5. The low-rank constrained reconstruction method for five-dimensional seismic data according to claim 1, characterized in that: In step S4, the low-rank reconstruction data tensor for: in, is the unit tensor, α is the proportional coefficient between the reconstructed tensor and the observed data, is the sampling matrix.

6. The low-rank constrained reconstruction method for five-dimensional seismic data according to claim 5, characterized in that: In the k+1th iteration, the matrix is decomposed for: Decomposition Matrix for in, for The conjugate transpose of It is 4D seismic data.

7. The low-rank constrained reconstruction method for five-dimensional seismic data according to claim 1, characterized in that: In step S5, the seismic data is interpolated using an iterative optimization method. When the number of iterations is less than 300 and the relative error of data reconstruction is less than 10 -4 The iterative process terminates when .

8. A low-rank constrained reconstruction system for five-dimensional seismic data, characterized by: include: The conversion module converts the seismic data reconstruction problem into a low-rank constrained optimization problem and constructs a seismic data reconstruction model; Data module, reads the original 5D seismic data, divides the 5D seismic data with missing traces into different frequencies, and constructs 4D seismic data Initial module, the 4D seismic data obtained by the data module In the seismic data reconstruction model constructed by the input conversion module, the regularization parameter u and the decomposition tensor rank R1,…,R N , initialize the parameters of the seismic data reconstruction model and obtain the initial decomposition matrix Y 0 and the initial low-rank reconstructed data tensor Calculation module, obtain the initial decomposition matrix Y for the initial module 0 and the initial low-rank reconstructed data tensor Iterate and use the sketch method and block coordinate descent method to calculate the low-rank reconstructed data tensor obtained in the previous step of the kth iteration Several components obtained by TR decomposition Decomposition matrix Decomposition Matrix Tensor reconstruction Obtain the low-rank reconstruction data tensor for the next step Reconstruct the module and calculate the module to meet the iteration stop condition. As real data The low-rank reconstruction results are used to restore all frequency components to the original data format, realizing five-dimensional seismic data reconstruction.

9. A computer-readable storage medium storing one or more programs, characterized in that: The one or more programs include instructions that, when executed by a computing device, cause the computing device to perform any one of the methods according to claims 1 to 7.

10. A computing device, characterized in that include: One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include instructions for executing any one of the methods according to claims 1 to 7.

Images