A method and system for high-dimensional seismic data reconstruction

Abstract

This invention relates to a method and system for high-dimensional seismic data reconstruction, comprising the following steps: processing raw seismic data to obtain an initial regular high-dimensional data volume; reading local block data from the obtained initial regular high-dimensional data volume, applying low-rank constraints to different tensor mode expansion matrices based on the Frobenius-nuclear mixture norm, and reconstructing the read local block data; repeating the previous step to reconstruct all local block data to obtain the final high-dimensional seismic data reconstruction result. This invention can improve the reconstruction accuracy and efficiency of tensor decomposition methods, enabling more efficient and higher-precision reconstruction results for high-dimensional seismic data. Therefore, this invention can be widely applied in the field of geophysical exploration.

Description

Technical Field

[0001] This invention belongs to the field of geophysical exploration, specifically relating to a method and system for high-dimensional seismic data reconstruction based on the Frobenius-nuclear (F-norm-nuclear) hybrid norm. Background Technology

[0002] 3D seismic data acquisition can yield 5D CMP (Common Midpoint) gathers or OVT (Offset Vector) gathers. However, in actual data acquisition, constraints such as geographical environment and economic conditions can lead to missing data and noise in the acquired data. Therefore, seismic data reconstruction is necessary for subsequent migration imaging, multiple wave suppression, and other processes.

[0003] Methods for high-dimensional data reconstruction are generally divided into two categories: Multichannel Singular Spectrum Analysis (MSSA) and Tensor Decomposition (TDD), both of which perform data reconstruction in the frequency spatial domain. MSSA assumes that noise-free, complete data is low-rank, while missing seismic traces and the presence of random noise increase the rank of the Hankel matrix. This method rearranges individual frequency slices of data into Hankel matrices or block Hankel matrices, and then uses Singular Value Decomposition (SVD) to reduce the rank. Since this method is based on the plane wave assumption (data consists of linear phase axes), high-dimensional data reconstruction is generally performed within local data windows or on CMP gathers after NMO (dynamically corrected) data, where the phase axes are typically linear or approximately linear. However, as the dimensionality of seismic data increases, the computational cost of MSSA gradually becomes a burden. On the one hand, the traditional SVD method can be replaced by stochastic QR decomposition and Lanczos bidiagonalization; on the other hand, the relationship between the Hankel matrix and the cyclic matrix can be utilized to improve computational efficiency. In addition, to improve the performance of random noise attenuation, optimal rank selection and singular value shrinkage methods for the Hankel matrix are proposed.

[0004] Tensor decomposition treats multidimensional seismic data in the frequency spatial domain as a low-rank multilinear array or tensor. However, the definition of tensor rank is not unique and is more complex than that of matrix rank, leading to several different definitions of tensor rank, such as CANDECOMP / PARAFAC rank, Tucker rank, multi-rank, and tensor tubal rank, which correspond to different tensor decomposition methods. In geophysical applications, Kreimer and Sacchi used the High-Order SVD (HOSVD) method for 5D seismic data reconstruction. Kreimer et al. used the nuclear norm instead of the Tucker rank, which is a convex relaxation of the rank. Parallel matrix decomposition methods utilize low-rank matrix decomposition to improve computational efficiency. Furthermore, Ely et al. extended tensor SVD (t-SVD) to high-order tensors for high-dimensional data reconstruction. Cavalcante and Porsani designed a direction-dependent tensor decomposition algorithm that can replace multilinear algebraic schemes. It only computes the covariance matrix of the mode-n expansion of the fourth-order tensor, and is to some extent equivalent to HOSVD.

[0005] Compared to the MSSA method, the tensor decomposition-based method is more efficient. It only requires the assumption that the data is low-rank and has no constraints on the obtained basis functions themselves, making it more applicable to real data, but the reconstruction accuracy is relatively worse. Summary of the Invention

[0006] To address the aforementioned problems, the purpose of this invention is to provide a high-dimensional seismic data reconstruction method and system based on the Frobenius-nuclear hybrid norm, which can improve the reconstruction accuracy and efficiency of tensor decomposition methods, enabling high-dimensional seismic data reconstruction to be more efficient and achieve higher accuracy reconstruction results.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] In a first aspect, the present invention provides a method for reconstructing high-dimensional seismic data, comprising the following steps:

[0009] An initial rule-based high-dimensional data volume is obtained by processing the original seismic data;

[0010] Local block data is read from the obtained initial rule high-dimensional data volume, low-rank constraints are applied to the tensor mode expansion matrices based on the Frobenius-nuclear mixture norm, and data reconstruction is performed on the read local block data;

[0011] Repeat the previous step to reconstruct all local block data and obtain the final high-dimensional seismic data reconstruction result.

[0012] Furthermore, the initial rule-based high-dimensional data volume obtained by processing the original seismic data includes:

[0013] Dynamic correction is performed on the raw seismic data to obtain CMP gather data or OVT gather data;

[0014] The obtained CMP or OVT gather data is processed into surface elements to obtain the initial high-dimensional data volume of rules.

[0015] Furthermore, the step of reading local block data from the obtained initial rule data volume and reconstructing the read local block data based on the Frobenius-nuclear mixture norm and different tensor mode expansion forms includes:

[0016] Read local block data and perform FFT on the local block data along the time dimension to obtain frequency spatial domain data composed of multiple single frequency slices;

[0017] Data reconstruction was performed on each single-frequency slice data to obtain the reconstruction results of all frequency slice data.

[0018] IFFT is performed on the reconstruction results of all single-frequency slice data to convert the frequency spatial domain data into time spatial domain data.

[0019] Furthermore, the step of reconstructing the data for each single-frequency slice separately to obtain the reconstruction results for all frequency slice data includes:

[0020] Read single frequency slice data, apply low-rank constraints to different tensor mode expansion matrices using the Frobenius-nuclear mixing norm, and calculate the reconstruction results of single frequency slice data using the ADMM method;

[0021] Repeat the previous step to calculate all single-frequency slice data and obtain the reconstruction results of all single-frequency slice data.

[0022] Furthermore, the reconstruction result of a single frequency slice data calculated using the ADMM method includes:

[0023] Constructing the augmented Lagrangian function of the inverse problem transforms the low-rank constrained problem into an unconstrained optimization problem:

[0024]

[0025] μ is used to adjust the degree to which the solution results match the constraints. V represents (n) Auxiliary variables; Represents the factor matrix V (n) The conjugate matrix; Represents the factor matrix U (n) The conjugate matrix of Y; (n) and W (n) I represents the Lagrange multiplier; T represents the identity matrix; 2 / 3μ (·) denotes the soft thresholding operator; P, S, and Q are intermediate variables generated during the algorithm iteration process; svd(·) denotes the singular value decomposition algorithm; · / denotes the division of matrix or tensor elements;

[0026] For U respectively (n) , V (n) , Perform alternating solutions until the above is reached. The above iteration process terminates when the update amount is less than a certain threshold.

[0027] Furthermore, the update formulas for each variable are as follows:

[0028]

[0029]

[0030]

[0031] PSQ T =svd(V (n) +W (n) / μ)

[0032]

[0033] Secondly, the present invention provides a high-dimensional seismic data reconstruction system, comprising:

[0034] The data preprocessing module is used to process the raw seismic data to obtain an initial rule-based high-dimensional data volume;

[0035] The data reconstruction module reads local block data from the obtained initial rule high-dimensional data volume, applies low-rank constraints to different tensor mode expansion matrices based on the Frobenius-nuclear mixture norm, and reconstructs the read local block data.

[0036] The results output module is used to reconstruct data from all local block data to obtain the final high-dimensional seismic data reconstruction results.

[0037] Furthermore, the data reconstruction module includes:

[0038] The frequency domain conversion module is used to read local block data and perform FFT on the local block data along the time dimension to obtain frequency spatial domain data composed of multiple single frequency slices.

[0039] The reconstruction module is used to reconstruct data for each single-frequency slice data separately, and obtain the reconstruction results of all frequency slice data.

[0040] The time-domain transformation module is used to perform IFFT on the reconstruction results of all the obtained single-frequency slice data, converting the frequency spatial domain data into time spatial domain data.

[0041] Thirdly, the present invention provides a computer-readable storage medium for storing one or more programs, said one or more programs including instructions that, when executed by a computing device, cause the computing device to perform any of the methods.

[0042] Fourthly, the present invention provides a computing device comprising: 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 performing any of the methods.

[0043] The present invention, by adopting the above technical solution, has the following advantages: Compared with conventional tensor decomposition methods, the present invention utilizes the Frobenius-nuclear mixture norm to constrain the matrices after expanding tensor data in different modes, thereby obtaining reconstruction results with better accuracy. Therefore, the present invention can be widely applied in the field of geophysical exploration. Attached Figure Description

[0044] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts. In the drawings:

[0045] Figure 1 This is a schematic diagram of the high-dimensional seismic data reconstruction method in an embodiment of the present invention;

[0046] Figure 2 It is a 3D sub-data of a noise-free and complete 5D theoretical data volume synthesized in the embodiments of the present invention, which contains three linear in-phase axes with different amplitudes;

[0047] Figure 3 The data in this embodiment of the invention contains -1dB Gaussian white noise and 50% randomly missing channels;

[0048] Figure 4 The result is after processing by the method of this invention, with a signal-to-noise ratio of 23dB;

[0049] Figure 5This refers to the error result between the reconstruction result and the theoretically synthesized data in the embodiments of this invention. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention are within the scope of protection of the present invention.

[0051] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0052] In some embodiments of the present invention, a method for reconstructing high-dimensional seismic data is provided. First, a low-rank constraint is applied to the tensor mode expansion matrices using the Frobenius-nuclear mixture norm; then, the alternating direction multiplier method (ADMM) is used for data reconstruction. This invention can improve the reconstruction accuracy and efficiency of tensor decomposition methods, enabling more efficient and higher-precision reconstruction results for high-dimensional seismic data.

[0053] Correspondingly, other embodiments of the present invention provide a high-dimensional seismic data reconstruction system, device, and storage medium.

[0054] Example 1

[0055] like Figure 1 As shown, this embodiment provides a method for reconstructing high-dimensional seismic data, specifically including the following steps:

[0056] Step 1: Process the raw seismic data to obtain an initial regular high-dimensional data volume;

[0057] Step 2: Read local block data from the obtained initial rule high-dimensional data volume, apply low-rank constraints to the tensor mode expansion matrices based on the Frobenius-nuclear mixture norm, and reconstruct the read local block data;

[0058] Step 3: Repeat step 2 to reconstruct all data blocks and obtain the final high-dimensional seismic data reconstruction result.

[0059] Preferably, in step 1 above, the initial regular high-dimensional data volume is obtained based on the processing of the original seismic data, including:

[0060] Read the CMP gather data or OVT gather data after NMO;

[0061] The read data is processed by Binning to obtain an initial high-dimensional data volume of rules; however, the initial high-dimensional data volume of rules contains noise and has missing data.

[0062] Preferably, step 2 above includes the following steps:

[0063] Step 2.1: Read the local block data and perform FFT on the local block data along the time dimension to obtain the frequency space domain data composed of multiple single-frequency slices;

[0064] Step 2.2: Perform data reconstruction on each single-frequency slice data separately to obtain the reconstruction results of all frequency slice data;

[0065] Step 2.3: Perform IFFT on the reconstruction results of all obtained single-frequency slice data to convert the frequency spatial domain data into time spatial domain data.

[0066] Preferably, step 2.2 above includes the following steps:

[0067] Step 2.2.1: Read the single frequency slice data, apply low-rank constraints to the tensor mode expansion matrices with the Frobenius-nuclear mixing norm, calculate the inverse problem using the sampling ADMM method, and obtain the reconstruction result of the single frequency slice data;

[0068] Step 2.2.2: Repeat step 2.2.1 to process all single-frequency slice data and obtain the reconstruction results of all single-frequency slice data.

[0069] Preferably, in step 2.2.1 above, the formula for calculating the inverse problem is:

[0070]

[0071] Where D represents a single frequency slice of data, and (I1, I2, I3, and I4 represent the magnitude of data D in each dimension); The data is noise-free and complete, and X (n) For tensor The modal n-expansion matrix, where n = ({1,2},{2,3},{1,3}); For X (n)The Frobenius-nuclear mixture norm; λ is a hyperparameter used to balance the data error term and the regularization term; F is the Frobenius norm of the matrix; N is the dimension of the data; U (n) and V (n) The factor matrix is ​​obtained by expanding the matrix decomposition of mode n; This refers to the spatial sampling operator for data.

[0072] Preferably, in step 2.2.2 above, when using the ADMM method to solve the inverse problem, the following steps are included:

[0073] Constructing the augmented Lagrangian function of the inverse problem transforms the constrained problem into the following unconstrained optimization problem:

[0074]

[0075] For U respectively (n) , V (n) , Perform alternating solutions until the above is reached. The above iteration process terminates when the update amount is less than a certain threshold.

[0076] The update formulas for each variable are as follows:

[0077]

[0078]

[0079]

[0080]

[0081] In the formula, μ is used to adjust the degree to which the solution matches the constraints; V represents (n) Auxiliary variables; Represents the factor matrix V (n) The conjugate matrix; Represents the factor matrix U (n) The conjugate matrix of Y; (n) and W (n) I represents the Lagrange multiplier; T represents the identity matrix; 2 / 3μ (·) denotes the soft threshold operator; P, S, and Q are intermediate variables generated during the algorithm iteration process; svd(·) denotes the singular value decomposition algorithm; · / denotes the division of matrix or tensor elements.

[0082] Example 2

[0083] In this embodiment, Example 1 will be further described.

[0084] like Figure 2 As shown, taking the synthesized noise-free complete rule data as an example, the size of the synthesized data is 301×12×12×12×12, the time sampling interval is 2ms, and the spatial sampling interval of the other four dimensions is 12.5m.

[0085] like Figure 3 As shown, assume the data is contaminated with -1dB Gaussian white noise, and then 50% of the data is randomly missing.

[0086] like Figure 4 As shown, data reconstruction is performed based on the Frobenius-nuclear mixing norm and different tensor mode expansion forms.

[0087] like Figure 5 The figure shows the data error results.

[0088] Example 3

[0089] The above-described embodiment 1 provides a method for reconstructing high-dimensional seismic data. Correspondingly, this embodiment provides a system for reconstructing high-dimensional seismic data. The system provided in this embodiment can implement the high-dimensional seismic data reconstruction method of embodiment 1. The system can be implemented through software, hardware, or a combination of both. For example, the system may include integrated or separate functional modules or units to perform the corresponding steps in the methods of embodiment 1. Since the system in this embodiment is basically similar to the method embodiment, the description process in this embodiment is relatively simple. Relevant details can be found in the description of embodiment 1. The system embodiment provided in this embodiment is merely illustrative.

[0090] The high-dimensional seismic data reconstruction system provided in this embodiment includes:

[0091] The data preprocessing module is used to read the CMP gather data or OVT gather data after NMO and perform Binning processing on the data to obtain a true rule-based high-dimensional data volume.

[0092] The block data reconstruction module is used to read local block data and reconstruct the data based on the Frobenius-nuclear mixture norm and different tensor mode expansion forms.

[0093] The results output module is used to reconstruct all data blocks and obtain the final high-dimensional data reconstruction result.

[0094] Example 4

[0095] This embodiment provides a processing device corresponding to the high-dimensional seismic data reconstruction method provided in Embodiment 1. The processing device can be a client-side processing device, such as a mobile phone, laptop, tablet computer, desktop computer, etc., to execute the method of Embodiment 1.

[0096] The processing device includes a processor, a memory, a communication interface, and a bus. The processor, memory, and communication interface are connected via the bus to communicate with each other. The memory stores a computer program that can run on the processor. When the processor runs the computer program, it executes the high-dimensional seismic data reconstruction method provided in Embodiment 1.

[0097] In some embodiments, the memory may be high-speed random access memory (RAM), and may also include non-volatile memory, such as at least one disk storage device.

[0098] In other embodiments, the processor can be a general-purpose processor of various types, such as a central processing unit (CPU) or a digital signal processor (DSP), and is not limited thereto.

[0099] Example 5

[0100] The high-dimensional seismic data reconstruction method of Embodiment 1 can be specifically implemented as a computer program product. The computer program product may include a computer-readable storage medium on which computer-readable program instructions for executing the high-dimensional seismic data reconstruction method of Embodiment 1 are loaded.

[0101] A computer-readable storage medium can be a tangible device that holds and stores instructions for use by an instruction execution device. A computer-readable storage medium can be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination thereof.

[0102] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for reconstructing high-dimensional seismic data, characterized in that, Includes the following steps: An initial rule-based high-dimensional data volume is obtained by processing the original seismic data; Local block data is read from the obtained initial rule high-dimensional data volume, low-rank constraints are applied to the tensor mode expansion matrices based on the Frobenius-nuclear mixture norm, and data reconstruction is performed on the read local block data; Repeat the previous step to reconstruct all local block data and obtain the final high-dimensional seismic data reconstruction result; The step of reading local block data from the obtained initial rule data volume and reconstructing the read local block data based on the Frobenius-nuclear mixture norm and different tensor mode expansion forms includes: Read local block data and perform FFT on the local block data along the time dimension to obtain frequency spatial domain data composed of multiple single frequency slices; Data reconstruction was performed on each single-frequency slice data to obtain the reconstruction results of all frequency slice data. IFFT is performed on the reconstruction results of all single-frequency slice data to convert the frequency spatial domain data into time spatial domain data. The process of reconstructing data for each single-frequency slice to obtain the reconstruction results for all frequency slice data includes: Read single frequency slice data, apply low-rank constraints to different tensor mode expansion matrices using the Frobenius-nuclear mixing norm, and calculate the reconstruction results of single frequency slice data using the ADMM method; The reconstruction results of all single-frequency slice data are obtained by performing calculations on all single-frequency slice data in sequence. The reconstruction results of a single frequency slice data calculated using the ADMM method include: Constructing the augmented Lagrangian function of the inverse problem transforms the low-rank constrained problem into an unconstrained optimization problem: in, Used to adjust the degree to which the solution results match the constraints; express Auxiliary variables; and Represents the Lagrange multipliers; This provides noise-free and complete data. for The modal expansion matrix n; For the dimensions of the data; Data sliced ​​for a single frequency; Spatial sampling operator for data; For hyperparameters; To each Perform alternating solutions until the above is reached. The above iteration process terminates when the update amount is less than a certain threshold.

2. The high-dimensional seismic data reconstruction method as described in claim 1, characterized in that, The initial rule-based high-dimensional data volume obtained by processing the original seismic data includes: Dynamic correction is performed on the raw seismic data to obtain CMP gather data or OVT gather data; The obtained CMP or OVT gather data is processed into surface elements to obtain the initial high-dimensional data volume of rules.

3. The high-dimensional seismic data reconstruction method as described in claim 1, characterized in that, The update formulas for each variable are: In the formula, Representation of factor matrix Auxiliary variables; Representation of factor matrix The conjugate matrix; Representation of factor matrix The conjugate matrix; Represents the identity matrix; This represents the soft threshold operator; , , These are intermediate variables generated during the algorithm iteration process; This represents the singular value decomposition algorithm; This indicates the division of elements of a matrix or tensor.

4. A high-dimensional seismic data reconstruction system, characterized in that, include: The data preprocessing module is used to process the raw seismic data to obtain an initial rule-based high-dimensional data volume; The data reconstruction module reads local block data from the obtained initial rule high-dimensional data volume, applies low-rank constraints to different tensor mode expansion matrices based on the Frobenius-nuclear mixture norm, and reconstructs the read local block data. The results output module is used to reconstruct data from all local block data to obtain the final high-dimensional seismic data reconstruction results. The data reconstruction module includes: The frequency domain conversion module is used to read local block data and perform FFT on the local block data along the time dimension to obtain frequency spatial domain data composed of multiple single frequency slices. The reconstruction module is used to reconstruct data for each single-frequency slice data separately, and obtain the reconstruction results of all frequency slice data. The time-domain transformation module is used to perform IFFT on the reconstruction results of all the obtained single-frequency slice data, converting the frequency spatial domain data into time spatial domain data. The process of reconstructing data for each single-frequency slice to obtain the reconstruction results for all frequency slice data includes: Read single frequency slice data, apply low-rank constraints to different tensor mode expansion matrices using the Frobenius-nuclear mixing norm, and calculate the reconstruction results of single frequency slice data using the ADMM method; The reconstruction results of all single-frequency slice data are obtained by performing calculations on all single-frequency slice data in sequence. The reconstruction results of a single frequency slice data calculated using the ADMM method include: Constructing the augmented Lagrangian function of the inverse problem transforms the low-rank constrained problem into an unconstrained optimization problem: in, Used to adjust the degree to which the solution results match the constraints; express Auxiliary variables; and Represents the Lagrange multipliers; This provides noise-free and complete data. for The modal expansion matrix n; For the dimensions of the data; Data sliced ​​for a single frequency; Spatial sampling operator for data; For hyperparameters; To each Perform alternating solutions until the above is reached. The above iteration process terminates when the update amount is less than a certain threshold.

5. A computer-readable storage medium for 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 described in claims 1 to 3.

6. 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, the one or more programs including instructions for performing any one of the methods described in claims 1 to 3.

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