CN113341460B - Circulating minimization seismic data reconstruction method based on continuous operator splitting - Google Patents
Circulating minimization seismic data reconstruction method based on continuous operator splitting Download PDFInfo
- Publication number
- CN113341460B CN113341460B CN202110637320.8A CN202110637320A CN113341460B CN 113341460 B CN113341460 B CN 113341460B CN 202110637320 A CN202110637320 A CN 202110637320A CN 113341460 B CN113341460 B CN 113341460B
- Authority
- CN
- China
- Prior art keywords
- reconstruction
- seismic data
- data
- operator
- original
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 139
- 230000009977 dual effect Effects 0.000 claims abstract description 41
- 238000005457 optimization Methods 0.000 claims abstract description 29
- 230000008569 process Effects 0.000 claims description 25
- 238000004364 calculation method Methods 0.000 claims description 11
- 238000005070 sampling Methods 0.000 claims description 10
- 125000004122 cyclic group Chemical group 0.000 claims description 7
- 238000013075 data extraction Methods 0.000 claims description 7
- 239000011159 matrix material Substances 0.000 claims description 6
- 238000003860 storage Methods 0.000 claims description 6
- 238000010276 construction Methods 0.000 claims description 5
- 238000009826 distribution Methods 0.000 claims description 5
- 238000000605 extraction Methods 0.000 claims description 3
- 230000009466 transformation Effects 0.000 claims description 2
- 238000010586 diagram Methods 0.000 description 9
- 238000004590 computer program Methods 0.000 description 7
- 238000012545 processing Methods 0.000 description 5
- 238000002474 experimental method Methods 0.000 description 4
- 230000006870 function Effects 0.000 description 4
- 230000009286 beneficial effect Effects 0.000 description 3
- 230000008901 benefit Effects 0.000 description 3
- 230000008859 change Effects 0.000 description 3
- 230000000694 effects Effects 0.000 description 3
- 238000001914 filtration Methods 0.000 description 3
- 238000004519 manufacturing process Methods 0.000 description 3
- 230000004048 modification Effects 0.000 description 3
- 238000012986 modification Methods 0.000 description 3
- 230000002411 adverse Effects 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 238000002790 cross-validation Methods 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 230000008707 rearrangement Effects 0.000 description 1
- 238000011084 recovery Methods 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. for interpretation or for event detection
- G01V1/30—Analysis
- G01V1/306—Analysis for determining physical properties of the subsurface, e.g. impedance, porosity or attenuation profiles
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. for interpretation or for event detection
- G01V1/32—Transforming one recording into another or one representation into another
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V2210/00—Details of seismic processing or analysis
- G01V2210/60—Analysis
- G01V2210/62—Physical property of subsurface
Landscapes
- Engineering & Computer Science (AREA)
- Remote Sensing (AREA)
- Physics & Mathematics (AREA)
- Life Sciences & Earth Sciences (AREA)
- Acoustics & Sound (AREA)
- Environmental & Geological Engineering (AREA)
- Geology (AREA)
- General Life Sciences & Earth Sciences (AREA)
- General Physics & Mathematics (AREA)
- Geophysics (AREA)
- Geophysics And Detection Of Objects (AREA)
Abstract
The invention provides a circulating minimization seismic data reconstruction method based on continuous operator splitting, which is used for acquiring acquired original seismic data and extracting an observation operator from the acquired original seismic data in a self-adaptive manner; constructing an optimization problem of seismic data reconstruction according to an inversion theory based on the original seismic data and the observation operator; converting the constructed reconstruction optimization problem into a dual sub problem and an original sub problem by adopting a continuous strategy and a variational operator splitting method; minimizing the dual sub problem by using the adjacent gradient, minimizing the original sub problem by using the non-local mean value, and continuously circulating until the convergence condition is met to obtain the optimal reconstruction feasible solution; and keeping the original seismic data unchanged, and placing the optimal feasible reconstruction solution at the position which is not observed to realize the reconstruction of the seismic data. The method has higher flexibility and adaptability, can efficiently and highly accurately reconstruct the undersampled seismic data, and effectively improves the continuity of seismic reflection.
Description
Technical Field
The invention belongs to the technical field of seismic data reconstruction, and particularly relates to a circulating minimization seismic data reconstruction method based on continuous operator splitting.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
In the field acquisition process of seismic data, due to the influences of factors such as the landform and the landscape of a work area (desert, mountain land, marsh, forest and the like), surface buildings (town, dam, factory, traffic facility and the like) and the like, a seismic source and a detector can not be placed on a pre-designed survey network frequently, so that the phenomenon of undersampling of the seismic data is caused in space. Undersampling of seismic data can result in loss of geophysical information reflecting characteristics of subsurface media, thereby seriously affecting the accuracy of subsequent oil and gas resource exploration. In order to recover the missing geophysical information and improve the accuracy of subsequent oil and gas exploration, high-quality reconstruction of undersampled seismic data becomes an important task.
To solve the above problems, the inventors have found that various seismic data reconstruction methods have been proposed, which can be roughly classified into four categories, but these seismic data reconstruction methods have certain limitations, and the following specific technical analyses are performed:
the first category is reconstruction methods based on prediction error filters, such as temporal-spatial prediction error filtering, frequency-bistatic prediction error filtering, and unsteady frequency-wavenumber prediction error filtering. The method firstly estimates a prediction error filter from the low-frequency component of the data according to the principle of least square method, and then predicts the high-frequency component of the data by using the filter, thereby realizing the reconstruction of the undersampled data. Since the method requires that the seismic data satisfy the condition of equidistant sampling, it is only suitable for reconstruction of regular undersampled data.
The second category, wave equation based reconstruction methods, which reconstruct seismic data based on the propagation principle of seismic waves. In particular, reconstruction is achieved by inverting an operator that connects the subsurface model to known data. Although the physical significance of the method is clear, the method is limited by the estimation accuracy of the underground speed prior.
And the third kind is a reconstruction method based on compressed sensing, and the method achieves the aim of reconstructing undersampled data by improving the sparsity in a transform domain. Although such methods are simple in principle, they require optimization of sparse transforms, optimization algorithms, and multiple iteration parameters, and cross-validation makes the practical application of such methods not very efficient.
And the fourth category is a reconstruction method based on a reduced rank theory. The basic assumption of such an approach is that the hankel matrix of seismic data rearrangement has low rank characteristics, which are destroyed by undersampling, resulting in an increased rank of the hankel matrix. Thus, such methods achieve reconstruction of undersampled data by reducing the rank of the hankel matrix. In fact, only seismic data containing linear homoaxes can satisfy the low-rank assumption, that is, the method is only suitable for reconstructing seismic data containing linear homoaxes, and cannot solve the problem of high-precision reconstruction of nonlinear homoaxes.
Disclosure of Invention
The invention provides a circulating minimization seismic data reconstruction method based on continuous operator splitting, which has higher flexibility and adaptability, can efficiently and highly accurately reconstruct undersampled seismic data, effectively improves the continuity of seismic reflection, greatly improves the signal-to-noise ratio and fidelity of reconstructed data, and provides complete and credible basic data for subsequent oil and gas resource exploration work such as construction explanation, reservoir description and the like.
According to some embodiments, the invention adopts the following technical scheme:
a circular minimization seismic data reconstruction method based on continuous operator splitting comprises the following steps:
acquiring acquired original seismic data, and adaptively extracting an observation operator from the acquired original seismic data;
constructing an optimization problem of seismic data reconstruction according to an inversion theory based on the original seismic data and the observation operator;
converting the constructed reconstruction optimization problem into a dual sub problem and an original sub problem by adopting a continuous strategy and a variational operator splitting method;
minimizing the dual sub problem by using the adjacent gradient, minimizing the original sub problem by using the non-local mean value, and continuously circulating until the convergence condition is met to obtain the optimal reconstruction feasible solution;
keeping the original seismic data unchanged, and placing the optimal feasible reconstruction solution at the position which is not observed to realize the reconstruction of the seismic data.
As an alternative embodiment, the specific process from which the observation operator is adaptively extracted includes: according to the spatial distribution rule of missing tracks, empty tracks and dead tracks in the field data acquisition, adaptively extracting an observation operator G according to the following formula:
wherein [ G ]]ijRow i and column j elements representing operator G, where i e [1, Nt],j∈[1,Nx]，NtNumber of seismic sampling points, NxFor the number of seismic sampling traces, Θ represents the set of spatial location indices for empty, missing, and dead traces.
As an alternative embodiment, the optimization problem of seismic data reconstruction is:
wherein G is an observation operator, D is collected incomplete seismic data, M is complete seismic data to be reconstructed,
squared in the L2 norm, λ is a penalty parameter, and Φ (-) represents a priori knowledge of the seismic data.
As an alternative embodiment, the dual and primitive sub-problems are described as:
wherein Z isk+1For dual feasible solutions, Mk+1For reconstruction of a feasible solution, betakIn the case of a dual step size,
is the square of the norm of L2, DTFor transposing undersampled data D, ηkFor reconstructing the step size, GTFor the transpose of the observation operator G, k is the number of iterations.
As an alternative embodiment, in the process of minimizing the dual subproblem by using the adjacent gradient, the partial derivative of the dual subproblem is made zero, and the computation solution of the dual feasible solution is performed.
As an alternative embodiment, the specific process of minimizing the primitive subproblem using non-local means includes:
(1) keeping the dual feasible solution unchanged, and calculating process variables;
(2) a local window is defined from the process variable, and a data extraction window is slid in the local window to form a data subset;
(3) solving a reconstruction feasible solution based on the process variables, the data subsets and the reconstruction step length;
(4) and (4) sliding the local window, and repeating the steps (2) - (3) until the local window traverses the whole process variable.
In an alternative embodiment, the convergence condition is that the number of iterations is greater than a predetermined value.
As an alternative embodiment, the specific process of placing the optimal feasible solution for reconstruction at the unobserved location includes: obtaining an optimal reconstruction feasible solution MKAnd then, on the basis of keeping the original seismic data D unchanged, updating the seismic channels at the positions which are not observed according to an assignment formula, and further obtaining high-precision reconstruction data, wherein the assignment formula is as follows:
M*＝(I-G)MK+D
wherein I is an identity matrix, MKFor optimal reconstruction of a feasible solution, K is the set maximum number of iterations, M*Is the reconstructed complete data.
A cyclic minimization seismic data reconstruction system based on continuous operator splitting, comprising:
an extraction module configured to acquire acquired raw seismic data from which observation operators are adaptively extracted;
the construction optimization problem module is configured to construct an optimization problem of seismic data reconstruction according to an inversion theory based on the original seismic data and the observation operator;
the problem conversion module is configured to convert the constructed reconstruction optimization problem into a dual sub problem and an original sub problem by adopting a continuous strategy and a variable-fraction operator splitting method;
the solution calculation module is configured to minimize the dual sub-problem by using the adjacent gradient, minimize the original sub-problem by using the non-local mean value, and continuously circulate until the convergence condition is met to obtain the optimal reconstruction feasible solution;
and the data reconstruction module is configured to keep the original seismic data unchanged, and place the optimal feasible reconstruction solution at the position of the unobserved position to realize the reconstruction of the seismic data.
An electronic device comprising a memory and a processor and computer instructions stored on the memory and executed on the processor, the computer instructions, when executed by the processor, performing the steps of the above method.
A computer readable storage medium storing computer instructions which, when executed by a processor, perform the steps of the above method.
Compared with the prior art, the invention has the beneficial effects that:
the method can realize high-precision reconstruction of the seismic data, has simple and efficient process, no applicable limitation on the seismic data, eliminates the limitation and has good adaptability.
The invention converts the complex reconstruction problem into two simple sub-problems by a continuous strategy and a variational operator splitting method, effectively reduces the calculation complexity, obviously improves the reconstruction efficiency of the undersampled data and is more beneficial to the application in the actual production. In addition, the cyclic optimization of the two sub-problems by the adjacent gradient and the non-local mean value also enables the invention to effectively reduce the reconstruction amplitude artifact and improve the signal-to-noise ratio and the fidelity of the reconstruction data.
Compared with the conventional compressed sensing reconstruction method, the method has the advantages that on the basis of greatly improving the reconstruction efficiency, the change rule of the amplitude along with the offset can be better kept, and the continuity of seismic reflection is improved; compared with the traditional rank reduction reconstruction method, the method can simultaneously realize the high-precision reconstruction of the linear in-phase axis and the nonlinear in-phase axis, and has wider application range and application prospect.
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.
FIG. 1 is a flow chart of a method of cyclic minimization seismic data reconstruction based on continuous operator splitting.
Figure 2 is a forward modeling of model data for a reconstruction experiment.
FIG. 3 is a comparison graph of the reconstruction results of the model data by the conventional reconstruction method and the method of the present invention.
FIG. 4 is a comparison of the difference profile of the different method reconstruction results of FIG. 3 with the original model data.
FIG. 5 is field seismic data used for reconstruction experiments.
FIG. 6 is a comparison graph of the reconstruction results of the field data by the conventional reconstruction method and the method of the present invention.
FIG. 7 is a cross-sectional comparison of the difference between the reconstruction results of the different methods in FIG. 6 and the original field data.
The specific implementation mode is as follows:
the invention is further described with reference to the following figures and examples.
It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The invention provides a circulating minimization seismic data reconstruction method based on continuous operator splitting, which has higher flexibility and adaptability, can efficiently and highly accurately reconstruct undersampled seismic data, effectively improves the continuity of seismic reflection, greatly improves the signal-to-noise ratio and fidelity of reconstructed data, and provides complete and credible basic data for subsequent oil and gas resource exploration work such as construction explanation, reservoir description and the like.
The core steps of the invention comprise: firstly, according to an inversion theory, the seismic data acquired in the field and the extracted observation operator are used for constructing an optimization problem of seismic data reconstruction in a self-adaptive manner; secondly, in order to realize simple and efficient seismic data reconstruction, a constructed reconstruction optimization problem is converted into a simple dual sub problem and an original sub problem by adopting a continuous strategy and a variational operator splitting method; minimizing the dual sub-problem and the original sub-problem circularly through the adjacent gradient and the non-local mean value until the iteration times reach the convergence standard, and obtaining the optimal feasible reconstruction solution; and fourthly, on the basis of keeping the original acquired data unchanged, placing the optimal reconstruction feasible solution at the position which is not observed according to an assignment formula, and further realizing the high-precision reconstruction of the seismic data.
The invention is implemented by the following technical scheme, which specifically comprises the following steps:
(1) and adaptively extracting observation operators from the seismic data acquired in the field. According to the spatial distribution rule of missing tracks, empty tracks and dead tracks in field collected data, adaptively extracting an observation operator G according to the formula (1):
wherein [ G ]]ijThe ith row and j column element representing operator G (where i e [1, N ]t],j∈[1,Nx]，NtNumber of seismic sampling points, NxSampling traces for seismicNumber), Θ represents the set of spatial location indices for empty lanes, missing lanes, and dead lanes.
(2) And according to an inversion theory, constructing an optimization problem of seismic data reconstruction by using the acquired seismic data and the extracted observation operator. Specifically, the optimization problem of seismic data reconstruction can be constructed in the form of:
wherein D is the collected incomplete seismic data, M is the complete seismic data to be reconstructed,
squared in the L2 norm, λ is a penalty parameter, and Φ (-) represents a priori knowledge of the seismic data.
(3) And converting the constructed reconstruction optimization problem into a simple dual sub problem and an original sub problem by adopting a continuous strategy and a variational operator splitting method. Specifically, the dual sub-problem and the original sub-problem may be described as:
in the formula, Zk+1For dual feasible solutions, Mk+1For reconstruction of a feasible solution, betakIn the case of a dual step size,
is the square of the norm of L2, DTFor transposing undersampled data D, ηkFor reconstructing the step size, GTFor the transpose of the observation operator G, k is the number of iterations.
(4) Minimizing the dual sub-problem using the proximity gradient to obtain a dual feasible solution Zk+1. In particular, let the partial derivatives of the dual problemAnd (5) obtaining a calculation formula of a dual feasible solution as shown in the formula (5):
(5) minimizing primordial subproblems using non-local means to obtain a reconstruction feasible solution Mk+1. Specifically, the optimization of the original sub-problem by using the non-local mean value comprises the following steps:
(5-1) keeping the duality feasible solution Zk+1The process variable A is calculated by equation (6) without changek+1：
Ak+1＝Mk-ηkGTZk+1 (6)
(5-2) from the Process variable Ak+1Middle demarcation local window Ν ∈ Rp×pAnd sliding a data extraction window Q ∈ R in the local windows ×s(s<p) to form a data subset U ═ ak+1(x1),Ak+1(x2),...,Ak+1(xn)]Wherein A isk+1(xi) Representing data extraction windows
Of (2) process variable data, xi(1 ≦ i ≦ n) is the center of the data extraction window, and n is the total number of data extraction windows.
(5-3) calculating a reconstruction feasible solution M according to the formula (7)k+1(xi)：
In the formula, Mk+1(xi) Is represented by xiReconstruction in the window of data extraction for the center is feasible,
||·||2representing the square of the euclidean distance.
(5-4) slide local window Ν, and repeat steps (5-2) and (5-3) until the local window traverses the entire process variable ak +1Until now.
(6) And repeating the fourth step to the fifth step until the iteration times K are greater than the preset value K, and stopping iteration.
(7) And updating the seismic channels at the positions which are not observed by using the assignment formula to realize the high-quality reconstruction of the seismic data. Obtaining an optimal reconstruction feasible solution MKAnd then, on the basis of keeping the original collected seismic data D unchanged, updating the seismic channels at the positions which are not observed according to the formula (8), and further obtaining high-precision reconstruction data.
M*＝(I-G)MK+D (8)
Wherein I is an identity matrix, MKFor optimal reconstruction of a feasible solution, K is the set maximum number of iterations, M*Is the reconstructed complete data.
As an exemplary embodiment, FIG. 1 is a flow diagram of a method for cyclic minimization of seismic data reconstruction based on continuous operator splitting.
Firstly, adaptively extracting observation operators from seismic data acquired in the field according to the spatial distribution rule of missing channels, empty channels and dead channels. And then according to an inversion theory, constructing an optimization problem of seismic data reconstruction by using the seismic data acquired in the field and the extracted observation operator, and then converting the reconstruction optimization problem into a simple dual sub-problem and an original sub-problem by adopting a continuous strategy and a variational operator splitting method. And circularly minimizing the dual sub-problem and the original sub-problem through the adjacent gradient and the non-local mean value until the iteration number reaches the convergence standard, and obtaining the optimal feasible reconstruction solution. And finally, on the basis of keeping the original acquired data unchanged, placing the obtained reconstruction feasible solution at the position which is not observed according to an assignment formula, and further realizing the high-precision reconstruction of the seismic data.
Fig. 2 is modeled data for a reconstruction experiment in forward evolution, where fig. 2a is fully sampled data in forward evolution and fig. 2b is undersampled data sampled at 50% random. As can be seen from the figure, random sampling causes the loss of partial seismic traces of the model data, and causes the discontinuity phenomenon of the seismic co-directional axis, which can have adverse effects on the subsequent geophysical processing and interpretation processes.
Fig. 3 is a comparison graph of reconstruction results of the conventional reconstruction method and the method of the present invention on model data, where fig. 3a is a reconstruction result of a compressed sensing reconstruction method, fig. 3b is a reconstruction result of a reduced rank reconstruction method, and fig. 3c is a reconstruction result of the method of the present invention. It can be seen from fig. 3 that the missing seismic traces processed by the three methods all achieve recovery, but the compressive sensing method cannot effectively maintain the change rule of the amplitude with the offset, as shown in the circle of fig. 3 a. Because the model data meets the low-rank assumption of the reduced-rank reconstruction method, the reduced-rank reconstruction method obtains a relatively good reconstruction result. In order to quantitatively compare the reconstruction accuracy of the reduced rank reconstruction method and the reconstruction accuracy of the method, the SNR (signal to noise ratio) of 20log is introduced10(||M*||2/||M*-M||2) To perform the evaluation. Specifically, the higher the signal-to-noise ratio of the reconstruction result is, the closer the reconstruction result is to the real data is, and the higher the reconstruction accuracy is. The SNR of a reconstruction result of the compressed sensing reconstruction method is 16.56dB, and the calculation time is 76.34 s; the SNR of the reconstruction result of the reduced rank reconstruction method is 22.08dB, and the calculation time is 56.52 s; the SNR of the reconstruction result of the method is 27.43dB, and the calculation time is 25.03 s. From the aspect of signal to noise ratio, the reconstruction precision of the method is far higher than that of a compressed sensing reconstruction method and a reduced rank reconstruction method. In addition, the reconstruction time consumption of the method is far lower than that of the traditional compressed sensing reconstruction method and the reduced rank reconstruction method. Therefore, compared with the traditional reconstruction method, the reconstruction method has higher reconstruction accuracy and can remarkably improve the reconstruction efficiency.
Fig. 4 is a comparison graph of difference profiles between the reconstruction result of the different method and the original model data in fig. 3, fig. 4a is a difference profile between the reconstruction result of the compressed sensing reconstruction method and the original model data, fig. 4b is a difference profile between the reconstruction result of the reduced rank reconstruction method and the original model data, and fig. 4c is a difference profile between the reconstruction result of the method of the present invention and the original model data. As can be seen from the figure, the reconstruction error of the compressed sensing reconstruction method is the largest, the reconstruction error of the reduced rank reconstruction method is the second, and the reconstruction error of the method is the smallest, so that the method has the advantage of better keeping the change rule of the amplitude along with the offset.
FIG. 5 is field seismic data for a reconstruction experiment, where FIG. 5a is fully sampled field seismic data and FIG. 5b is undersampled data from 50% random observations. As can be seen from the figure, the seismic data in the field contains more and more complex nonlinear seismic event axes, and the existence of the nonlinear event axes poses a serious challenge to the high-precision reconstruction of the seismic data.
Fig. 6 is a comparison graph of the reconstruction results of the field data by the conventional reconstruction method and the method of the present invention, wherein fig. 6a is the reconstruction result of the compressed sensing reconstruction method, fig. 6b is the reconstruction result of the reduced rank reconstruction method, and fig. 6c is the reconstruction result of the method of the present invention. The SNR of the reconstruction result of the compressed sensing reconstruction method is 15.39dB, and the calculation time is 338.98 s; the SNR of the reconstruction result of the reduced rank reconstruction method is 11.21dB, and the calculation time is 224.84 s; the SNR of the reconstruction result of the method is 19.39dB, and the calculation time is 82.14 s. By analyzing the signal-to-noise ratio and calculating time, the method disclosed by the invention can realize the optimal reconstruction effect and effectively reduce the reconstruction time consumption compared with the traditional compressed sensing reconstruction method and the reduced rank reconstruction method, thereby being more beneficial to application in actual production.
FIG. 7 is a comparison graph of the difference cross section between the reconstruction result of the different method and the original field data in FIG. 6, FIG. 7a is a difference cross section between the reconstruction result of the compressed sensing reconstruction method and the original field data, FIG. 7b is a difference cross section between the reconstruction result of the reduced rank reconstruction method and the original field data, and FIG. 7c is a difference cross section between the reconstruction result of the method of the present invention and the original field data. As can be seen from the figure, the amplitude artifact of the reduced-rank reconstruction method is the largest because the in-phase axis of the field seismic data is non-linear, and the non-linear in-phase axis does not satisfy the basic assumption of the reduced-rank reconstruction method, so that the reconstruction effect is the worst. In contrast, the method disclosed by the invention does not depend on any hypothesis of the seismic data, so that the amplitude artifact can be effectively avoided when the nonlinear in-phase axis is reconstructed, and the seismic data reconstruction with high precision is realized.
The invention also provides the following product examples:
a cyclic minimization seismic data reconstruction system based on continuous operator splitting, comprising:
an extraction module configured to acquire acquired raw seismic data from which observation operators are adaptively extracted;
the construction optimization problem module is configured to construct an optimization problem of seismic data reconstruction according to an inversion theory based on the original seismic data and the observation operator;
the problem transformation module is configured to transform the constructed reconstruction optimization problem into a dual sub problem and an original sub problem by adopting a continuous strategy and a variational operator splitting method;
the solution calculation module is configured to minimize the dual sub-problem by using the adjacent gradient, minimize the original sub-problem by using the non-local mean value, and continuously circulate until the convergence condition is met to obtain the optimal reconstruction feasible solution;
and the data reconstruction module is configured to keep the original seismic data unchanged, and place the optimal feasible reconstruction solution at the position of the unobserved position to realize the reconstruction of the seismic data.
An electronic device comprising a memory and a processor and computer instructions stored on the memory and executed on the processor, the computer instructions, when executed by the processor, performing the steps of the above method.
A computer readable storage medium storing computer instructions which, when executed by a processor, perform the steps of the above method.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.
Claims (8)
1. A circular minimization seismic data reconstruction method based on continuous operator splitting is characterized by comprising the following steps: the method comprises the following steps:
acquiring acquired original seismic data, and adaptively extracting an observation operator from the acquired original seismic data;
constructing an optimization problem of seismic data reconstruction according to an inversion theory based on the original seismic data and the observation operator;
converting the constructed reconstruction optimization problem into a dual sub problem and an original sub problem by adopting a continuous strategy and a variational operator splitting method;
minimizing the dual sub problem by using the adjacent gradient, minimizing the original sub problem by using the non-local mean value, and continuously circulating until the convergence condition is met to obtain the optimal reconstruction feasible solution;
keeping the original seismic data unchanged, and placing the optimal feasible reconstruction solution at the position which is not observed to realize the reconstruction of the seismic data;
the specific process of adaptively extracting the observation operator from the observation operator comprises the following steps: according to the spatial distribution rule of the missing track, the empty track and the dead track in the field data acquisition, an observation operator G is adaptively extracted according to the following formula:
wherein [ G ]]ijRow i and column j elements representing operator G, where i e [1, Nt],j∈[1,Nx]，NtNumber of seismic sampling points, NxFor the seismic sampling trace number, Θ represents the spatial position index of the empty, missing and dead tracesCollecting;
the optimization problem of seismic data reconstruction is as follows:
wherein G is an observation operator, D is collected incomplete seismic data, M is complete seismic data to be reconstructed,
is the square of the norm of L2, λ is a penalty parameter, Φ (·) represents the prior knowledge of the seismic data;
the dual and primitive sub-problems are described as:
wherein Z isk+1For dual feasible solutions, Mk+1For reconstruction of a feasible solution, betakIn the case of a dual step size,
is the square of the norm of L2, DTFor transposing undersampled data D, ηkFor reconstruction of the step size, GTFor the transpose of the observation operator G, k is the number of iterations.
2. The method as claimed in claim 1, wherein the method comprises the following steps: and in the process of minimizing the dual sub problem by using the adjacent gradient, making the partial derivative of the dual sub problem zero, and calculating and solving the dual feasible solution.
3. The method as claimed in claim 1, wherein the method comprises the following steps: the specific process of minimizing the primitive subproblem by using the non-local mean value comprises the following steps:
(1) keeping the dual feasible solution unchanged, and calculating a process variable;
(2) a local window is defined from the process variable, and a data extraction window is slid in the local window to form a data subset;
(3) solving a reconstruction feasible solution based on the process variables, the data subsets and the reconstruction step length;
(4) and (4) sliding the local window, and repeating the steps (2) - (3) until the local window traverses the whole process variable.
4. The method as claimed in claim 1, wherein the method comprises the following steps: the convergence condition is that the iteration times are larger than a preset value.
5. The method as claimed in claim 1, wherein the method comprises the following steps: the specific process of placing the optimal reconstruction feasible solution at the unobserved position comprises the following steps: obtaining an optimal reconstruction feasible solution MKAnd then, on the basis of keeping the original seismic data D unchanged, updating the seismic channels at the positions which are not observed according to an assignment formula, and further obtaining high-precision reconstruction data, wherein the assignment formula is as follows:
M*＝(I-G)MK+D
wherein I is an identity matrix, MKFor optimal reconstruction of a feasible solution, K is the set maximum number of iterations, M*Is the reconstructed complete data.
6. A circulating minimization seismic data reconstruction system based on continuous operator splitting is characterized in that: the method comprises the following steps:
an extraction module configured to acquire acquired raw seismic data from which observation operators are adaptively extracted;
the construction optimization problem module is configured to construct an optimization problem of seismic data reconstruction according to an inversion theory based on the original seismic data and the observation operator;
the problem transformation module is configured to transform the constructed reconstruction optimization problem into a dual sub problem and an original sub problem by adopting a continuous strategy and a variational operator splitting method;
the solution calculation module is configured to minimize the dual sub-problem by using the adjacent gradient, minimize the original sub-problem by using the non-local mean value, and continuously circulate until the convergence condition is met to obtain the optimal reconstruction feasible solution;
the data reconstruction module is configured to keep the original seismic data unchanged, and place the optimal feasible reconstruction solution at an unobserved position to realize the reconstruction of the seismic data;
the specific process of adaptively extracting the observation operator from the observation operator comprises the following steps: according to the spatial distribution rule of the missing track, the empty track and the dead track in the field data acquisition, an observation operator G is adaptively extracted according to the following formula:
wherein [ G ]]ijRow i and column j elements representing operator G, where i e [1, Nt],j∈[1,Nx]，NtNumber of seismic sampling points, NxRepresenting the number of seismic sampling traces, wherein theta represents a spatial position index set of empty traces, missing traces and dead traces;
the optimization problem of seismic data reconstruction is as follows:
wherein G is an observation operator, D is collected incomplete seismic data, M is complete seismic data to be reconstructed,
is a flat of L2 normA, lambda is a punishment parameter, and phi (-) represents the priori knowledge of the seismic data;
the dual and primitive sub-problems are described as:
wherein Z isk+1For dual feasible solutions, Mk+1For reconstruction of a feasible solution, betakIn the case of a dual step size,
is the square of the norm of L2, DTFor transposing undersampled data D, ηkFor reconstructing the step size, GTFor the transpose of the observation operator G, k is the number of iterations.
7. An electronic device, characterized by: comprising a memory and a processor and computer instructions stored on the memory and executed on the processor, which when executed by the processor, perform the steps of a method of continuous operator splitting based cyclic minimization seismic data reconstruction according to any one of claims 1 to 5.
8. A computer-readable storage medium characterized by: for storing computer instructions which, when executed by a processor, perform the steps of a method of cyclic minimization of seismic data reconstruction based on continuous operator splitting according to any of claims 1 to 5.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110637320.8A CN113341460B (en) | 2021-06-08 | 2021-06-08 | Circulating minimization seismic data reconstruction method based on continuous operator splitting |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110637320.8A CN113341460B (en) | 2021-06-08 | 2021-06-08 | Circulating minimization seismic data reconstruction method based on continuous operator splitting |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113341460A CN113341460A (en) | 2021-09-03 |
| CN113341460B true CN113341460B (en) | 2022-05-27 |
Family
ID=77474817
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110637320.8A Active CN113341460B (en) | 2021-06-08 | 2021-06-08 | Circulating minimization seismic data reconstruction method based on continuous operator splitting |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113341460B (en) |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101609162A (en) * | 2009-07-17 | 2009-12-23 | 中国石化集团胜利石油管理局 | Pre-stack seismic non-linear three-parameter association inversion method |
Family Cites Families (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102288997A (en) * | 2010-08-10 | 2011-12-21 | 中国石油大学(华东) | Technology for inverting near-surface quality factor three-dimensional data volume by using microlog |
| CN104422954A (en) * | 2013-08-20 | 2015-03-18 | 中国石油化工股份有限公司 | Sparse sampling method in seismic data regularization |
| US9702999B2 (en) * | 2014-10-17 | 2017-07-11 | Chevron U.S.A. Inc. | System and method for velocity analysis in the presence of critical reflections |
| CN105700016B (en) * | 2016-02-19 | 2018-09-25 | 中国石油集团东方地球物理勘探有限责任公司 | The method of organic bank reservoir seismic prediction |
-
2021
- 2021-06-08 CN CN202110637320.8A patent/CN113341460B/en active Active
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101609162A (en) * | 2009-07-17 | 2009-12-23 | 中国石化集团胜利石油管理局 | Pre-stack seismic non-linear three-parameter association inversion method |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113341460A (en) | 2021-09-03 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Mousavi et al. | Deep-learning seismology | |
| Yu et al. | Monte Carlo data-driven tight frame for seismic data recovery | |
| Wang et al. | Fast dictionary learning for high-dimensional seismic reconstruction | |
| CN110208862B (en) | Seismic inversion method based on mixed high-order fractional-order ATpV sparse regularization | |
| CN113687433B (en) | Bi-LSTM-based magnetotelluric signal denoising method and system | |
| CN110857998B (en) | Elastic reverse time migration method and system based on lowrank finite difference | |
| CN113093272A (en) | Time domain full waveform inversion method based on convolutional coding | |
| Qian et al. | DTAE: Deep tensor autoencoder for 3-D seismic data interpolation | |
| CN110569728A (en) | Kernel signal extraction method based on dictionary training and orthogonal matching pursuit | |
| CN104730576A (en) | Curvelet transform-based denoising method of seismic signals | |
| Gao et al. | Deep learning vertical resolution enhancement considering features of seismic data | |
| CN113341460B (en) | Circulating minimization seismic data reconstruction method based on continuous operator splitting | |
| CN111045084B (en) | Multi-wave self-adaptive subtraction method based on prediction feature extraction | |
| CN114428278A (en) | Seismic data reconstruction method and device based on compressed sensing, electronic equipment and medium | |
| CN110161565B (en) | Seismic data reconstruction method | |
| CN116927771A (en) | Method, device, equipment and medium for predicting total organic carbon data of shale reservoir | |
| Sheng et al. | Arrival-time picking of microseismic events based on MSNet | |
| CN113419278B (en) | Well-seismic joint multi-target simultaneous inversion method based on state space model and support vector regression | |
| Wen et al. | Fast recovery of weak signal based on three‐dimensional curvelet transform and generalised cross validation | |
| CN114897737A (en) | Hyperspectral image denoising method based on non-paired unsupervised neural network | |
| CN110850473B (en) | Seismic wave impedance inversion method based on sparse transform learning | |
| CN113722893A (en) | Seismic record inversion method, device, equipment and storage medium | |
| Li et al. | Simple framework for the contrastive learning of visual representations-based data-driven tight frame for seismic denoising and interpolation | |
| CN114460633B (en) | Seismic denoising and interpolation method based on weighted frame transformation-low-dimensional manifold model | |
| CN107871028B (en) | Method and device for grading stratum |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |