Seismic data interpolation method based on implicit prior deep convolutional dictionary network

Abstract

This invention discloses a seismic data interpolation method based on an implicit prior deep convolutional dictionary network, belonging to the field of seismic data processing technology. It solves the problems of existing traditional seismic data interpolation methods, which struggle to handle complex seismic data and produce large reconstruction errors. This invention transforms complete seismic data into a linear combination of a convolutional dictionary and corresponding coefficients. Combined with a sampling matrix, seismic data is collected to obtain observation data. By introducing auxiliary variables and combining the dictionary matrix with the representation coefficients, the seismic data interpolation problem is transformed into a constrained optimization problem, solving its objective function to obtain an iterative formula for the representation coefficients. The iterative formula for the representation coefficients is model-mapped, an unfolding module is established, and a structure based on an implicit prior deep convolutional dictionary network is constructed. Observational data and a sampling matrix are input to this network to obtain the final complete seismic data. This invention achieves high-precision interpolation for randomly missing seismic data and can be applied to seismic data processing.

Description

Technical Field

[0001] This invention relates to seismic data interpolation methods, and more particularly to seismic data interpolation methods based on implicit prior depth convolutional dictionary networks, belonging to the field of seismic data processing technology. Background Technology

[0002] With the continuous growth in demand for oil and gas resources, seismic exploration has been widely used as an important means of oil and gas exploration. However, due to limitations in economic costs and complex surface conditions, the actual seismic data acquired is often incomplete, with missing seismic traces, which seriously affects the accuracy of subsequent data processing and interpretation. Therefore, interpolating incomplete seismic records to reconstruct complete data is a key step in seismic data processing.

[0003] Existing seismic data interpolation methods can be divided into two categories: model-driven and data-driven. Model-driven methods are based on explicit priors such as seismic wave equations, low-rank structures, or sparse representations, and have good interpretability, but they are insufficient in adapting to different types of data. Data-driven methods learn seismic data features directly from the data through deep neural networks, without relying on prior assumptions, and have stronger adaptability, but lack interpretability. Among them, convolutional sparse coding networks represent seismic data as a linear combination of convolutional dictionaries and sparse coefficients based on convolutional sparse coding theory, thereby transforming the seismic data interpolation problem into an optimization problem with sparsity constraints.

[0004] To solve this optimization problem, the Convolutional Sparse Coding Network (CSCN) unfolds the iterative shrinking threshold algorithm into a deep network structure, where each layer corresponds to one iteration step. Transposed convolutional layers and convolutional layers are used to replace the dictionary and its transpose, enabling end-to-end training. In this process, the CSCN adopts the assumption of sparse coefficients and uses the iterative shrinking threshold as a proximal operator integrated into the network to represent coefficient updates, achieving sparse representation and interpolation of seismic data. However, the proximal operator used in the CSCN is a fixed-form soft threshold operator, which is only applicable to relatively simple sparse priors and is difficult to handle seismic data with complex structures or weak phase axes, thus limiting the interpolation capability of the CSCN. Secondly, the threshold of the proximal operator needs to be manually set during training, making it difficult to automatically adapt to different missing rates and different data scenarios, and its reconstruction results often contain errors.

[0005] In summary, a seismic data interpolation method based on an implicit prior depth convolutional dictionary network is needed. Summary of the Invention

[0006] A brief overview of the invention is given below to provide a basic understanding of certain aspects of it. It should be understood that this overview is not an exhaustive summary of the invention. It is not intended to identify key or essential parts of the invention, nor is it intended to limit the scope of the invention. Its purpose is merely to present certain concepts in a simplified form as a prelude to the more detailed description that follows.

[0007] In view of this, in order to solve the problem that traditional seismic data interpolation methods in the prior art are unable to handle complex seismic data and have large errors in reconstruction results, this invention provides a seismic data interpolation method based on an implicit prior depth convolutional dictionary network.

[0008] The technical solution is as follows: a seismic data interpolation method based on an implicit prior depth convolutional dictionary network, comprising the following steps:

[0009] S1. Based on the theory of convolutional sparse coding, the complete seismic data is transformed and represented as a linear combination of a convolutional dictionary and corresponding coefficients. Combined with the sampling matrix, seismic data is collected to obtain observation data.

[0010] S2. By introducing auxiliary variables and combining the dictionary matrix and representation coefficients, the seismic data interpolation problem is transformed into a constrained optimization problem to solve its objective function;

[0011] S3. The objective function is solved by using a deep expansion strategy, which involves updating the dictionary matrix, representation coefficients and auxiliary variables, and combining the constructed learnable proximal operators to obtain the iterative formula for the representation coefficients.

[0012] S4. Perform model mapping on the iterative formula of the representation coefficients, establish an unfolding module, construct a network structure based on implicit prior deep convolutional dictionary, input observation data and sampling matrix to it, and obtain the final complete seismic data, that is, complete the seismic data interpolation.

[0013] Furthermore, in S1, according to the convolutional sparse coding theory, the complete seismic data is represented as the convolution sum of multiple convolutional dictionary atoms and their corresponding sparse coefficients;

[0014] Complete earthquake data Represented as

[0015]

[0016] in, For the first One convolutional atom, For the first The representation coefficients corresponding to each convolution atom, based on the translation invariance of the convolution dictionary, allow the convolution sum to be rewritten in the form of matrix multiplication. and They represent respectively by and Stacked dictionary matrices and their representation coefficients;

[0017] The process of acquiring seismic data can be represented as follows:

[0018]

[0019] in, For observation data, A sampling matrix consisting of columns of all 0s and all 1s. This represents the matrix dot product operation.

[0020] Furthermore, in S2, auxiliary variables are introduced. The optimization objective is decomposed into a structured form, separating the data fidelity term and the structured prior, thus transforming the seismic data interpolation problem into a constrained optimization problem to solve its objective function.

[0021] The objective function is expressed as:

[0022]

[0023] in, This is an implicit prior hypothesis regarding the coefficients.

[0024] Furthermore, in S3, based on the alternating minimization strategy, the solution process of the objective function is decomposed into steps targeting... The three subproblems are solved, that is, the dictionary matrix is ​​obtained through backpropagation. The update is achieved by designing the proximal operator as a learnable proximal operator to realize the auxiliary variable. The update will combine the output of the learnable proximal operator with the dictionary matrix. The update of the representation coefficients is combined with the implementation of the update. Update;

[0025] dictionary matrix The update process is represented as follows:

[0026]

[0027] Auxiliary variables The update process is represented as follows:

[0028]

[0029] Represents coefficients The update process is represented as follows:

[0030] .

[0031] Representing coefficients The gradient descent direction of the data fidelity term and the auxiliary variable during the update process By combining the proximal constraints, the representation coefficients are obtained. The iterative formula;

[0032] Represents coefficients The iterative formula is expressed as:

[0033] ,

[0034] in, For the first The representation coefficients obtained from the next iteration. Let D be the transpose of the dictionary matrix D. Net is used as a learnable proximal operator to learn implicit priors.

[0035] Furthermore, in step S4, a transposed convolutional layer is used according to the convolution dictionary structure. and convolutional layers Replace the dictionary matrix respectively and its transpose matrix The coefficients are obtained. The learnable and updatable formula completes the construction of the expanded module;

[0036] Represents coefficients The learnable update formula is expressed as:

[0037] ,

[0038] Wherein, represents the coefficient. The learnable update formula corresponds to the first in the implicit prior deep convolutional dictionary network structure. One expandable module, For the process The updated representation coefficients obtained after expanding each module;

[0039] The network structure based on implicit prior deep convolutional dictionary includes an unfolded module and a transposed convolutional layer. The initialized observation data and sampling matrix As input to a network structure based on implicit prior deep convolutional dictionary;

[0040] Through transposed convolutional layers The final complete seismic data was recovered. ;

[0041] Final complete earthquake data Represented as:

[0042] .

[0043] The beneficial effects of the present invention are as follows: The present invention can be applied to the interpolation process in seismic data processing; the present invention enhances the continuity, structural integrity and signal-to-noise ratio of undersampled seismic records; the present invention improves the accuracy and resolution of subsequent processing steps such as velocity analysis and imaging inversion.

[0044] Under the same training set and conditions, the deep convolutional dictionary network of this invention was tested and compared with existing convolutional sparse coding networks on pre-stack and post-stack data to verify the beneficial effects of this invention compared with existing technologies in seismic data interpolation, as follows:

[0045] First, interpolation was performed on the pre-stack data containing 50% randomly missing seismic traces, and the signal-to-noise ratio was calculated. Referring to Figure 4, the complete pre-stack data and the observation data with 50% randomly missing seismic traces are shown. The complete pre-stack data contains 178 seismic traces and 178 time sampling points. Interpolation was performed on the incomplete observation data. The interpolation result obtained by this invention has a signal-to-noise ratio of 39.0 dB, which is significantly higher than the 33.1 dB of the interpolation result of the convolutional sparse coding network.

[0046] Referring to Figure 5, the interpolation results of the convolutional sparse coding network and the method of the present invention are shown. It can be seen that the present invention obtains a more continuous in-phase axis, especially the weak signal indicated by the arrow. In addition, the residual between the interpolation result and the complete data is calculated. Referring to Figure 6, the residual amplitude obtained by the present invention is lower, indicating that the present invention can effectively reduce the reconstruction error.

[0047] To further demonstrate the beneficial effects of this invention, interpolation was performed on post-stack data containing randomly missing 66.7% seismic traces. Referring to Figure 7, the complete post-stack data and the observation data with randomly missing 66.7% seismic traces are shown. The complete post-stack data contains 512 seismic traces and 512 time sampling points with a sampling interval of 0.004 s. The signal-to-noise ratio of the interpolation result obtained by this invention is 1.9 dB higher than that of the convolutional sparse coding network. Referring to Figure 8, the interpolation results show that the result of the convolutional sparse coding network exhibits outliers at large-interval missing points, indicating that it performs poorly in handling large-interval missing points. In comparison, this invention recovers the missing seismic traces more completely.

[0048] refer to Figure 9 To more clearly demonstrate the beneficial effects of the present invention, the 266th seismic trace from the complete seismic data and the interpolation results is selected for comparison. This shows the comparison curve between the interpolation results of the convolutional sparse coding network and the method of the present invention and the single trace of the complete data. The single trace in the interpolation results obtained by the present invention is closer to the single trace of the complete data, thereby verifying the advantages of the present invention in terms of interpolation accuracy.

[0049] In summary, this invention achieves high-precision interpolation on randomly missing seismic data through deep unfolded network structure design, and has significant technical advantages over existing technologies in weak signal recovery and large-spacing missing data processing. Attached Figure Description

[0050] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0051] Figure 1 This is a flowchart illustrating the seismic data interpolation method based on an implicit prior depth convolutional dictionary network.

[0052] Figure 2 A schematic diagram of the network structure for learnable proximal operators;

[0053] Figure 3 This is a schematic diagram of the structure of a network based on an implicit prior depthwise convolutional dictionary.

[0054] Figure 4 is a schematic diagram of the first set of complete pre-stack data and observation data, where (a) is the complete pre-stack data and (b) is the observation data containing 50% randomly missing seismic traces;

[0055] Figure 5 is a schematic diagram comparing the interpolation results of pre-stack data containing 50% randomly missing seismic traces, where (a) is the interpolation result of the convolutional sparse coding network and (b) is the interpolation result of the deep convolutional dictionary network of the present invention.

[0056] Figure 6 is a schematic diagram comparing the residual results of pre-stack data containing 50% randomly missing seismic traces, where (a) is the residual result of the convolutional sparse coding network and (b) is the residual result of the deep convolutional dictionary network of the present invention.

[0057] Figure 7 is a schematic diagram of the second set of complete post-stack data and observation data, where (a) is the complete post-stack data and (b) is the observation data containing 66.7% randomly missing seismic traces;

[0058] Figure 8 is a schematic diagram of the interpolation results of post-stack data containing 66.7% randomly missing seismic traces, where (a) is the interpolation result of the convolutional sparse coding network and (b) is the interpolation result of the deep convolutional dictionary network.

[0059] Figure 9 This is a schematic diagram comparing the convolutional sparse coding network and the deep convolutional dictionary network of this invention for a single channel of complete data. Detailed Implementation

[0060] To make the technical solutions and advantages of the embodiments of the present invention clearer, the exemplary embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not an exhaustive list of all embodiments. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0061] refer to Figures 1-9 This embodiment describes a seismic data interpolation method based on an implicit prior depth convolutional dictionary network, specifically including the following steps:

[0062] S1. Based on the theory of convolutional sparse coding, the complete seismic data is transformed and represented as a linear combination of a convolutional dictionary and corresponding coefficients. Combined with the sampling matrix, seismic data is collected to obtain observation data.

[0063] S2. By introducing auxiliary variables and combining the dictionary matrix and representation coefficients, the seismic data interpolation problem is transformed into a constrained optimization problem to solve its objective function;

[0064] S3. The objective function is solved by using a deep expansion strategy, which involves updating the dictionary matrix, representation coefficients and auxiliary variables, and combining the constructed learnable proximal operators to obtain the iterative formula for the representation coefficients.

[0065] S4. Perform model mapping on the iterative formula of the representation coefficients, establish an unfolding module, construct a network structure based on implicit prior deep convolutional dictionary, input observation data and sampling matrix to it, and obtain the final complete seismic data, that is, complete the seismic data interpolation.

[0066] Specifically, this invention is deployed in hardware devices such as GPU servers, high-performance computing platforms, or cloud systems, and provides automatic interpolation functions to the outside world through APIs or microservices. At the same time, this invention can also be used as an scalable network unit in a deep learning framework, or deployed on edge computing devices after being pruned, to realize real-time signal reconstruction in multiple scenarios.

[0067] Furthermore, in S1, according to the convolutional sparse coding theory, the complete seismic data is represented as the convolution sum of multiple convolutional dictionary atoms and their corresponding sparse coefficients;

[0068] Complete earthquake data Represented as

[0069]

[0070] in, For the first One convolutional atom, For the first The representation coefficients corresponding to each convolution atom, based on the translation invariance of the convolution dictionary, allow the convolution sum to be rewritten in the form of matrix multiplication. and They represent respectively by and Stacked dictionary matrices and their representation coefficients;

[0071] The process of acquiring seismic data can be represented as follows:

[0072]

[0073] in, For observation data, This is a sampling matrix consisting of columns of all zeros and all one values, used to represent undersampling locations during the actual data acquisition process. This represents the matrix dot product operation.

[0074] Specifically, by utilizing implicit priors of coefficients obtained from a large amount of seismic data, the network's generalization ability is improved, eliminating the need for manual parameter adjustment and enhancing reconstruction results.

[0075] Furthermore, in S2, auxiliary variables are introduced. The optimization objective is decomposed into a structured form, separating the data fidelity term and the structured prior, thus transforming the seismic data interpolation problem into a constrained optimization problem to solve its objective function.

[0076] The objective function is expressed as:

[0077]

[0078] in, This is an implicit prior hypothesis regarding the coefficients.

[0079] Furthermore, in S3, based on the alternating minimization strategy, the solution process of the objective function is decomposed into steps targeting... The three subproblems are solved, that is, the dictionary matrix is ​​obtained through backpropagation. The update is achieved by designing the proximal operator as a learnable proximal operator to realize the auxiliary variable. The update will combine the output of the learnable proximal operator with the dictionary matrix. The update of the representation coefficients is combined with the implementation of the update. Update;

[0080] dictionary matrix The update process is represented as follows:

[0081]

[0082] Auxiliary variables The update process is represented as follows:

[0083]

[0084] Represents coefficients The update process is represented as follows:

[0085] .

[0086] Representing coefficients The gradient descent direction of the data fidelity term and the auxiliary variable during the update process By combining the proximal constraints, the representation coefficients are obtained. The iterative formula;

[0087] Represents coefficients The iterative formula is expressed as:

[0088] ,

[0089] in, For the first The representation coefficients obtained from the next iteration. Let D be the transpose of the dictionary matrix D. Net is used as a learnable proximal operator to learn implicit priors, which can significantly enhance the network's ability to express complex seismic structures without the need for manual threshold adjustment.

[0090] Specifically, in deep convolutional dictionary networks, the dictionary matrix... The update is achieved through backpropagation, which can learn an adaptive convolution dictionary through end-to-end training;

[0091] Designing the near-end operator as a learnable convolutional neural network to complete the auxiliary variable The updates enable it to learn about the representation coefficients from large amounts of seismic data. The implicit priors are used, thus eliminating reliance on manually designed regularization forms.

[0092] Furthermore, in S4, the coefficients will be represented The iterative formula is mapped to an end-to-end trainable model, and transposed convolutional layers are used based on the convolution dictionary structure. and convolutional layers Replace the dictionary matrix respectively and its transpose matrix The coefficients are obtained. The learnable and updatable formula completes the construction of the expanded module;

[0093] Represents coefficients The learnable update formula is expressed as:

[0094] ,

[0095] Wherein, represents the coefficient. The learnable update formula corresponds to the first in the implicit prior deep convolutional dictionary network structure. One expandable module, For the process The updated representation coefficients obtained after expanding each module;

[0096] The network structure based on implicit prior deep convolutional dictionary includes an unfolded module and a transposed convolutional layer. The initialized observation data and sampling matrix As input to a network structure based on implicit prior deep convolutional dictionary;

[0097] Through transposed convolutional layers The final complete seismic data was recovered. ;

[0098] Final complete earthquake data Represented as:

[0099] .

[0100] For details, please refer to Figure 2 The learnable proximal operator Net adopts a convolutional neural network structure based on U-Net, consisting of two parts: encoding and decoding. The network has 64 input and output channels, and the number of feature channels along the network depth direction is 64, 64, 64, 72, 72, 64, 64, and 64 respectively. In the encoding stage, the network extracts features through 3×3 convolutional layers and ReLU activation function, and introduces 2×2 pooling layers to reduce feature resolution. In the decoding stage, upsampling is achieved through 2×2 transposed convolution, and features are reconstructed by combining 3×3 convolutional layers. To fully integrate multi-scale information, skip connections are introduced between corresponding layers in the encoding and decoding stages, and feature fusion is performed by element-wise addition. The final output of the network is achieved by a single 3×3 convolutional layer without using an activation function.

[0101] refer to Figure 3 By constructing a network structure based on an implicit prior deep convolutional dictionary, this invention achieves deep unfolding of the convolutional sparse model. The dictionary is updated through backpropagation of the network, which effectively improves the accuracy and robustness of seismic data interpolation.

[0102] Although the invention has been described with reference to a limited number of embodiments, those skilled in the art will understand from the foregoing description that other embodiments are conceivable within the scope of the invention described herein. Furthermore, it should be noted that the language used in this specification has been chosen primarily for readability and instructional purposes, and not for the purpose of interpreting or limiting the subject matter of the invention. Therefore, many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the appended claims. The disclosure of the invention is illustrative and not restrictive, and the scope of the invention is defined by the appended claims.

Claims

1. A seismic data interpolation method based on an implicit prior depth convolutional dictionary network, characterized in that, Includes the following steps: S1. Based on the theory of convolutional sparse coding, the complete seismic data is transformed and represented as a linear combination of a convolutional dictionary and corresponding coefficients. Combined with the sampling matrix, seismic data is collected to obtain observation data. S2. By introducing auxiliary variables and combining the dictionary matrix and representation coefficients, the seismic data interpolation problem is transformed into a constrained optimization problem to solve its objective function; S3. The objective function is solved by using a deep expansion strategy, which involves updating the dictionary matrix, representation coefficients and auxiliary variables, and combining the constructed learnable proximal operators to obtain the iterative formula for the representation coefficients. S4. Model mapping is performed on the iterative formula of the representation coefficients, an expansion module is established, and a network structure based on implicit prior deep convolutional dictionary is constructed. The observation data and sampling matrix are input to it to obtain the final complete seismic data, that is, the seismic data interpolation is completed. In S2, auxiliary variables are introduced. The optimization objective is decomposed into a structured form, separating data fidelity terms and structured priors, thus transforming the seismic data interpolation problem into the objective function of a constrained optimization model. The objective function is expressed as: in, This is an implicit prior hypothesis regarding the coefficients. In S3, based on the alternating minimization strategy, the solution process of the objective function is decomposed into steps targeting... The three subproblems are solved, that is, the dictionary matrix is ​​obtained through backpropagation. The update is achieved by designing the proximal operator as a learnable proximal operator to realize the auxiliary variable. The update will combine the output of the learnable proximal operator with the dictionary matrix. The update of the representation coefficients is combined with the implementation of the update. Update; dictionary matrix The update process is represented as follows: Auxiliary variables The update process is represented as follows: Represents coefficients The update process is represented as follows: Representing coefficients The gradient descent direction of the data fidelity term and the auxiliary variable during the update process By combining the proximal constraints, the representation coefficients are obtained. The iterative formula; Represents coefficients The iterative formula is expressed as: ， in, For the first The representation coefficients obtained from the next iteration. Let represent the transpose of the dictionary matrix D. Net is used as a learnable proximal operator to learn implicit priors.

2. The seismic data interpolation method based on an implicit prior depth convolutional dictionary network according to claim 1, characterized in that, In S1, according to the theory of convolutional sparse coding, complete seismic data is represented as the convolution sum of multiple convolutional dictionary atoms and their corresponding sparse coefficients; Complete earthquake data Represented as in, For the first One convolutional atom, For the first The representation coefficients corresponding to each convolution atom, based on the translation invariance of the convolution dictionary, allow the convolution sum to be rewritten in the form of matrix multiplication. and They represent respectively by and Stacked dictionary matrices and their representation coefficients; The process of acquiring seismic data can be represented as follows: in, For observation data, A sampling matrix consisting of columns of all 0s and columns of all 1s. This represents the matrix dot product operation.

3. The seismic data interpolation method based on an implicit prior depth convolutional dictionary network according to claim 2, characterized in that, In step S4, a transposed convolutional layer is used according to the convolution dictionary structure. and convolutional layers Replace the dictionary matrix respectively and its transpose matrix The coefficients are obtained. The learnable and updatable formula completes the construction of the expanded module; Represents coefficients The learnable update formula is expressed as: ， Wherein, represents the coefficient. The learnable update formula corresponds to the first in the implicit prior deep convolutional dictionary network structure. One expandable module, For the process The updated representation coefficients obtained after expanding each module; The network structure based on implicit prior deep convolutional dictionary includes an unfolded module and a transposed convolutional layer. The initialized observation data and sampling matrix As input to a network structure based on implicit prior deep convolutional dictionary; Through transposed convolutional layers The final complete seismic data was recovered. ; Final complete earthquake data Represented as: 。

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