CN112817044B - Method and system for optimizing difference coefficient of frequency domain acoustic wave equation - Google Patents
Method and system for optimizing difference coefficient of frequency domain acoustic wave equation Download PDFInfo
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Abstract
The embodiment of the invention provides a method and a device for optimizing difference coefficients of a frequency domain acoustic wave equation; the difference coefficient optimization method is suitable for the condition that longitudinal and transverse sampling intervals of a finite difference grid are unequal, and comprises the following steps: determining a finite difference grid of the frequency domain acoustic wave equation; carrying out difference approximation on the frequency domain acoustic wave equation by the finite difference grid, and establishing a finite difference format; constructing an optimized objective function according to a finite difference format; solving the optimized difference coefficient of the optimized objective function according to the optimized function; therefore, the technical problem that in the prior art, a traditional 25-point finite difference grid of a rotating coordinate system is used in a finite difference method in forward modeling of a frequency domain, but the grid is only suitable for the condition that longitudinal and transverse sampling intervals are equal, so that the application range is narrow is solved, and the technical effects of reliability and wide applicability are achieved.
Description
Technical Field
The invention relates to the technical field of forward modeling calculation, in particular to a method and a system for optimizing a difference coefficient of a frequency domain acoustic wave equation.
Background
The frequency domain full waveform inversion fully utilizes the amplitude, phase and frequency information of a full wave field, and a velocity model with high precision can be obtained by inversion with less frequency.
The frequency domain forward modeling is the basis of frequency domain full waveform inversion, plays an important role in seismic wave numerical simulation, and has the advantages of suitability for multi-shot parallel operation, no time dispersion, flexible frequency band selection, small error and the like compared with the time domain forward modeling. Scholars have proposed many forms of finite difference grids for improving forward accuracy of frequency domain, wherein a rotating coordinate system 25-point finite difference format is the most common, but the method is only suitable for the case that the vertical and horizontal sampling intervals are equal, but cannot be applied to the case that the vertical and horizontal sampling intervals are unequal.
Thus, there remains a need in the art for improvements.
Disclosure of Invention
In order to solve the above technical problems, an object of the present invention is to provide a method, a system, and a machine-readable storage medium for optimizing a difference coefficient of a frequency domain acoustic wave equation.
In order to achieve the above object, in a first aspect of the present application, there is provided a difference coefficient optimization method for a frequency domain acoustic wave equation, which is applicable to a case where longitudinal and transverse sampling intervals of a finite difference grid are unequal, the difference coefficient optimization method including: determining a finite difference grid of the frequency domain acoustic wave equation; carrying out difference approximation on the frequency domain acoustic wave equation by the finite difference grid, and establishing a finite difference format; constructing an optimization objective function according to a finite difference format; and solving the optimized difference coefficient of the optimized objective function according to the optimized function.
In this embodiment of the present application, the approximating the difference of the finite difference grid to the frequency domain acoustic wave equation to obtain a finite difference format includes: carrying out difference approximation on a second-order partial derivative term in a frequency domain acoustic wave equation by the finite difference grid to obtain a first difference model; carrying out difference approximation on the mass acceleration item in the frequency domain acoustic wave equation by the finite difference grid to obtain a second difference model; and obtaining the finite difference format according to the first difference model and the second difference model.
In the embodiment of the application, the optimization objective function is constructed according to a finite difference format; and solving the optimized difference coefficient of the optimized objective function according to the optimized function comprises the following steps: constructing an optimized objective function based on the finite difference format by using a phase velocity dispersion equation; obtaining the optimization coefficient of the objective function according to the optimization function; and obtaining a normalized phase velocity frequency dispersion curve according to the optimization coefficient so as to verify the reliability of the objective function.
In the embodiment of the application, the finite difference grid is a 25-point frequency domain finite difference grid.
In an embodiment of the present application, the method further includes: and performing forward modeling on the frequency domain acoustic wave equation by using the optimized difference coefficient.
In an embodiment of the present application, the forward modeling of the frequency domain acoustic wave equation by using the optimized difference coefficient includes: absorbing the boundary condition of the frequency domain acoustic wave equation by using a perfect matching layer; training through numerical values in a preset training model; and determining the reliability of the stochastic inversion method according to the training result.
In an embodiment of the present application, the training model is at least one of a layered medium, a concave medium, and a Marmousi model.
In an embodiment of the present application, the training result includes: at least one of a frequency slice, a wave field snapshot, and a seismic recording.
In a second aspect of the embodiment of the present application, there is further provided a difference coefficient optimization apparatus for a frequency domain acoustic wave equation, including a determining module, configured to determine a finite difference grid of the frequency domain acoustic wave equation, and a calculating module, configured to perform difference approximation on the frequency domain acoustic wave equation by using the finite difference grid, and establish a finite difference format; the optimization module is used for constructing an optimization objective function according to the finite difference format and solving an optimization difference coefficient of the optimization objective function according to the optimization function; and the simulation module is used for carrying out forward simulation on the frequency domain acoustic wave equation by utilizing the optimized difference coefficient.
In another aspect, embodiments of the present application further provide a computer-readable storage medium having stored thereon instructions for enabling a processor to execute the difference coefficient optimization method of frequency domain acoustic wave equations according to the claims when executed by the processor.
By the technical scheme, in conclusion, the frequency domain acoustic wave equation is subjected to difference approximation through the finite difference grid, the finite difference format is established, and the optimized objective function is established by utilizing the finite difference format; solving the optimized difference coefficient of the optimized objective function according to the optimized function; therefore, the technical problem that in the prior art, a conventional 25-point finite difference grid of a rotating coordinate system is adopted in a finite difference method in a frequency domain forward modeling, but the grid is only suitable for the condition that longitudinal and transverse sampling intervals are equal, so that the application range is narrow is solved, and the technical effects of reliability and wide applicability are achieved.
Additional features and advantages of embodiments of the present invention will be described in the detailed description which follows.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the embodiments of the invention without limiting the embodiments of the invention. In the drawings:
FIG. 1 is a flowchart of a method for optimizing difference coefficients of a frequency domain acoustic wave equation according to an embodiment of the present invention;
fig. 2 is a schematic diagram illustrating a conventional differential grid in a method for optimizing a differential coefficient of a frequency domain acoustic wave equation according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a difference formula of a method for optimizing difference coefficients of a frequency domain acoustic wave equation provided in an embodiment of the present invention;
fig. 4 is a flowchart of step S102 in a method for optimizing difference coefficients of a frequency domain acoustic wave equation according to an embodiment of the present invention;
fig. 5 is a flowchart of step S103 in a method for optimizing difference coefficients of a frequency domain acoustic wave equation according to an embodiment of the present invention;
fig. 6 is a schematic diagram of a normalized phase velocity dispersion curve obtained by performing step S1033 in the method for optimizing difference coefficients of a frequency domain acoustic wave equation according to the embodiment of the present invention;
fig. 7 is a flowchart of step S104 in a method for optimizing difference coefficients of a frequency domain acoustic wave equation according to an embodiment of the present invention;
fig. 8a is a schematic diagram illustrating that the model corresponding to step S1042 is a layer model in the method for optimizing difference coefficients of a frequency domain acoustic wave equation according to the embodiment of the present invention;
fig. 8b is a schematic diagram of the model corresponding to step S1042 executed in the method for optimizing difference coefficients of a frequency domain acoustic wave equation according to the embodiment of the present invention is a concave model;
fig. 8c is a schematic diagram of the model corresponding to the step S1042 executed in the method for optimizing the difference coefficient of the frequency domain acoustic wave equation provided in the embodiment of the present invention is a Marmousi model;
fig. 9a is a schematic diagram of a forward result obtained when the model corresponding to step S1043 is a layered medium and is sliced at a frequency of 30Hz in the difference coefficient optimization method for a frequency domain acoustic wave equation provided in the embodiment of the present invention;
fig. 9b is a schematic diagram of a forward result obtained when the model corresponding to step S1043 is a layered medium and is in a 0.25S wave field snapshot of the layered medium in the method for optimizing the difference coefficient of the frequency domain acoustic wave equation provided in the embodiment of the present invention;
fig. 9c is a schematic diagram of a forward result of seismic recording in a layered medium when the model corresponding to step S1043 is a layered medium in the method for optimizing the difference coefficient of the frequency domain acoustic wave equation provided in the embodiment of the present invention;
fig. 10a is a schematic diagram of a forward result obtained when the model corresponding to step S1043 is a concave medium and the frequency slice is 30Hz in the method for optimizing difference coefficients of a frequency domain acoustic wave equation provided in the embodiment of the present invention;
fig. 10b is a schematic diagram of a forward result under a 0.25S wave field snapshot when the model corresponding to step S1043 is a concave medium in the method for optimizing difference coefficients of a frequency domain acoustic wave equation provided in the embodiment of the present invention;
fig. 10c is a schematic diagram of a forward result obtained by performing step S1043 on a model as a concave medium and performing seismic recording on the concave medium in the method for optimizing difference coefficients of a frequency domain acoustic wave equation provided in the embodiment of the present invention;
fig. 11a is a schematic diagram of a partial forward result under a 30Hz frequency slice when the corresponding model in step S1043 is a Marmousi model in the method for optimizing difference coefficients of a frequency domain acoustic wave equation provided in the embodiment of the present invention;
fig. 11b is a schematic diagram of a partial forward result under a 0.25S wave field snapshot, where the model corresponding to step S1043 in the method for optimizing the difference coefficient of the frequency domain acoustic wave equation provided in the embodiment of the present invention is a Marmousi model;
fig. 11c is a schematic diagram of a partial forward result under seismic recording, where the model corresponding to step S1043 is a Marmousi model in the method for optimizing difference coefficients of a frequency domain acoustic wave equation provided in the embodiment of the present invention; and
fig. 12 is a block diagram of a difference coefficient optimization apparatus for frequency domain acoustic wave equations according to an embodiment of the present invention.
Description of the reference numerals
100. A difference coefficient optimizing means;
10. a determination module; 20. A calculation module;
30. an optimization module; 40. And a simulation module.
Detailed Description
In the following description, for purposes of explanation and not limitation, specific details are set forth, such as particular system structures, techniques, etc. in order to provide a thorough understanding of the embodiments of the invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present invention with unnecessary detail.
The following describes in detail embodiments of the present invention with reference to the drawings. It should be understood that the detailed description and specific examples, while indicating embodiments of the invention, are given by way of illustration and explanation only, not limitation.
The inventor finds that in the conventional frequency domain full waveform inversion method, the finite difference grid is usually obtained by vertical and horizontal sampling intervals, such as a rotating coordinate system 25-point finite difference format. This method has a high accuracy, and the dispersion error is close to zero in a low frequency band, but it cannot be applied to a case where vertical and horizontal sampling intervals are not equal. Therefore, the embodiment of the invention provides a difference coefficient optimization method of a frequency domain acoustic wave equation to perform frequency domain acoustic wave forward modeling, the embodiment of the invention is improved based on a 25-point method of a rotating coordinate system, a new coefficient distribution and solving format is used, a phase velocity dispersion equation is used for constructing an objective function, finally a difference coefficient is solved and is brought into a frequency domain forward modeling process, and a test result proves the reliability of the method, so that the optimization of the difference coefficient applicable to unequal longitudinal and transverse sampling intervals is achieved, and the application capability of the non-standard field is increased.
Referring to fig. 1, fig. 1 is a flowchart illustrating a method for optimizing a difference coefficient of a frequency domain acoustic wave equation according to an embodiment of the present invention. The embodiment of the invention mainly provides a forward modeling method for a frequency domain acoustic wave equation, which aims to solve the problem that the existing method cannot adapt to the condition of unequal longitudinal and transverse sampling intervals, and reduces the forward modeling application range, so that the expected forward modeling effect cannot be achieved.
In one aspect of the embodiment of the present invention, the method for optimizing a difference coefficient includes:
s101, determining a finite difference grid of a frequency domain acoustic wave equation;
s102, carrying out difference approximation on a frequency domain acoustic wave equation by using a finite difference grid, and establishing a finite difference format;
s103, constructing an optimization objective function according to a finite difference format; and solving the optimized difference coefficient of the optimized objective function according to the optimized function.
In order to more conveniently describe the embodiments of the present invention and to make the embodiments clear, terms related to the above steps are explained:
the term "frequency domain acoustic wave equation" referred to above is an equation of an acoustic wave in the frequency domain, in particular an equation of a variation with frequency through an acoustic wave. Which may be expressed as a Laplacian operator, a mass acceleration term, and a seismic source term.
In the embodiment of the invention, firstly, the inapplicable limitation of a 25-point frequency domain finite difference forward modeling grid under a rotating coordinate system under the condition of unequal longitudinal and transverse sampling intervals needs to be analyzed; the method comprises the following steps:
in an embodiment of the present invention, a frequency domain two-dimensional acoustic wave equation (i.e., a frequency domain acoustic wave equation) can be written as:
where in equation 1, P is the displacement component, ω is the angular frequency, and v is the velocity.
Referring to fig. 2, fig. 2 is a schematic diagram illustrating a conventional differential grid in the method for optimizing the differential coefficient of the frequency domain acoustic wave equation according to the embodiment of the present invention; when forward modeling is performed by using the finite difference method, the conventional fourth-order 25-point difference format has high precision, and the difference format corresponding to 1 is as follows in formula 2:
in formula 2, p m，n Corresponding to the displacement component at grid m, n. a is a 1 ～a 6 And b is 1 ～b 6 Are all differential coefficients.
It is understood that since the above-mentioned conventional fourth-order 25-point differential format is a common technical means for those skilled in the art, it is not overly elaborated in the embodiments of the present invention.
Analyzing the above equation 2, it can be seen that when Δ x ≠ Δ z, the difference approximation of laplacian terms does not hold, and the hybrid 25 difference format will not be applicable. (hybrid differential format: a hybrid format that combines the advantages of the hub differential format and the windward format).
Referring to fig. 3, fig. 3 is a schematic diagram illustrating a difference form of a method for optimizing difference coefficients of a frequency domain acoustic wave equation according to an embodiment of the present invention; in view of the above, embodiments of the present invention need to provide a difference coefficient optimization method applicable to cases where Δ x ≠ Δ z, i.e. where the vertical and horizontal sampling intervals are unequal. Firstly, the vertical and horizontal sampling intervals need to be determined, and a difference coefficient optimization method of a 25-point frequency domain finite difference forward modeling grid under a rotating coordinate system is improved, so that a 25-point finite difference grid which is suitable for the condition that the vertical and horizontal sampling intervals are unequal is obtained as shown in fig. 2. It is understood that the 25-point finite difference grid provided in fig. 2 is only an exemplary preferred function, and the 25-point finite difference grid is not fully defined, and the non-mental simple modifications to the diagram are also within the scope of the present invention.
It can be understood that the finite difference grids with equal longitudinal and transverse sampling intervals refer to uniform subdivision of the medium, and all the grids used are equal in size and same in shape.
It is understood that the term "Finite difference grid" mentioned above is one of the basic steps of the Finite Difference Method (FDM), which divides the time and space area under study into several grids by means of time and space steps, and replaces the order derivatives appearing in the partial Differential equations used by the Differential approximation formed by the unknown functions on the grid nodes. And the acoustic dispersion region under study is subdivided into a grid system according to a certain geometric shape (such as the rectangle shown in the figure), namely the finite difference grid of the invention.
Referring to fig. 4, fig. 4 is a flowchart of step S102 in the method for optimizing difference coefficients of a frequency domain acoustic wave equation according to the embodiment of the present invention; in this embodiment of the present invention, the step of performing difference approximation on the frequency domain acoustic wave equation by using the finite difference grid in step S102, and establishing the finite difference format may include:
s1021, carrying out difference approximation on a second-order partial derivative term in a frequency domain acoustic wave equation by using a finite difference grid to obtain a first difference model;
step S1022, carrying out difference approximation on the mass acceleration item in the frequency domain acoustic wave equation by the finite difference grid to obtain a second difference model;
and S1023, obtaining a finite difference format according to the first difference model and the second difference model.
In steps S1021 to S1223, step S1021 is first performed to perform finite difference approximation on the second order partial derivative term in the frequency domain acoustic wave equation by using a 25-point finite difference grid adapted to non-equidistant vertical and horizontal sampling to obtain the following formula 3 and formula 4 (i.e., a first difference model).
Wherein in formula 3 and formula 4, the difference coefficient satisfies:
c 0 +2c 1 +2c 2 +4c 3 +2c 4 +2c 5 +4c 6 +4c 7 +4c 8 =0 (equation 5)
d 0 +2d 1 +2d 2 +4d 3 +2d 4 +2d 5 +4d 6 +4d 7 +4d 8 =0 (equation 6)
p m，n Corresponding to the displacement component at grid m, n. a is 1 ～a 6 And b is 1 ～b 6 Are all differential coefficients
Then, step S1021 is executed, namely, a 25-point finite difference grid which is adaptive to non-equidistant vertical and horizontal sampling is utilized to carry out finite difference approximation on the mass acceleration item in the frequency domain acoustic wave equation; thereby obtaining the following equation 7 (i.e., the second difference model).
Wherein the coefficients satisfy:
b 0 +2b 1 +2b 2 +4b 3 +2b 4 +2b 5 +4b 6 +4b 7 +4b 8 =1 (equation 8)
Finally, step S1023 is executed, that is, the above two finite difference approximation formulas, that is, formula 3, formula 4, and formula 7 are substituted into the original equation of the frequency domain two-dimensional acoustic wave equation to obtain the 25-point finite difference format (that is, the following formula 9) of the whole equation, which is suitable for non-equidistant vertical and horizontal sampling:
referring to fig. 5, fig. 5 is a flowchart of step S103 in the method for optimizing difference coefficients of a frequency domain acoustic wave equation according to the embodiment of the present invention; constructing an optimization objective function according to a finite difference format in step S103; and solving the optimized difference coefficient of the optimized objective function according to the optimization function comprises the following steps:
step S1031, constructing an optimization objective function based on a finite difference format by using a phase velocity dispersion equation;
step S1032, obtaining an objective function according to the optimization function to obtain an optimization coefficient;
and step S1033, obtaining a normalized phase velocity dispersion curve according to the optimization coefficient so as to verify the reliability of the objective function.
It is to be understood that, in steps S1031 to S1033, step S1031 is first performed, that is, a 25-point finite difference coefficient optimization objective function adapted to the non-equidistant vertical and horizontal sampling is constructed by using the phase velocity dispersion equation.
In one example, the objective function may be as follows:
wherein, inIn the above equations 10 and 11, V ph The phase velocity, G the wavelength,
is the wavenumber, θ is the angle of incidence.
It can be seen that the phase velocity dispersion equation is defined as wavenumber
Phase velocity V ph Function between the angles of incidence theta.
Step S1032 is then executed, that is, an optimization coefficient is obtained according to the optimization function to obtain an objective function, specifically: the integral is changed to a sum according to the above equations 10 to 14, and the multivariate function optimization function is used to find the optimization coefficient, such as fmincon in matlab function command, for the above objective function, so as to obtain the result:
a0＝-0.9765；a1＝0.0047；a2＝0.0049；a3＝0.0479；a4＝0.0871；a5＝0.0871； a6＝0.0474；a7＝0.0474；a8＝0.0095；
b0＝0.2830；b1＝0.1098；b2＝0.1098；b3＝0.0547；b4＝0.0059；b5＝0.0059； b6＝0.0042；b7＝0.0042；b8＝0.0004；
c1＝0.0558；c2＝-0.0750；c3＝0.0365；c4＝0.0506；c5＝-0.0750；c6＝0.0263； c7＝0.0365；c8＝0.0263；
d1＝0.0599；d2-0.0750；d3＝0.0448；d4＝0.0511；d5＝-0.0750；d6＝0.0272； d7＝0.0448；d8＝0.0272；
it is understood that fmincon is the matlab function used to solve for the nonlinear multivariate function minimum. The same effect can be achieved by other instructions in other software forms, the embodiment of the present invention is provided only for exemplary purposes, the instruction can be changed, the syntax format of the instruction is not limited, and the same effect only needs to be satisfied, and all of the embodiments of the present invention belong to the protection scope covered by the present invention.
Referring to fig. 6, fig. 6 is a schematic diagram illustrating a normalized phase velocity dispersion curve obtained by performing step S1033 in the method for optimizing difference coefficients of a frequency domain acoustic wave equation according to the embodiment of the present invention; and finally, executing step S1033, and verifying the reliability of the obtained finite difference coefficient by using the obtained coefficient, namely the optimized coefficient, and calculating to obtain a normalized phase velocity dispersion curve. Namely, the reliability of the obtained finite difference coefficient is determined by comparing the finite difference coefficient with the goodness of fit of the phase velocity dispersion curve.
In one embodiment of the present invention, the stochastic inversion method based on the statistical characteristic parameters further includes: and step S104, carrying out forward modeling on the frequency domain acoustic wave equation by using the optimized difference coefficient to determine reliability.
In the foregoing embodiments, the forward modeling of the frequency domain acoustic wave equation by using the optimized finite difference coefficient (i.e., the optimized difference coefficient) in the foregoing step 103 may include: and substituting the optimized finite difference coefficient into a frequency domain two-dimensional acoustic wave equation to realize acoustic wave forward modeling.
Referring to fig. 7, fig. 7 is a flowchart of step S104 in the method for optimizing difference coefficients of a frequency domain acoustic wave equation according to the embodiment of the present invention; further, forward modeling the frequency domain acoustic wave equation with the optimized difference coefficient to determine the reliability in step S104 may include:
s1041, absorbing boundary conditions of a frequency domain acoustic wave equation by using a complete matching layer;
step S1042, training through a numerical value in a preset training model;
and S1043, determining the reliability of the stochastic inversion method according to the training result.
In step S1041, the PML absorption boundary condition is used to reduce or eliminate the interference of the boundary reflection on the numerical test simulation result; the difference format for adding the boundary conditions is:
it will be appreciated that in step S1041, the Perfect Matching Layer (PML) is formed by providing a special dielectric layer at the regional truncation boundary, the wave impedance of which is perfectly matched to that of the adjacent medium, and the incident wave will enter the PML without reflection through the interface.
In step S1042, the training model may be a numerical simulation test of a programmed simple model; the simple medium models may be: layered media, recessed media, marmousi model. Namely, the training model is at least one of a lamellar medium, a concave medium and a Marmousi model.
In step S1043, the reliability of the stochastic inversion method is determined according to the training result, that is, the reliability of the coefficient optimization method is verified by performing comparative analysis on the numerical simulation test result graph.
Wherein the training results include: at least one of a frequency slice, a wavefield snapshot, and a seismic recording.
Referring to fig. 8a, fig. 8a is a schematic diagram illustrating that the model corresponding to step S1043 is a layered model in the method for optimizing difference coefficients of a frequency domain acoustic wave equation according to the embodiment of the present invention;
referring to fig. 8b, fig. 8b is a schematic diagram illustrating that the corresponding model in step S1043 is a concave model in the method for optimizing difference coefficients of a frequency domain acoustic wave equation according to the embodiment of the present invention; and
referring to fig. 8c, fig. 8c is a schematic diagram of the model corresponding to the step S1043 being a Marmousi model in the method for optimizing the difference coefficient of the frequency domain acoustic wave equation according to the embodiment of the present invention.
Referring to fig. 9a to 9c, fig. 9a is a schematic diagram of a forward result obtained when the model corresponding to step S1043 is a layered medium and the frequency slice is 30Hz in the method for optimizing difference coefficients of a frequency domain acoustic wave equation according to the embodiment of the present invention; fig. 9b is a schematic diagram of a forward result obtained when the model corresponding to step S1043 is a layered medium and is in a 0.25S wave field snapshot of the layered medium in the method for optimizing the difference coefficient of the frequency domain acoustic wave equation provided in the embodiment of the present invention; fig. 9c is a schematic diagram of a forward result of seismic recording in a layered medium when the model corresponding to step S1043 is a layered medium in the method for optimizing the difference coefficient of the frequency domain acoustic wave equation provided in the embodiment of the present invention; referring to fig. 10a to 10c, fig. 10a is a schematic diagram of a forward result obtained by performing step S1043 on a model of a concave medium under a 30Hz frequency slice in the method for optimizing difference coefficients of a frequency domain acoustic wave equation according to an embodiment of the present invention; fig. 10b is a schematic diagram of a forward result under a 0.25S wave field snapshot when the model corresponding to step S1043 is a concave medium in the method for optimizing difference coefficients of a frequency domain acoustic wave equation provided in the embodiment of the present invention; fig. 10c is a schematic diagram of a forward result obtained when the model corresponding to step S1043 is a concave medium and is subjected to seismic recording in the concave medium in the difference coefficient optimization method for a frequency domain acoustic wave equation according to the embodiment of the present invention; referring to fig. 11a to fig. 11c, fig. 11a is a schematic diagram of a partial forward result under a 30Hz frequency slice when the corresponding model in step S1043 is the Marmousi model in the method for optimizing difference coefficients of frequency domain acoustic wave equations according to the embodiment of the present invention; fig. 11b is a schematic diagram of a partial forward result under a 0.25S wave field snapshot when the model corresponding to step S1043 is a Marmousi model in the difference coefficient optimization method for a frequency domain acoustic wave equation provided in the embodiment of the present invention; fig. 11c is a schematic diagram of a partial forward result under seismic recording, where the model corresponding to step S1043 in the method for optimizing the difference coefficient of the frequency domain acoustic wave equation provided in the embodiment of the present invention is a Marmousi model.
From the above illustration, it can be seen that the method has feasibility and development prospect from the obtained frequency slice, wave field snapshot and seismic record result.
The forward modeling of the frequency domain is the basis of full waveform inversion of the frequency domain, and researchers propose many forms of finite difference grids for improving the forward modeling precision of the frequency domain, wherein a 25-point finite difference format of a rotating coordinate system is the most commonly used format, but the method is only suitable for the case that longitudinal and transverse sampling intervals are equal, and cannot be applied to the case that the longitudinal and transverse sampling intervals are unequal. The method is based on a 25-point method of a rotating coordinate system, a new coefficient distribution and solving format is used, an objective function is constructed by a phase velocity dispersion equation, a difference coefficient is finally solved and is brought into a frequency domain forward modeling process, and the reliability of the method is proved by test results.
In summary, the embodiment of the invention performs difference approximation on the frequency domain acoustic wave equation through the finite difference grid, establishes the finite difference format, and constructs the optimized objective function by using the finite difference format; solving the optimized difference coefficient of the optimized objective function according to the optimized function; therefore, the technical problem that in the prior art, a traditional 25-point finite difference grid of a rotating coordinate system is used in a finite difference method in forward modeling of a frequency domain, but the grid is only suitable for the condition that longitudinal and transverse sampling intervals are equal, so that the application range is narrow is solved, and the technical effects of reliability and wide applicability are achieved.
Referring to fig. 9, fig. 9 is a schematic block diagram of a difference coefficient optimization apparatus for frequency domain acoustic wave equations according to an embodiment of the present invention; the embodiment of the present invention further provides a difference coefficient optimization apparatus 100 for a frequency domain acoustic wave equation, including:
a determination module 10 for determining a finite difference grid of frequency domain acoustic wave equations,
the calculation module 20 is used for carrying out difference approximation on the frequency domain acoustic wave equation by the finite difference grid and establishing a finite difference format;
the optimization module 30 is configured to construct an optimization objective function according to the finite difference format, and solve an optimization difference coefficient of the optimization objective function according to the optimization function;
and the simulation module 40 is used for performing forward simulation on the frequency domain acoustic wave equation by using the optimized difference coefficient.
It can be understood that each module of the apparatus 100 may implement part or all of the methods of the above method embodiments to solve the technical problem that in the prior art, the limited difference method in the forward modeling of the frequency domain uses a conventional 25-point limited difference grid of the rotating coordinate system, but the grid is only suitable for the case where the vertical and horizontal sampling intervals are equal, which results in a narrow application range, and achieves the technical effects of reliability and wide applicability. The above method embodiments have been described with respect to the specific implementation of the apparatus provided by the embodiments of the present invention, and will not be repeated here.
It will also be understood by those skilled in the art that if the method or the differential coefficient optimization device of the present invention is simply changed, the functions added by the above methods are combined, or the device is replaced, for example, the model materials of the components are replaced, the use environment is replaced, the positional relationship of the components is simply replaced, etc.; or the products formed by the components are integrally arranged; or a detachable design; it is within the scope of the present invention to replace the methods and apparatus of the present invention with any method/apparatus/device that combines the components to form a method/apparatus/device with specific functionality.
The device also comprises a memory, wherein the difference coefficient optimization method of the frequency domain acoustic wave equation can be stored in the memory as a program unit, and the program unit stored in the memory is executed by a processor to realize corresponding functions.
The processor comprises a kernel, and the kernel calls the corresponding program unit from the memory. The kernel can be set to be one or more, and the difference coefficient of the frequency domain sound wave equation is optimized by adjusting the kernel parameters.
The memory may include volatile memory in a computer readable medium, random Access Memory (RAM) and/or nonvolatile memory such as Read Only Memory (ROM) or flash memory (flash RAM), and the memory includes at least one memory chip.
An embodiment of the present invention provides a machine-readable storage medium on which a program is stored, the program implementing a difference coefficient optimization method of a frequency domain acoustic wave equation when executed by a processor.
The embodiment of the invention provides a processor, which is used for running a program, wherein a difference coefficient optimization method of a frequency domain acoustic wave equation is executed when the program runs.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application 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 application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. 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.
In a typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory.
The memory may include forms of volatile memory in a computer readable medium, random Access Memory (RAM) and/or non-volatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). The memory is an example of a computer-readable medium.
Computer-readable media, including both permanent and non-permanent, removable and non-removable media, may implement the information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static Random Access Memory (SRAM), dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), read Only Memory (ROM), electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include transitory computer readable media (transmyedia) such as modulated data signals and carrier waves.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrases "comprising one of 8230; \8230;" 8230; "does not exclude the presence of additional like elements in a process, method, article, or apparatus that comprises the element.
The above are merely examples of the present application and are not intended to limit the present application. Various modifications and changes may occur to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.
Claims (7)
1. A difference coefficient optimization method of a frequency domain acoustic wave equation is suitable for the condition that longitudinal and transverse sampling intervals of a finite difference grid are unequal, and is characterized by comprising the following steps:
determining a finite difference grid of the frequency domain acoustic wave equation;
carrying out difference approximation on a second-order partial derivative term in a frequency domain acoustic wave equation by using a finite difference grid to obtain a first difference model;
carrying out difference approximation on the mass acceleration item in the frequency domain acoustic wave equation by the finite difference grid to obtain a second difference model;
obtaining the finite difference format according to the first difference model and the second difference model;
constructing an optimized objective function based on the finite difference format by utilizing a phase velocity dispersion equation;
obtaining the objective function according to an optimization function to obtain an optimized difference coefficient;
obtaining a normalized phase velocity frequency dispersion curve according to the optimized difference coefficient so as to verify the reliability of the target function;
wherein the finite difference grid is a 25-point frequency domain finite difference grid.
2. The difference coefficient optimization method according to claim 1, further comprising: and performing forward modeling on the frequency domain acoustic wave equation by using the optimized difference coefficient to determine reliability.
3. The difference coefficient optimization method according to claim 2, wherein the forward modeling the frequency domain acoustic wave equation using the optimized difference coefficients to determine reliability comprises:
absorbing the boundary condition of the frequency domain acoustic wave equation by using a complete matching layer;
training through numerical values in a preset training model;
and determining the reliability of the difference coefficient optimization method according to the training result.
4. The difference coefficient optimization method according to claim 3, wherein the training model is at least one of a layered medium, a concave medium, and a Marmousi model.
5. The difference coefficient optimization method according to claim 3, wherein the training result-based method comprises: at least one of a frequency slice, a wave field snapshot, and a seismic recording.
6. A difference coefficient optimization device of a frequency domain acoustic wave equation is suitable for the condition that longitudinal and transverse sampling intervals of finite difference grids are unequal, and is characterized by comprising the following steps:
the determining module is used for determining a finite difference grid of a frequency domain acoustic wave equation, wherein the finite difference grid is a 25-point frequency domain finite difference grid;
the calculation module is used for carrying out difference approximation on a second-order partial derivative term in the frequency domain acoustic wave equation by using the finite difference grid to obtain a first difference model; carrying out difference approximation on the mass acceleration item in the frequency domain acoustic wave equation by the finite difference grid to obtain a second difference model; obtaining the finite difference format according to the first difference model and the second difference model;
the optimization module is used for constructing an optimization objective function based on the finite difference format by utilizing a phase velocity dispersion equation; obtaining the objective function according to an optimization function to obtain an optimized difference coefficient;
and the verification module is used for obtaining a normalized phase velocity dispersion curve according to the optimized difference coefficient so as to verify the reliability of the target function.
7. A computer-readable storage medium having stored thereon instructions for enabling a processor to execute the difference coefficient optimization method of frequency domain acoustic wave equations according to any one of claims 1 to 5 when executed by the processor.
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