CN114397700B - Method, device, equipment and storage medium for interpolating pre-stack seismic data of node seismograph based on graph signal constraint - Google Patents
Method, device, equipment and storage medium for interpolating pre-stack seismic data of node seismograph based on graph signal constraint Download PDFInfo
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Abstract
The invention discloses a method, a device, equipment and a storage medium for interpolating pre-stack seismic data of a node seismograph based on graph signal constraint.
Description
Technical Field
The invention belongs to the technical field of seismic exploration, relates to a pre-stack seismic data interpolation method for node seismograph acquisition based on graph signal constraint, and in particular relates to a pre-stack seismic data interpolation method, device and equipment for node seismograph based on graph signal constraint and a storage medium.
Background
The method is influenced by various adverse factors of field acquisition of the seismic data, particularly by irregular (random) large-scale deployment of node seismograph equipment in recent years, so that the seismic signals acquired by the node seismograph are subjected to missing, bad channels and space aliasing. This missing seismic data severely impacts subsequent seismic data processing and interpretation, such as high resolution processing, offset imaging, construction interpretation, reservoir characterization, etc. Thus, interpolation (restoration) of complete, regular pre-stack seismic data from pre-stack seismic data acquired from incomplete, irregular node seismometers is of great significance for subsequent seismic processing and interpretation.
Interpolation of seismic data can be divided into three categories according to the mathematical principles of interpolation: interpolation methods based on wave equation, interpolation methods based on filter, and seismic interpolation methods based on mathematical transformation. The seismic interpolation method based on the wave equation is to interpolate according to causal correlation between seismic data. Fomel (2003) proposes a seismic interpolation method based on wave equation and finite difference filtering. Ramfrez (2006) proposes a seismic interpolation method based on the idea of wave equation finite aperture offset. Although the method has better effect, the seismic interpolation method based on the fluctuation method has higher accuracy requirement on the velocity field. The filter-based seismic interpolation method mainly designs a prediction filter algorithm to realize a seismic interpolation technology. Porsani (1999) proposed a modified Spitz method with good effect on regular signals, but this class of methods has polynomials for irregular sampling, limiting the effect of seismic interpolation. The seismic interpolation method based on mathematical transformation is a widely applied seismic interpolation method at present, and the method mainly comprises the steps of converting missing seismic data into a mathematical transformation domain, and interpolating the seismic data in the mathematical transformation domain so as to obtain complete seismic data. Feng Fei et al (2013) combine curvelet transform and focus transform to propose a seismic data interpolation method based on the problem of L1 norm regularization. Liu Cai et al (2013) propose a Seislet-based seismic interpolation method that can implement anti-aliasing interpolation. Liu and Sacchi (2004) propose a seismic interpolation method based on Fourier transform. In addition, mathematical transformations such as Radom transforms (Yu et al, 2007), dictionary learning (Sun et al, 2018) and the like are also often used for seismic interpolation. The above technique has the following disadvantages:
1) The seismic interpolation method based on the fluctuation method has higher requirements on the precision of the velocity field, and the inaccurate velocity field can influence the performance of the seismic interpolation.
2) The seismic interpolation method based on mathematical transformation realizes the seismic interpolation by using sparsity constraint, but the geometric structure of the seismic data is not considered by the method.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide a method, a device, equipment and a storage medium for interpolating pre-stack seismic data of a node seismograph based on graph signal constraint, which can effectively solve the technical problems that the geometric structure of the seismic data is not considered in the prior art, and the speed field is inaccurate due to the fact that the precision cannot be met, and the method can obtain complete and high-quality seismic data.
In order to achieve the above purpose, the invention is realized by adopting the following technical scheme:
the invention discloses a node seismograph pre-stack seismic data interpolation method based on graph signal constraint, which comprises the following steps: aiming at incomplete seismic data interpolation before stack, simultaneously considering the geometric structure and low rank of the seismic data, constructing the seismic data into an undirected graph, generating a graph variation regularization term according to the undirected graph, introducing the regularization term and a nuclear norm regularization term into a proposed optimization problem, and solving the optimization problem by using a Bregman segmentation algorithm to obtain complete and high-quality seismic data.
Preferably, the method for interpolating pre-stack seismic data of the node seismograph based on graph signal constraint comprises the following steps:
1) Acquiring incomplete two-dimensional observation data before stack, and preprocessing the two-dimensional observation data;
2) According to the preprocessed seismic data, generating an undirected graph by considering the geometric structure of the seismic data, and constructing an optimization model containing graph regularization items;
3) Solving an optimization model according to a Bregman segmentation algorithm to obtain an output optimal X opt ；
4) Optimal X for output opt Performing anti-blocking processing to obtain reconstructed seismic data S opt 。
Further preferably, step 1) is specifically operated as follows:
acquiring incomplete node seismograph two-dimensional observation data before stack, marking the incomplete node seismograph two-dimensional observation data as S, dividing the node seismograph two-dimensional earthquake data into N blocks, wherein the size of each block is M=P×Q, and P and Q are the sizes of the blocks; reordering each block of p×q size into column vectors results in preprocessed seismic data
Assume that the sampling matrix is J.epsilon.0, 1 M×N When the time is, the seismic data after preprocessingAnd reconstructed seismic data +.>Expressed as: />Representing a matrix dot product, N representing gaussian white noise.
Still more preferably, step 2) is specifically performed as follows:
when the seismic data after preprocessingKnowing that solving the reconstructed seismic data X uses the inverse problem to solve:
wherein ,representing the Frobenius norm, +.>Representing reconstructed seismic data constraints, λ being a regularization parameter; the preprocessed seismic data has low rank characteristics, and the geometric structure of the seismic data is considered, so that the method is rewritten as follows:
wherein |X|| * Represents the nuclear norms, lambda 1 and λ1 Is a regularization parameter;
representing a diagram changeRegularization term that considers geometry, μ, between partitioned data max (A) Representing the maximum eigenvalue of matrix a.
Still more preferably, step 3) is specifically performed as follows:
introducing an intermediate variable Z, and writing the optimization model into a constrained optimization model:
s.t.X＝Z
converting the constrained optimization model into an unconstrained optimization model according to the Lagrangian multiplier method:
wherein U represents an intermediate variable, U T Representing the transpose of the variable U, ρ being a regularization parameter;
the optimization model is divided into three sub-optimization problems according to the Bregman segmentation principle:
U k+1 ＝U k +ρ(X k+1 -Z k+1 ) (18)
the first sub-optimization problem is a typical L2 norm optimization problem, the solution of which is:
where vec (·) represents the rearrangement of a certain matrix into one by columnThe column vector, diag (·) indicates that a certain column vector is generated into a diagonal matrix, and the diagonal elements of the diagonal matrix are the column vector. wherein />Represent Kronecker product, I N Representing an N-dimensional identity matrix, I MN A identity matrix representing MN dimensions;
the solution of the second sub-optimization problem is:
wherein SVDT (X, ρ) =eΛ (Q, ρ) V T Λ (Q, ρ) =sign (Q) max (|q| - ρ, 0); e, Q, V are matrixes obtained after singular value decomposition of the matrix X; sign (·) represents a sign function;
by iterating the three sub-optimization problems until the stopping condition is met, namely the maximum iteration number or the error loss function is reachedReaching 0.01 and outputting the optimal X opt 。
Still more preferably, in step 2), a graph variation constraint term is introduced in consideration of the geometry between the partitioned data, a non-oriented graph is generated from the preprocessed pre-stack seismic data, and then the graph variation constraint term is defined according to the non-oriented graph;
pre-processed pre-stack seismic dataGenerating an undirected graph-> wherein ,is the combination of the undirected graph nodes, and the number of the undirected graph nodes is N; />Is the geometry of all sides of the undirected graph; matrix A is the weight matrix of the undirected graph, and the (i, j) th element in the weight matrix A is +.>Representing a weight between an ith node and a jth node;
the (i, j) th element in the weight matrix AThe definition is as follows:
the graph variation regularization term is defined as:
wherein ,μmax (A) Representing the maximum eigenvalue of matrix a.
The invention also discloses a device for realizing the node seismograph pre-stack seismic data interpolation method based on the graph signal constraint, which comprises the following steps:
the seismic data acquisition unit is used for preprocessing the pre-stack seismic data to obtain incomplete two-dimensional observation data before stack;
the model construction unit is used for carrying out model construction on the preprocessed seismic data to obtain an optimized model;
the model solving unit is used for carrying out Bregman segmentation algorithm solving on the optimized model to obtain an output optimal X opt ；
An anti-blocking processing unit for optimal X opt Processing to obtain reconstructed seismic data S opt 。
The invention also discloses a computer device, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the steps of the node seismograph pre-stack seismic data interpolation method based on the graph signal constraint when executing the computer program.
The invention also discloses a computer readable storage medium, which stores a computer program, and the computer program realizes the steps of the node seismograph pre-stack seismic data interpolation method based on graph signal constraint when being executed by a processor.
Compared with the prior art, the invention has the following beneficial effects:
the invention discloses a pre-stack seismic data interpolation method based on graph signal constraint, in particular to a pre-stack seismic data interpolation method based on graph signal constraint, which aims at the acquisition of an irregular (random) deployment node seismograph. In contrast to wave equation based seismic interpolation methods, the proposed method does not require an accurate velocity field. Compared with a seismic interpolation method of a mathematical transformation domain, the method provided by the invention introduces the constraint of a geological structure and can obtain more accurate seismic data.
Drawings
Fig. 1 is a flow chart of the present invention.
FIG. 2 is a result of a synthetic seismic data reconstruction; wherein (a) is a default 30% synthetic seismic record; (b) reconstructing the synthetic seismic record.
FIG. 3 is a result of reconstruction of pre-stack shot gather seismic data; wherein, (a) is original prestack shot gather seismic data; (b) a default 30% prestack shot gather seismic record; (c) reconstructed pre-stack shot gather seismic records.
Fig. 4 generates a schematic diagram of an undirected graph.
Detailed Description
In order that those skilled in the art will better understand the present invention, a technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in which it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and the claims of the present invention and the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that the embodiments of the invention described herein may be implemented in sequences other than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
The invention is described in further detail below with reference to the attached drawing figures:
the invention discloses a pre-stack seismic data interpolation method based on graph signal constraint, in particular to a pre-stack seismic data interpolation method based on graph signal constraint, which aims at the acquisition of an irregular (random) deployment node seismograph. The method specifically comprises the following steps:
1) Obtaining incomplete two-dimensional observation data S before stack, and preprocessing the seismic data before stack:
and acquiring incomplete two-dimensional observation data before stack, and particularly acquiring incomplete pre-stack seismic data acquired by a node seismograph, wherein the incomplete pre-stack seismic data is marked as S. Since the seismic data is a complete trace default, a block rearrangement of the seismic data is required. The two-dimensional seismic data is divided into N blocks, where each block has a size of m=p×q, where P and Q are the sizes of the blocks. Reordering each block of p×q size into a column vector results in processed dataAssume that the sampling matrix is J.epsilon.0, 1 M×N When the seismic data is pre-processed +.>And reconstructed seismic data +.>Expressed as: /> wherein />Representing a matrix dot product, N representing gaussian white noise.
2) Constructing an optimization model according to the preprocessed seismic data:
when the seismic data after preprocessingKnowing that solving the reconstructed seismic data X can utilize the inverse problem to solve:
wherein ,representing the Frobenius norm, +.>Representing reconstructed seismic data constraints, λ is a regularization parameter. The preprocessed seismic data has low rank characteristics, and the geometric structure of the seismic data is considered, so that the seismic data can be rewritten as follows:
wherein |X|| * Representing the kernel norm. Lambda (lambda) 1 and λ1 Is a regularization parameter.A graph variation regularization term is represented that considers the geometry between the partitioned data. Mu (mu) max (A) Representing the maximum eigenvalue of matrix a.
Pre-processing the seismic dataGenerating an undirected graph-> wherein ,/>Is the combination of the undirected graph nodes, and the number of the undirected graph nodes is N; />Is the geometry of all sides of the undirected graph; matrix a is the weight matrix of the undirected graph. The (i, j) th element in the weight matrix A +.>Representing the weight between the i-th node and the j-th node. In the present invention, the (i, j) th element ∈of the weight matrix A>The definition is as follows:
3) Solving an optimization model according to a Bregman segmentation algorithm:
in order to solve the optimization model conveniently, an intermediate variable Z is introduced, and the optimization model can be written as a constrained optimization model:
s.t.X＝Z
further, the constrained optimization model is converted into an unconstrained optimization model according to the Lagrangian multiplier method:
wherein U represents an intermediate variable, U T Representing the transpose of the variable U. ρ is a regularization parameter.
According to the Bregman segmentation principle, the optimization model can be divided into three sub-optimization problems:
U k+1 ＝U k +ρ(X k+1 -Z k+1 ) (30)
the first sub-optimization problem is a typical L2 norm optimization problem, the solution of which is:
where vec (·) represents the matrix to be a certainRearranged by column into a column vector. diag (·) indicates that a certain column vector is generated into a diagonal matrix, and the elements on the diagonal of the diagonal matrix are the column vector. wherein />Represent Kronecker product, I N Representing an identity matrix of N dimensions. I MN Representing the identity matrix of the MN dimension.
The solution of the second sub-optimization problem is:
where SVDT (X, ρ) =eiΛ (Q, ρ) VT, Λ (Q, ρ) =sign (Q) max (|q| - ρ, 0). E, Q, V are matrices obtained after singular value decomposition of matrix X. sign (·) represents a sign function.
Then the three sub-optimization problems are iterated until the stopping condition is met, and the optimal X is output opt 。
4) Optimal X for output opt Performing anti-blocking processing to obtain reconstructed seismic data S opt 。
Numerical simulation results
Synthesizing seismic record data
Fig. 1 shows a flow chart of the present invention. The synthetic data is processed according to the flowchart, and the result is shown in fig. 2. FIG. 2 shows the results after reconstruction of the synthetic seismic data at 30% default. FIG. 2 (a) is a random default 30% synthetic seismic data having 60 seismic records, each having 512 time sampling points, with a sampling interval of 1ms. FIG. 2 (b) shows the results after reconstitution according to the method of the present invention. It can be found that the linear in-phase axis reconstruction has better effect than the curve-type in-phase axis reconstruction, especially the in-phase axis with uniform transverse distribution.
Actual prestack shot gather seismic data profile
FIG. 3 shows the results of a node seismometer acquired pre-stack shot gather seismic data after a default 30% reconstruction. Fig. 3 (a) is original prestack shot gather seismic data with 100 traces of 800 time samples each, with a time sampling interval of 1ms. Fig. 3 (b) is 30% of the seismic data defaults, with the black portion being where random defaults. Fig. 3 (c) results after reconstitution. Obviously, the method provided by the invention can reconstruct the original seismic data to a certain extent, and provides an advantageous basis for further improving the method. In order to further illustrate the regularization generation process of the graph, taking fig. 3 as an example, the original data is firstly segmented, and the segmented data is extracted into column vectors to generate a new matrix. And constructing an undirected graph according to the similarity among each block, generating a weight matrix A, then generating a graph variation regularization term, and introducing the graph variation regularization term into a new generation matrix.
The above is only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited by this, and any modification made on the basis of the technical scheme according to the technical idea of the present invention falls within the protection scope of the claims of the present invention.
Claims (6)
1. A node seismograph pre-stack seismic data interpolation method based on graph signal constraint, comprising: aiming at incomplete pre-stack seismic data interpolation, simultaneously considering the geometric structure and low rank of the seismic data, constructing the seismic data into an undirected graph, generating a graph variation regularization term according to the undirected graph, introducing the regularization term and a nuclear norm regularization term into a proposed optimization problem, and solving the optimization problem by using a Bregman segmentation algorithm to obtain complete and high-quality seismic data;
the method specifically comprises the following steps:
1) Obtaining incomplete two-dimensional observation data before stack, and preprocessing the two-dimensional observation data, wherein the specific operation is as follows:
acquiring two-dimensional observation data of a node seismograph, which is incomplete before stack, and is marked as S, dividing the two-dimensional observation data of the node seismograph into N blocks, wherein the size of each block is M=P×Q, and the two-dimensional observation data of the node seismograph is divided into N blocksP and Q are the sizes of the blocks; reordering each block of p×q size into column vectors results in preprocessed seismic data
Assume that the sampling matrix is J.epsilon.0, 1 M×N When the time is, the seismic data after preprocessingAnd reconstructed seismic dataExpressed as: /> Representing a matrix dot product, E gaussian white noise;
2) According to the preprocessed seismic data, generating an undirected graph by considering the geometric structure of the seismic data, and constructing an optimization model containing graph regularization items; the specific operation is as follows:
when the seismic data after preprocessingKnowing that solving the reconstructed seismic data X uses the inverse problem to solve:
wherein ,representing the Frobenius norm, +.>Representing reconstructed seismic data constraints, λ being a regularization parameter; the preprocessed seismic data has low rank characteristics, and the geometric structure of the seismic data is considered, so that the method is rewritten as follows:
wherein |X|| * Represents the nuclear norms, lambda 1 and λ2 Is a regularization parameter;
representing a graph variation regularization term that considers geometry, μ, between partitioned data max (A) Representing the maximum eigenvalue of matrix a;
3) Solving an optimization model according to a Bregman segmentation algorithm to obtain an output optimal X opt ；
4) Optimal X for output opt Performing anti-blocking processing to obtain reconstructed seismic data S opt 。
2. The method of interpolating nodal seismograph pre-stack seismic data based on graph signal constraints of claim 1 wherein step 3) specifically operates as follows:
introducing an intermediate variable Z, and writing the optimization model into a constrained optimization model:
converting the constrained optimization model into an unconstrained optimization model according to the Lagrangian multiplier method:
wherein U represents a variable, U T Representing the transpose of the variable U, ρ being a regularization parameter;
the optimization model is divided into three sub-optimization problems according to the Bregman segmentation principle:
U k+1 ＝U k +ρ(X k+1 -Z k+1 ) (7)
the first sub-optimization problem is a typical L2 norm optimization problem, the solution of which is:
where vec (·) represents the rearrangement of a certain matrix by column into a column vector, diag (·) represents the generation of a diagonal matrix of a certain column vector with the diagonal elements of the diagonal matrix being the column vector wherein />Represent Kronecker product, I N Representing an N-dimensional identity matrix, I MN A identity matrix representing MN dimensions;
the solution of the second sub-optimization problem is:
wherein the method comprises the steps of，SVDT(X,ρ)＝EΛ(Q,ρ)V T Λ (Q, ρ) =sign (Q) max (|q| - ρ, 0); e, Q, V are matrixes obtained after singular value decomposition of the matrix X; sign (·) represents a sign function;
by iterating the three sub-optimization problems until the stopping condition is met, namely the maximum iteration number or the error loss function is reachedReaching 0.01 and outputting the optimal X opt 。
3. The method for interpolating pre-stack seismic data of a node seismograph based on graph signal constraint according to claim 1, wherein in step 2), a graph variation constraint item is introduced in consideration of the geometry between the partitioned data, a non-directional graph is generated from the preprocessed pre-stack seismic data, and then the graph variation constraint item is defined according to the non-directional graph;
pre-processed pre-stack seismic dataGenerating an undirected graph-> wherein ,/>Is the combination of the undirected graph nodes, and the number of the undirected graph nodes is N; epsilon is the geometry of all sides of the undirected graph; matrix A is the weight matrix of the undirected graph, and the (i, j) th element in the weight matrix A is +.>Representing a weight between an ith node and a jth node;
the (i, j) th element in the weight matrix AIs defined as：
The graph variation regularization term is defined as:
wherein ,μmax (A) Representing the maximum eigenvalue of matrix a.
4. A device for implementing a method for interpolating pre-stack seismic data of a node seismograph based on graph signal constraint according to any one of claims 1 to 3, characterized by comprising:
the seismic data acquisition unit is used for preprocessing the pre-stack seismic data to obtain incomplete two-dimensional observation data before stack;
the model construction unit is used for carrying out model construction on the preprocessed seismic data to obtain an optimized model;
the model solving unit is used for carrying out Bregman segmentation algorithm solving on the optimized model to obtain an output optimal X opt ；
An anti-blocking processing unit for optimal X opt Processing to obtain reconstructed seismic data S opt 。
5. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor, when executing the computer program, implements the steps of the node seismograph pre-stack seismic data interpolation method based on graph signal constraints of any one of claims 1 to 3.
6. A computer readable storage medium storing a computer program, wherein the computer program when executed by a processor implements the steps of the node seismograph pre-stack seismic data interpolation method based on graph signal constraints of any one of claims 1 to 3.
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