CN114397700A - Node seismograph pre-stack seismic data interpolation method, device, equipment and storage medium based on graph signal constraint - Google Patents

Node seismograph pre-stack seismic data interpolation method, device, equipment and storage medium based on graph signal constraint Download PDF

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CN114397700A
CN114397700A CN202210095036.7A CN202210095036A CN114397700A CN 114397700 A CN114397700 A CN 114397700A CN 202210095036 A CN202210095036 A CN 202210095036A CN 114397700 A CN114397700 A CN 114397700A
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王治国
杨阳
高静怀
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Xian Jiaotong University
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Abstract

The invention discloses a graph signal constraint-based pre-stack seismic data interpolation method, a device, equipment and a storage medium for a node seismograph, which aim at pre-stack seismic data interpolation acquired by an irregularly (randomly) deployed node seismograph, simultaneously consider the geometric structure and low rank of seismic data, construct the seismic data into an undirected graph, generate a graph variation regularization term according to the undirected graph, introduce the regularization term and a nuclear norm regularization term into the provided optimization problem, and solve the optimization problem by using a Bregman segmentation algorithm, thereby obtaining complete and high-quality seismic data.

Description

Node seismograph pre-stack seismic data interpolation method, device, equipment and storage medium based on graph signal constraint
Technical Field
The invention belongs to the technical field of seismic exploration, and relates to a graph signal constraint-based pre-stack seismic data interpolation method acquired by a nodal seismograph, in particular to a graph signal constraint-based pre-stack seismic data interpolation method, a graph signal constraint-based pre-stack seismic data interpolation device, equipment and a storage medium for the nodal seismograph.
Background
The influence of various adverse factors of field acquisition of seismic data, particularly irregular (random) large-scale deployment of node seismograph equipment in recent years, causes the appearance of missing, bad track and spatial false frequency of seismic signals acquired by the node seismograph. Such missing seismic data severely affects the processing and interpretation of subsequent seismic data, such as techniques of high resolution processing, migration imaging, structural interpretation, reservoir characterization, and the like. Therefore, interpolating (recovering) complete and regular pre-stack seismic data from pre-stack seismic data acquired by incomplete and irregular node seismographs has important significance for subsequent seismic processing and interpretation.
The interpolation of seismic data can be divided into three categories according to the mathematical principle of interpolation: wave equation-based interpolation methods, filter-based interpolation methods, and mathematical transform-based seismic interpolation methods. The seismic interpolation method based on the wave equation is to interpolate according to the causal correlation between seismic data. Fomel (2003) proposes a seismic interpolation method based on wave equations and finite difference filtering. Ramfrez (2006) proposes a seismic interpolation method based on the wave equation finite aperture migration concept. Although the method has good effect, the seismic interpolation method based on the fluctuation method has higher requirement on the precision of the velocity field. The seismic interpolation method based on the filter mainly designs a prediction filter algorithm to realize the seismic interpolation technology. Porsani (1999) proposed a modified Spitz method that works well with regular signals, but this class of methods has a multi-solution to irregular sampling, limiting the effect of seismic interpolation. The seismic interpolation method based on mathematical transformation is a seismic interpolation method which is widely applied at present, and the method mainly converts missing seismic data into a certain mathematical transformation domain and interpolates the seismic data in the mathematical transformation domain so as to obtain complete seismic data. Von Fei et al (2013) combines curvelet transformation and focus transformation to provide a seismic data interpolation method based on the L1 norm regularization problem. Liu, et al (2013) propose a seismic interpolation method based on Seislet, which can realize anti-aliasing interpolation. Liu and Sacchi (2004) propose a seismic interpolation method based on Fourier transform. In addition to this, mathematical transformations such as Radom transformation (Yu et al, 2007), dictionary learning (Sun et al, 2018), and the like are often used for seismic interpolation. The above techniques have 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 seismic interpolation by using sparsity constraint, but the method does not consider the geometric structure of seismic data.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a node seismograph prestack seismic data interpolation method, a node seismograph prestack seismic data interpolation device, node seismograph prestack seismic data interpolation equipment and a node seismograph prestack seismic data interpolation storage medium based on graph signal constraint, which can effectively solve the technical problems that the geometric structure of seismic data is not considered in the prior art, and the velocity field is inaccurate due to the fact that the precision cannot be met, and can obtain complete and high-quality seismic data.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
the invention discloses a node seismograph prestack seismic data interpolation method based on graph signal constraint, which comprises the following steps of: aiming at the interpolation of incomplete seismic data before stacking, 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 the provided optimization problem, solving the optimization problem by using a Bregman segmentation algorithm, and obtaining complete and high-quality seismic data.
Preferably, the node seismograph prestack seismic data interpolation method based on the graph signal constraint comprises the following steps:
1) acquiring incomplete two-dimensional observation data before stacking, and preprocessing the two-dimensional observation data;
2) generating an undirected graph according to the preprocessed seismic data and considering the geometrical structure of the preprocessed seismic data, and constructing an optimization model containing graph regularization items;
3) solving the optimization model according to a Bregman segmentation algorithm to obtain the optimal X outputopt；
4) Optimal X for outputoptPerforming inverse blocking processing to obtain reconstructed seismic data Sopt。
Further preferably, the step 1) is specifically operated as follows:
acquiring incomplete node seismograph two-dimensional observation data before stacking, recording the data as S, and dividing the node seismograph two-dimensional seismic data into N blocks, wherein the size of each block is M-P multiplied by Q, and P and Q are the sizes of the blocks; reordering each block of P × Q size into a column vector to obtain preprocessed seismic data
Figure BDA0003490499390000031
Assume that the sampling matrix is J e {0,1}M×NThen preprocessed seismic data
Figure BDA0003490499390000032
And reconstructed seismic data
Figure BDA0003490499390000033
Expressed as:
Figure BDA00034904993900000310
indicating matrix dot product and N indicating white gaussian noise.
Still more preferably, the step 2) is specifically operated as follows:
when preprocessed seismic data
Figure BDA0003490499390000034
When known, solving the reconstructed seismic data X uses an inverse problem to solve:
Figure BDA0003490499390000035
wherein ,
Figure BDA0003490499390000036
represents the Frobenius norm,
Figure BDA0003490499390000037
representing constraints on reconstructed seismic data, λ being a regularization parameter(ii) a The preprocessed seismic data have low rank characteristics, and the geometry of the seismic data is considered, the above formula is rewritten as follows:
Figure BDA0003490499390000038
wherein | X | Y luminance*Denotes the nuclear norm, λ1 and λ1Is a regularization parameter;
Figure BDA0003490499390000039
representing a view variation regularization term that takes into account the inter-tile data geometry, μmax(A) Representing the maximum eigenvalue of matrix a.
Still more preferably, the step 3) is specifically operated as follows:
introducing an intermediate variable Z, and writing an optimization model into an optimization model with constraints:
Figure BDA0003490499390000041
s.t.X＝Z
converting the constrained optimization model into an unconstrained optimization model according to a Lagrange multiplier method:
Figure BDA0003490499390000042
wherein U represents an intermediate variable, UTRepresenting the transposition of a variable U, with rho being a regularization parameter;
according to the Bregman segmentation principle, the optimization model is divided into three sub-optimization problems:
Figure BDA0003490499390000043
Figure BDA0003490499390000044
Uk+1＝Uk+ρ(Xk+1-Zk+1) (18)
the first sub-optimization problem is a typical L2 norm optimization problem whose solution is:
Figure BDA0003490499390000045
wherein vec (·) indicates rearranging a certain matrix into a column vector according to columns, and diag (·) indicates generating a diagonal matrix from a certain column vector, and elements on the diagonal of the diagonal matrix are the column vector.
Figure BDA0003490499390000046
wherein
Figure BDA0003490499390000047
Represents the Kronecker product, INRepresenting an N-dimensional identity matrix, IMNAn identity matrix representing the dimension of MN;
the solution of the second sub-optimization problem is:
Figure BDA0003490499390000048
wherein, SVDT (X, rho) E Lambda (Q, rho) VTΛ (Q, ρ) ═ sign (Q) max (| Q | - ρ, 0); e, Q and 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 a stopping condition is met, i.e. the maximum iteration number or the error loss function is reached
Figure BDA0003490499390000049
Reaches 0.01, and outputs the optimal Xopt。
More preferably, in step 2), a graph variation constraint term is introduced by considering the geometric structure among the block data, an undirected graph is generated from the preprocessed prestack seismic data, and then the graph variation constraint term is defined according to the undirected graph;
pre-processed pre-stack seismic data
Figure BDA0003490499390000051
Generating an undirected graph
Figure BDA0003490499390000052
wherein ,
Figure BDA0003490499390000053
is the combination of the nodes of the undirected graph, and the number of the nodes of the undirected graph is N;
Figure BDA0003490499390000054
is the geometry of all edges of the undirected graph; the matrix A is a weight matrix of the undirected graph, and the (i, j) th element in the weight matrix A
Figure BDA0003490499390000055
Representing the weight between the ith node and the jth node;
the (i, j) th element in the weight matrix A
Figure BDA0003490499390000056
Is defined as:
Figure BDA0003490499390000057
the graph variation regularization term is defined as:
Figure BDA0003490499390000058
wherein ,μmax(A) Representing the maximum eigenvalue of matrix a.
The invention also discloses a device for realizing the node seismograph prestack 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 the pre-stack incomplete two-dimensional observation data;
the model construction unit is used for constructing a model of the preprocessed seismic data to obtain an optimized model;
a model solving unit for solving the optimized model by Bregman segmentation algorithm to obtain the optimal output Xopt；
An inverse blocking unit for aligning the optimal XoptProcessing to obtain reconstructed seismic data Sopt。
The invention also discloses computer equipment 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 is executed by a processor to realize the steps of the node seismograph pre-stack seismic data interpolation method based on the graph signal constraint.
Compared with the prior art, the invention has the following beneficial effects:
the invention discloses a prestack seismic data interpolation method based on graph signal constraint, in particular to prestack seismic data interpolation acquired by irregularly (randomly) deployed node seismographs. Compared with the seismic interpolation method based on the wave equation, the method provided by the invention does not need an accurate velocity field. Compared with the seismic interpolation method of the mathematical transform domain, the method provided by the invention introduces the constraint of the 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 reconstruction of synthetic seismic data; wherein (a) is a default 30% synthetic seismic record; (b) are reconstructed synthetic seismic records.
FIG. 3 is a result of a prestack shot gather seismic data reconstruction; wherein, (a) is the original pre-stack shot gather seismic data; (b) stacking the forward shot gather seismic records by default 30%; (c) and collecting seismic records for the reconstructed folded-ahead shot.
Fig. 4 generates a schematic diagram of an undirected graph.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or 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 accompanying drawings:
the invention discloses a prestack seismic data interpolation method based on graph signal constraint, in particular to prestack seismic data interpolation acquired by irregularly (randomly) deployed node seismographs. The method specifically comprises the following steps:
1) acquiring prestack incomplete two-dimensional observation data S, and preprocessing prestack seismic data:
and acquiring pre-stack incomplete two-dimensional observation data, particularly incomplete pre-stack seismic data acquired by a node seismograph, and recording the data as S. Since the seismic data is default for a full trace, the seismic data needs to be rearranged in blocks. Two-dimensional seismic data is divided into N blocks, where each block has a size M ═ P × Q, where P and Q are block sizes. Reordering each block of P × Q size into a column vector to obtain processed data
Figure BDA0003490499390000071
Assume that the sampling matrix is J e {0,1}M×NThen pre-processing the seismic data
Figure BDA0003490499390000072
And reconstructed seismic data
Figure BDA0003490499390000073
Expressed as:
Figure BDA0003490499390000078
wherein
Figure BDA0003490499390000079
Indicating matrix dot product and N indicating white gaussian noise.
2) Constructing an optimization model according to the preprocessed seismic data:
when preprocessed seismic data
Figure BDA0003490499390000074
When known, solving the reconstructed seismic data X may utilize an inverse problem to solve:
Figure BDA0003490499390000075
wherein ,
Figure BDA0003490499390000076
represents the Frobenius norm,
Figure BDA0003490499390000077
representing constraints on the reconstructed seismic data, λ is a regularization parameter. The preprocessed seismic data have low rank characteristics, and the geometry of the seismic data is considered, the above formula can be rewritten as follows:
Figure BDA0003490499390000081
wherein | X | Y luminance*Representing the nuclear norm. Lambda [ alpha ]1 and λ1Is a regularization parameter.
Figure BDA0003490499390000082
A graph variation regularization term is represented that takes into account the geometry between tile data. Mu.smax(A) Representing the maximum eigenvalue of matrix a.
Pre-processed seismic data
Figure BDA0003490499390000083
Generating an undirected graph
Figure BDA0003490499390000084
wherein ,
Figure BDA0003490499390000085
is the combination of the nodes of the undirected graph, and the number of the nodes of the undirected graph is N;
Figure BDA0003490499390000086
is the geometry of all edges of the undirected graph; matrix a is the weight matrix of the undirected graph. The (i, j) th element in the weight matrix A
Figure BDA0003490499390000087
Representing the weight between the ith node and the jth node. In the present invention, the (i, j) th element in the weight matrix A
Figure BDA0003490499390000088
Is defined as:
Figure BDA0003490499390000089
3) solving the optimization model according to a Bregman segmentation algorithm:
in order to solve the optimization model conveniently, an intermediate variable Z is introduced, and then the optimization model can be written as an optimization model with constraints:
Figure BDA00034904993900000810
s.t.X＝Z
further, the constrained optimization model is converted into an unconstrained optimization model according to a lagrange multiplier method:
Figure BDA00034904993900000811
wherein U represents an intermediate variable, UTRepresenting the transpose of the variable U. ρ is the regularization parameter.
According to the Bregman segmentation principle, the above-described optimization model can be divided into three sub-optimization problems:
Figure BDA00034904993900000812
Uk+1＝Uk+ρ(Xk+1-Zk+1) (30)
the first sub-optimization problem is a typical L2 norm optimization problem whose solution is:
Figure BDA00034904993900000813
where vec (·) denotes rearranging a matrix into a column vector by column. diag (·) denotes that a column vector is generated into a diagonal matrix, and the elements on the diagonal of the diagonal matrix are the column vector.
Figure BDA0003490499390000091
wherein
Figure BDA0003490499390000092
Represents the Kronecker product, INAn N-dimensional identity matrix is represented. I isMNAn identity matrix of dimension MN is represented.
The solution of the second sub-optimization problem is:
Figure BDA0003490499390000093
where, SVDT (X, ρ) ═ E Λ (Q, ρ) VT, Λ (Q, ρ) ═ sign (Q) max (| Q | - ρ, 0). E, Q and V are matrixes obtained after the matrix X is decomposed by singular values. sign (·) represents a sign function.
Outputting the optimal X by iterating the three sub-optimization problems until the stop condition is metopt。
4) Optimal X for outputoptPerforming inverse blocking processing to obtain reconstructed seismic data Sopt。
Numerical simulation result
Synthesizing seismic record data
FIG. 1 shows a flow chart of the present invention. The resultant data is processed according to the flowchart, and the result is shown in fig. 2. FIG. 2 shows the results after reconstruction of the default 30% of the synthetic seismic data. FIG. 2(a) is a random default of 30% synthetic seismic data having 60 seismic records with 512 time samples per record and a 1ms sampling interval. FIG. 2(b) shows the result of the reconstruction according to the method of the present invention. It can be found that the reconstruction of the same phase axis of the linear type has better effect than that of the same phase axis of the curve type, and especially the same phase axis with uniform transverse distribution.
Actual stacked-in-front shot gather seismic data profile
FIG. 3 shows the results of a default 30% reconstruction of pre-stack shot gather seismic data acquired by a nodal seismograph. FIG. 3(a) is raw pre-stack shot gather seismic data with 100 traces, 800 time samples per trace, and a time sample interval of 1 ms. Fig. 3(b) shows seismic data with a default of 30% and a random default of black parts. Fig. 3(c) shows the result after reconstruction. Obviously, the method provided by the invention can reconstruct the original seismic data to a certain extent, and provides a favorable basis for further improving the method subsequently. To further illustrate the graph regularization generation process provided by the present invention, taking fig. 3 as an example, first block the original data, and extract the blocked data into column vectors to generate a new matrix. According to the similarity between each block, an undirected graph is constructed, a weight matrix A is generated, then a graph variation regularization item is regenerated and introduced into a new generator matrix.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.

Claims (9)

1. A node seismograph prestack seismic data interpolation method based on graph signal constraint is characterized by comprising the following steps: aiming at the interpolation of incomplete seismic data before stacking, 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 the provided optimization problem, solving the optimization problem by using a Bregman segmentation algorithm, and obtaining complete and high-quality seismic data.
2. The graph signal constraint-based nodal seismograph pre-stack seismic data interpolation method of claim 1, comprising the steps of:
1) acquiring incomplete two-dimensional observation data before stacking, and preprocessing the two-dimensional observation data;
2) generating an undirected graph according to the preprocessed seismic data and considering the geometrical structure of the preprocessed seismic data, and constructing an optimization model containing graph regularization items;
3) solving the optimization model according to a Bregman segmentation algorithm to obtain the optimal X outputopt；
4) Optimal X for outputoptPerforming inverse blocking processing to obtain reconstructed seismic data Sopt。
3. The graph signal constraint-based nodal seismograph pre-stack seismic data interpolation method of claim 2, wherein step 1) specifically operates as follows:
acquiring incomplete node seismograph two-dimensional observation data before stacking, recording the data as S, and dividing the node seismograph two-dimensional seismic data into N blocks, wherein the size of each block is M-P multiplied by Q, and P and Q are the sizes of the blocks; reordering each block of P × Q size into a column vector to obtain preprocessed seismic data
Figure FDA0003490499380000011
Assume that the sampling matrix is J e {0,1}M×NThen preprocessed seismic data
Figure FDA0003490499380000012
And reconstructed seismic data
Figure FDA0003490499380000013
Expressed as:
Figure FDA0003490499380000014
Figure FDA0003490499380000015
indicating matrix dot product and N indicating white gaussian noise.
4. The graph signal constraint-based nodal seismograph pre-stack seismic data interpolation method of claim 3, wherein step 2) specifically operates as follows:
when preprocessed seismic data
Figure FDA0003490499380000016
When known, solving the reconstructed seismic data X uses an inverse problem to solve:
Figure FDA0003490499380000017
wherein ,
Figure FDA0003490499380000018
represents the Frobenius norm,
Figure FDA0003490499380000019
representing constraints on the reconstructed seismic data, λ being a regularization parameter; the preprocessed seismic data have low rank characteristics, and the geometry of the seismic data is considered, the above formula is rewritten as follows:
Figure FDA0003490499380000021
wherein | X | Y luminance*Denotes the nuclear norm, λ1 and λ1Is a regularization parameter;
Figure FDA0003490499380000022
representing a view variation regularization term that takes into account the inter-tile data geometry, μmax(A) Representing the maximum eigenvalue of matrix a.
5. The graph signal constraint-based nodal seismograph pre-stack seismic data interpolation method of claim 4, wherein step 3) specifically operates as follows:
introducing an intermediate variable Z, and writing an optimization model into an optimization model with constraints:
Figure FDA0003490499380000023
converting the constrained optimization model into an unconstrained optimization model according to a Lagrange multiplier method:
Figure FDA0003490499380000024
wherein U represents an intermediate variable, UTRepresenting the transposition of a variable U, with rho being a regularization parameter;
according to the Bregman segmentation principle, the optimization model is divided into three sub-optimization problems:
Figure FDA0003490499380000025
Figure FDA0003490499380000026
Uk+1＝Uk+ρ(Xk+1-Zk+1) (7)
the first sub-optimization problem is a typical L2 norm optimization problem whose solution is:
Figure FDA0003490499380000027
wherein vec (·) indicates rearranging a certain matrix into a column vector according to columns, and diag (·) indicates generating a diagonal matrix from a certain column vector, and elements on the diagonal of the diagonal matrix are the column vector.
Figure FDA0003490499380000028
wherein
Figure FDA0003490499380000031
Represents the Kronecker product, INRepresenting an N-dimensional identity matrix, IMNAn identity matrix representing the dimension of MN;
the solution of the second sub-optimization problem is:
Figure FDA0003490499380000032
wherein, SVDT (X, rho) E Lambda (Q, rho) VTΛ (Q, ρ) ═ sign (Q) max (| Q | - ρ, 0); e, Q and 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 a stopping condition is met, i.e. the maximum iteration number or the error loss function is reached
Figure FDA0003490499380000033
Reaches 0.01, and outputs the optimal Xopt。
6. The graph signal constraint-based node seismograph prestack seismic data interpolation method of claim 4, wherein in the step 2), a graph variation constraint term is introduced by considering the geometric structure among block data, the preprocessed prestack seismic data are generated into an undirected graph, and then the graph variation constraint term is defined according to the undirected graph;
pre-processed pre-stack seismic data
Figure FDA0003490499380000034
Generating an undirected graph
Figure FDA0003490499380000035
wherein ,
Figure FDA0003490499380000036
is the combination of the nodes of the undirected graph, and the number of the nodes of the undirected graph is N;
Figure FDA0003490499380000037
is the geometry of all edges of the undirected graph; the matrix A is a weight matrix of the undirected graph, and the (i, j) th element in the weight matrix A
Figure FDA0003490499380000038
Representing the weight between the ith node and the jth node;
the (i, j) th element in the weight matrix A
Figure FDA0003490499380000039
Is defined as:
Figure FDA00034904993800000310
the graph variation regularization term is defined as:
Figure FDA00034904993800000311
wherein ,μmax(A) Representing the maximum eigenvalue of matrix a.
7. The device for realizing the graph signal constraint-based node seismograph pre-stack seismic data interpolation method according to any one of claims 1 to 6, is characterized by comprising the following steps:
the seismic data acquisition unit is used for preprocessing the pre-stack seismic data to obtain the pre-stack incomplete two-dimensional observation data;
the model construction unit is used for constructing a model of the preprocessed seismic data to obtain an optimized model;
a model solving unit for solving the optimized model by Bregman segmentation algorithm to obtain the optimal output Xopt；
An inverse blocking unit for aligning the optimal XoptProcessing to obtain reconstructed seismic data Sopt。
8. A computer device comprising a memory and a processor, the memory storing a computer program, wherein the processor when executing the computer program implements the steps of the graph signal constraint based nodal seismograph pre-stack seismic data interpolation method of any one of claims 1 to 6.
9. A computer readable storage medium storing a computer program which when executed by a processor implements the steps of the graph signal constraint based nodal seismograph pre-stack seismic data interpolation method of any one of claims 1 to 6.
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