CN112255675B - Seismic data seismic source wave field reconstruction method, system, equipment, medium and application - Google Patents
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- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
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Abstract
The invention belongs to the technical field of seismic data migration and inversion, and discloses a seismic data seismic source wave field reconstruction method, a system, equipment, a medium and application. The method is based on a new staggered grid finite difference template, meanwhile, the boundary wave field and the wave field are linearly combined to reconstruct the seismic source wave field, the memory requirement of a computer is reduced, the corresponding frequency dispersion relation is deduced, the minimized objective function is established, the reconstruction coefficient is optimized by adopting the Lagrange multiplier algorithm, the reconstruction precision of the seismic source wave field can be greatly improved, the method can be applied to seismic data migration and inversion based on the wave equation to relieve the storage pressure, and the method has a good application prospect.
Description
Technical Field
The invention belongs to the technical field of seismic data migration and inversion, and particularly relates to a seismic data seismic source wave field reconstruction method, a seismic data seismic source wave field reconstruction system, seismic data seismic source wave field reconstruction equipment, a seismic data seismic source wave field reconstruction medium, application and a seismic data seismic source wave field reconstruction system.
Background
At present: seismic data migration and inversion based on wave equations (e.g., reverse time migration and full waveform inversion) require very large amounts of computation and memory. Reverse time migration and full waveform inversion extend the source wavefield forward along time, and when calculating the migration profile or parametric gradient, the source wavefield needs to be visited backward along time. Therefore, wavefields at all times in all grids need to be stored. It is clearly unacceptable for larger geological models. A simple solution is to output the wavefield to the disk and read it in from the disk when needed. However, the disk I/O itself is time consuming, especially for high performance computers, where disk reads and writes are much more expensive than floating point operations. The geophysicist presents random boundary conditions, checkpointing and limited boundary storage strategies in turn to relieve storage pressure. The seismic source wave field in the random boundary can be completely recovered in the backward propagation process, and the memory requirement can be greatly saved. The disadvantage is that some spurious noise is introduced, degrading the quality of the imaged or inverted profile. The checking method only stores wave field values at a few detection points, and reconstructs seismic source wave fields at different moments by carrying out wave field continuation from the nearest detection point. However, the method reduces the amount of memory at the cost of increased computation, and the number of detection points is used to balance memory requirements and recalculation ratio. The active boundary storage strategy recovers the source wavefields in the inner region during back-propagation by storing a small fraction of the wavefields in the boundary region. The method does not increase the calculation amount in one iteration to exceed two forward runs. The checking and active boundary storage strategies are by far the two most common memory-reduction schemes in reverse-time migration and full waveform inversion. However, most of the existing effective boundary storage strategies need to store M layers of boundary wave field values (M is a finite difference operator length parameter), and the memory requirement is still huge when the geological model is large (especially in the 3D case).
Through the above analysis, the problems and defects of the prior art are as follows: most of the existing effective boundary storage strategies need to store M layers of boundary wave field values, and the memory requirement is still huge when the geological model is large.
The difficulty in solving the above problems and defects is: seismic source wavefield reconstruction requires a tradeoff between accuracy and storage. The conventional method stores multilayer boundary wave fields, has high reconstruction precision but huge storage requirements, and is not suitable for large-scale models (particularly three-dimensional situations); the existing single-layer boundary storage method has small storage capacity, but the reconstruction precision is not enough, so that the requirements of high-precision seismic data imaging and inversion are difficult to meet. It is challenging to study a reconstruction method for a source wavefield with high precision and small storage.
The significance of solving the problems and the defects is as follows: seismic source wavefield reconstruction is widely used in exploration geophysical field seismic data reverse time migration and full waveform inversion. The method for developing the seismic source wave field reconstruction method capable of balancing the reconstruction precision and the storage requirement is significant, can greatly reduce the memory consumption of a computer on the premise of not reducing the reconstruction, imaging and inversion precision, and has wide application prospect.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a seismic data seismic source wave field reconstruction method, a seismic data seismic source wave field reconstruction system, seismic data seismic source wave field reconstruction equipment, seismic data seismic source wave field reconstruction media and application.
The invention is realized in such a way that a seismic data seismic source wave field reconstruction method, a system, equipment, a medium and application comprise the following steps:
(1) Constructing a new staggered grid finite difference reconstruction template;
and reconstructing the source wave fields of different layers by adopting the finite difference templates of the variable-order staggered grids.
(2) Discretizing a spatial partial derivative of the wave equation;
the spatial partial derivatives in the wave equation are discretized using a new interleaved-grid finite-difference template.
(3) Deducing a frequency dispersion relation;
and deducing a frequency dispersion relation under the new differential template based on the plane wave theory.
(4) Establishing a minimization target function;
and constructing an L2 norm minimization target function based on the relative dispersion error.
(5) Optimizing a reconstruction coefficient based on a Lagrange multiplier algorithm;
and solving the minimization problem by adopting a Lagrange multiplier algorithm to obtain an optimized reconstruction coefficient.
(6) And (5) seismic source wave field reconstruction of the seismic data.
And adopting a new reconstruction template and an optimized reconstruction coefficient to reconstruct the seismic source of the seismic data.
Further, the method for constructing the new staggered grid finite difference reconstruction template in the step (1) is as follows:
and constructing a staggered grid finite difference reconstruction template, wherein the number of grid points adopted for reconstructing the seismic source wave field of different layers in the new reconstruction template is different.
Further, the discrete method of the spatial partial derivatives of the wave equation in the step (2) is as follows:
and dispersing the spatial partial derivative in the wave equation by adopting a new reconstruction template, wherein the formula is as follows:
wherein, a i (i =1,2, \8230;, M) and b j,i (j =1,2, \8230;, M-1,i =1,2, \8230;, N + j + 1) is a reconstruction coefficient,
is a linear combination of M-1 layer boundary wavefields. New method only stores p -0.5 And a, the source wavefield reconstruction may be performed based on equation (1). The conventional method needs to store M layers of boundary wave fields, the new reconstruction method only needs to store 1 layer of boundary wave fields and linear combination (equivalent to 2 layers) of 1 boundary wave field, and the memory requirement is greatly reduced.
Further, in the step (3), the method for deriving the dispersion relation is as follows:
under the assumption of plane wave theory, the wavefield can be expressed as:
wherein the content of the first and second substances,
is an imaginary unit, k x Wave number in x-axis direction, p 0 Is an initial value. Substituting equation (2) into equation (1) can simplify:
equation (3) is the dispersion relation of the new reconstruction method.
Further, the establishment method of the minimization objective function in the step (4) is as follows:
based on equation (3), the relative dispersion error is defined as:
wherein the content of the first and second substances,
j =1,2, \ 8230;, M-1. Based on the relative dispersion error, an L2 norm minimization objective function is established as follows:
j =1,2, \8230, M-1, beta is k x The upper limit of h.
Further, the reconstruction coefficient optimization method based on the Lagrange multiplier algorithm in the step (5) is as follows:
in order to ensure the reconstruction accuracy when the wave number is 0, the following constraint conditions are adopted:
the optimization problem becomes the minimization problem of equations (7) and (8) under the constraint of equation (9), and is solved by the Lagrange multiplier method. The objective function becomes:
j＝1,2,…,M–1，λ 0 and λ j Are Lagrange multiplier coefficients. Taking the derivative of the objective function with respect to the reconstruction coefficients:
l =1,2, \8230;, M, k =1,2, \8230;, j. And (3) iterating the reconstruction coefficient by adopting a nonlinear conjugate gradient method based on the formulas (12) and (13) until a convergence condition is met (if the objective function is less than 0.001).
Further, the seismic source wavefield reconstruction method for the seismic data in the step (6) is as follows:
the reconstruction coefficient a obtained by optimization i And b j,i And a stored boundary wavefield p -0.5 And substituting the linear combination A of the sum wave field into the formula (1) to reconstruct the wave field of the seismic source.
It is a further object of the invention to provide a computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the steps of:
constructing a new staggered grid finite difference reconstruction template;
discretizing a spatial partial derivative of the wave equation;
deducing a frequency dispersion relation;
establishing a minimization target function;
optimizing a reconstruction coefficient based on a Lagrange multiplier algorithm;
and (5) seismic source wave field reconstruction of the seismic data.
It is another object of the present invention to provide a computer-readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of:
constructing a new staggered grid finite difference reconstruction template;
discretizing a spatial partial derivative of the wave equation;
deducing a frequency dispersion relation;
establishing a minimization target function;
optimizing a reconstruction coefficient based on a Lagrange multiplier algorithm;
and (5) seismic source wave field reconstruction of the seismic data.
Another object of the present invention is to provide a seismic-data source wavefield reconstruction system implementing the seismic-data source wavefield reconstruction method, the seismic-data source wavefield reconstruction system comprising:
the reconstruction template construction module is used for constructing a new staggered grid finite difference reconstruction template, and the number of grid points adopted for seismic source wave field reconstruction of different layers in the new staggered grid finite difference reconstruction template is different;
the discretization module is used for discretizing the spatial partial derivative in the wave equation through a new reconstruction template;
the derivation module is used for deriving the dispersion relation of the new reconstruction method based on the plane wave theory;
the target function establishing module is used for establishing a minimized target function based on the relative frequency dispersion error;
the optimization module is used for solving the derivative of the number standard function about the reconstruction coefficient by a Lagrange multiplier method and iterating the reconstruction coefficient by a nonlinear conjugate gradient method;
and the wave field reconstruction module is used for performing seismic source wave field reconstruction on the reconstructed coefficient obtained by optimization and the stored boundary wave field and wave field linear combination.
The invention also aims to provide a seismic data migration and inversion terminal, and the seismic data migration and inversion terminal carries the seismic data seismic source wave field reconstruction system.
By combining all the technical schemes, the invention has the advantages and positive effects that: the method adopts a new staggered grid finite difference template to approximate a spatial derivative; simultaneously storing the boundary wavefield and the wavefield linear combination to reconstruct the source wavefield; deducing a corresponding frequency dispersion relation, establishing a minimization objective function, and optimizing a reconstruction coefficient by adopting a Lagrange multiplier method; the effectiveness of the method is verified by numerical calculation. The new method can give consideration to reconstruction precision and storage capacity, greatly reduces the memory consumption of a computer on the premise of not reducing the reconstruction, imaging and inversion precision of seismic data, and has wide application prospect.
The method simultaneously stores the linear combination of the boundary wave field and the wave field to reconstruct the seismic source wave field so as to reduce the memory requirement, and adopts the reconstruction coefficient optimized based on the Lagrange multiplier algorithm to improve the reconstruction precision of the seismic source wave field. The method can improve the accuracy of source wave field reconstruction in seismic data migration and inversion (such as reverse time migration and full waveform inversion) based on the wave equation and relieve the storage pressure.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments of the present application will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present application, and it is obvious for those skilled in the art that other drawings can be obtained from the drawings without creative efforts.
FIG. 1 is a flow chart of a seismic source wavefield reconstruction method, system, apparatus, medium, and application provided by embodiments of the present invention.
Fig. 2 is a schematic diagram of a new interleaved grid finite difference reconstruction template provided by an embodiment of the present invention.
Fig. 3 is a schematic diagram of a Marmousi velocity model according to an embodiment of the present invention.
FIG. 4 is a schematic diagram of a reconstructed wavefield obtained by a different method according to an embodiment of the present invention;
in the figure: FIG. 4 ((a) forward propagating source wavefield; FIG. 4 (b) conventional method; FIG. 4 (c) seismic data source wavefield reconstruction method, system, apparatus, medium, and application.
FIG. 5 is an error diagram of a reconstructed wavefield according to various methods provided by embodiments of the present invention;
in the figure: FIG. 5 (a) conventional method; FIG. 5 (b) seismic data source wavefield reconstruction methods, systems, apparatus, media and applications.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
In view of the problems in the prior art, the present invention provides a seismic data seismic source wavefield reconstruction method, system, device, medium, application and system, and the present invention is described in detail below with reference to the accompanying drawings.
As shown in fig. 1, the method for reconstructing a seismic source wavefield of seismic data provided by the embodiment of the invention includes the following steps:
s101, constructing a new staggered grid finite difference reconstruction template;
s102, dispersing a spatial partial derivative of a wave equation;
s103, deducing a frequency dispersion relation;
s104, establishing a minimization target function;
s105, optimizing a reconstruction coefficient based on a Lagrange multiplier algorithm;
and S106, seismic source wave field reconstruction of the seismic data.
Those skilled in the art of the seismic-data source wavefield reconstruction method provided by the present invention may also use other steps, and the seismic-data source wavefield reconstruction method provided by the present invention in fig. 1 is only one specific example.
The method for constructing the new staggered grid finite difference template in the step S101 is as follows:
a staggered grid finite difference reconstruction template as shown in fig. 2 is constructed. Wherein, M is the finite difference operator length parameter, h is the space sampling interval, X is the space partial derivative needed to be reconstructed, black points are grid points directly used for wave field reconstruction, and gray points are linear combination of different layers of grid point wave fields used for wave field reconstruction. The grid points adopted for the reconstruction of the seismic source wave field of different layers (x = jh, j =0,1, \8230;, M-1) in the newly reconstructed template are different.
The dispersion method of the spatial partial derivatives of the wave equation in step S102 is as follows:
dispersing the spatial partial derivative in the wave equation by adopting a new reconstruction template, wherein the formula is as follows:
wherein, a i (i =1,2, \8230;, M) and b j,i (j =1,2, \8230;, M-1,i =1,2, \8230;, N + j + 1) is a reconstruction coefficient,
is a linear combination of the M-1 layer boundary wavefields. New method only stores p -0.5 And a, the source wavefield reconstruction may be performed based on equation (1). The conventional method needs to store M layers of boundary wave fields, the new reconstruction method only needs to store 1 layer of boundary wave fields and linear combination (equivalent to 2 layers) of 1 boundary wave field, and the memory requirement is greatly reduced.
The derivation method of the dispersion relation in step S103 is as follows:
under the assumption of plane wave theory, the wavefield can be expressed as:
wherein the content of the first and second substances,
is an imaginary unit, k x Wave number in x-axis direction, p 0 Is an initial value. Substituting the formula (2) into the formula (1) can be simplified to obtain:
the formula (3) is the dispersion relation of the new reconstruction method.
The method for establishing the minimization objective function in step S104 is as follows:
based on equation (3), the relative dispersion error is defined as:
wherein, the first and the second end of the pipe are connected with each other,
j =1,2, \ 8230;, M-1. Based on the relative dispersion error, an L2 norm minimization objective function is established as follows:
j =1,2, \ 8230;, M-1, β is k x The upper limit of h.
The method for optimizing the reconstruction coefficient based on the Lagrange multiplier algorithm in step S105 is as follows:
in order to ensure the reconstruction accuracy when the wave number is 0, the following constraint conditions are adopted:
the optimization problem becomes the minimization problem of equations (7) and (8) under the constraint of equation (9), and is solved by the Lagrange multiplier method. The objective function becomes:
j＝1,2,…,M–1，λ 0 and λ j Are Lagrange multiplier coefficients. Taking the derivative of the objective function with respect to the reconstruction coefficients:
l =1,2, \8230;, M, k =1,2, \8230;, j. And (5) based on the formulas (12) and (13), iterating the reconstruction coefficient by using a nonlinear conjugate gradient method until a convergence condition is met (if the target function is less than 0.001).
The seismic data source wave field reconstruction method in the step S106 is as follows:
the reconstruction coefficient a obtained by optimization i And b j,i And a stored boundary wavefield p -0.5 And substituting the linear combination A of the seismic source and the wave field into the formula (1) to reconstruct the wave field of the seismic source.
The effectiveness of the invention is further illustrated below with reference to specific examples.
As shown in fig. 3, the method proposed in the present invention is verified using the Marmousi velocity model, which is most commonly used in the field of exploration of geophysical. The model calculation region has 501 × 351 grid points, the space interval is 10.0m, the time step is 1ms, and the maximum recording time is 4s. The seismic source is a 20Hz Rake wavelet and is located at (9500m, 0m), and 501 detection points are uniformly distributed on the ground surface. The wave field forward propagation adopts a conventional staggered grid finite difference method, and the length of a difference operator is M =6.
As shown in fig. 4, the inversely reconstructed wavefields obtained by different reconstruction methods are given. For ease of comparison, we use the forward propagating source wavefield as the reference solution.
As shown in fig. 5, the error of the reconstructed wavefield with respect to the reference solution is given for different reconstruction methods. As can be seen from fig. 5, the conventional method and the proposed seismic data source wavefield reconstruction method, system, apparatus, medium, and application all yield results similar to the reference solution. But the storage capacity of the new method is only 33.3% of that of the conventional method. Therefore, the seismic source wave field reconstruction method provided by the embodiment of the invention can accurately and efficiently reconstruct the seismic source wave field.
It should be noted that the embodiments of the present invention can be realized by hardware, software, or a combination of software and hardware. The hardware portion may be implemented using dedicated logic; the software portions may be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or specially designed hardware. Those skilled in the art will appreciate that the apparatus and methods described above may be implemented using computer executable instructions and/or embodied in processor control code, such code being provided on a carrier medium such as a disk, CD-or DVD-ROM, programmable memory such as read only memory (firmware), or a data carrier such as an optical or electronic signal carrier, for example. The apparatus and its modules of the present invention may be implemented by hardware circuits such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of hardware circuits and software, e.g., firmware.
The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.
Claims (9)
1. A seismic source wavefield reconstruction method for seismic data, the seismic source wavefield reconstruction method comprising:
constructing a new staggered grid finite difference reconstruction template; reconstructing the seismic source wave fields of different layers by adopting a variable-order staggered grid finite difference template;
discretizing a spatial partial derivative of the wave equation; dispersing a spatial partial derivative in a wave equation by adopting a new staggered grid finite difference template;
deducing a frequency dispersion relation; deducing a frequency dispersion relation under a new differential template based on a plane wave theory;
establishing a minimization target function; constructing an L2 norm minimization target function based on the relative frequency dispersion error;
optimizing a reconstruction coefficient based on a Lagrange multiplier algorithm; solving the minimization problem by adopting a Lagrange multiplier algorithm to obtain an optimized reconstruction coefficient;
reconstructing a seismic source wave field of the seismic data, and reconstructing the seismic source of the seismic data by adopting a new reconstruction template and an optimized reconstruction coefficient;
the method for discretely adopting the spatial partial derivative of the wave equation is as follows: and dispersing the spatial partial derivative in the wave equation by adopting a new reconstruction template, wherein the formula is as follows:
wherein, a i And b j,i For reconstruction coefficients, i =1,2, \8230;, M, j =1,2, \8230;, M-1,
being linear of M-1 layer boundary wavefieldsAnd combining, wherein M is a length parameter of the difference operator, p is a seismic wave field, h is a space sampling interval, and x is a space coordinate.
2. The method for seismic source wavefield reconstruction of claim 1, wherein the new interleaved mesh finite difference reconstruction template is constructed by: and constructing a staggered grid finite difference reconstruction template, wherein the number of grid points adopted for reconstructing the seismic source wave field of different layers in the new reconstruction template is different.
3. The method of seismic source wavefield reconstruction of claim 1, wherein the dispersion relation is derived by: in plane wave theory, the wavefield is represented as:
wherein, the first and the second end of the pipe are connected with each other,
is an imaginary unit, k x Wave number in x-axis direction, p 0 Is an initial value, h is a spatial sampling interval;
will be provided with
Substituting into a formula:
wherein, a i And b j,i For reconstruction coefficients, i =1,2, \8230;, M, j =1,2, \8230;, M-1,
the method comprises the following steps of (1) linearly combining boundary wave fields of M-1 layers, wherein M is a difference operator length parameter;
the simplified frequency dispersion relation of the new reconstruction method is as follows:
4. the method of seismic source wavefield reconstruction of claim 1, wherein the minimization of the objective function is performed by: based on a frequency dispersion relation of a new reconstruction method, defining a relative frequency dispersion error as follows:
wherein, the first and the second end of the pipe are connected with each other,
based on the relative dispersion error, an L2 norm minimization objective function is established as follows:
wherein j =1,2, \8230, M-1, beta is k x The upper limit of h.
5. The method for reconstructing a seismic source wavefield in accordance with claim 1, wherein the Lagrange multiplier algorithm based reconstruction coefficients are optimized by: the following constraints are used:
wherein, a i And b j,i For the reconstruction coefficient, i =1,2, \8230, M, j =1,2, \8230, M-1, M is the length parameter of the difference operator;
solving by adopting Lagrange multiplier method, the objective function becomes:
wherein j =1,2, \8230, M-1, λ 0 And λ j Is a Lagrange multiplier coefficient, k x Is the wave number in the x-axis direction, h is the spatial sampling interval, and β is k x An upper limit of h;
the derivative of the objective function with respect to the reconstruction coefficients is taken:
wherein l =1,2, \8230, M, k =1,2, \8230, j, iteratively reconstructing coefficients by adopting a nonlinear conjugate gradient method until a convergence condition is met;
the seismic data seismic source wave field reconstruction method comprises the following steps: the reconstruction coefficient a obtained by optimization i And b j,i And a stored boundary wavefield p -0.5 And the linear combination A of the wave fields is substituted into the formula:
the reconstruction of the wave field of the seismic source is carried out,
is a linear combination of the M-1 layer boundary wavefields.
6. A computer device comprising a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the method of seismic source wavefield reconstruction as claimed in any one of claims 1 to 5.
7. A computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to carry out the method of seismic source wavefield reconstruction of seismic data according to any one of claims 1 to 5.
8. A seismic-feed source wavefield reconstruction system that implements the seismic-feed source wavefield reconstruction method of any one of claims 1-5, the seismic-feed source wavefield reconstruction system comprising:
the reconstruction template construction module is used for constructing a new staggered grid finite difference reconstruction template, and the number of grid points adopted for seismic source wave field reconstruction of different layers in the new staggered grid finite difference reconstruction template is different;
the discretization module is used for discretizing the spatial partial derivative in the wave equation through a new reconstruction template;
the derivation module is used for deriving the frequency dispersion relation of the new reconstruction method based on the plane wave theory;
the target function establishing module is used for establishing a minimized target function based on the relative frequency dispersion error;
the optimization module is used for solving the derivative of the number standard function about the reconstruction coefficient by a Lagrange multiplier method and iterating the reconstruction coefficient by a nonlinear conjugate gradient method;
and the wave field reconstruction module is used for performing seismic source wave field reconstruction on the optimized reconstruction coefficient and the stored boundary wave field and wave field linear combination.
9. A seismic data migration and inversion terminal, wherein said seismic data migration and inversion terminal is equipped with the seismic data source wavefield reconstruction system of claim 8.
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