A method and device for separating wave fields in seismic exploration of anisotropic elastic media

Abstract

The present application discloses a method and device for wave field separation of anisotropic elastic medium seismic exploration, which relates to the field of seismic exploration technology. The method includes: obtaining relevant model parameters of anisotropic elastic medium in seismic exploration; converting the seismic wave equation of VTI elastic medium in time domain into the wave number domain, and obtaining the polarization properties of P wave and S wave by solving the Christoffel equation; constructing an anisotropic wave field separation operator according to the polarization property, and approximating it by combining polynomial expansion and optimization strategy to obtain an approximate wave field separation operator; applying the approximate wave field separation operator to the original elastic wave field to obtain decoupled P wave and S wave data; based on the decoupled P wave and S wave data, performing seismic exploration processing and interpretation to obtain exploration results. The present application can effectively balance the accuracy and efficiency of the existing anisotropic elastic medium wave field separation method, and improve the accuracy and efficiency in the development of seismic exploration technology.

Description

Technical Field

[0001] The present application relates to the field of seismic exploration technology, and in particular to a method and device for separating wave fields in seismic exploration of anisotropic elastic media. Background Art

[0002] Seismic exploration is an important method to detect underground structures and properties using seismic waves. During the propagation of seismic waves, P waves and S waves are usually coupled with each other. Accurate separation of these two waves is crucial for understanding the propagation characteristics of waves in complex media and suppressing crosstalk noise in imaging.

[0003] In isotropic elastic media, the polarization directions of P waves and S waves are clear and can be directly separated by divergence and curl operators. However, in anisotropic elastic media, since the polarization directions of waves are no longer fixed, the classical separation methods are no longer applicable. Existing technologies for the separation of anisotropic P waves and S waves mainly include wavenumber domain separation methods and improved pseudo-Helmholtz decomposition operators.

[0004] Although the existing methods have achieved certain results, there are still some shortcomings. For example, the existing methods need to decompose the parameter model into multiple homogeneous medium regions, which is difficult to apply in complex medium structures. In addition, the methods that can be applied to heterogeneous media are difficult to use in actual exploration due to excessive computational consumption. Therefore, how to achieve the separation of anisotropic elastic medium wave fields more efficiently and accurately is still a key issue that needs to be solved urgently. Summary of the invention

[0005] In the embodiments of the present application, a method for separating wave fields in seismic exploration of anisotropic elastic media is provided, thereby solving the problem of how to separate wave fields in anisotropic elastic media more efficiently and accurately.

[0006] In a first aspect, an embodiment of the present application provides a method for wavefield separation of seismic exploration in an anisotropic elastic medium, the method comprising: obtaining parameters of a seismic exploration model for an anisotropic elastic medium; converting a time-domain VTI elastic medium seismic wave equation into a wavenumber domain, and obtaining polarization properties of P waves and S waves by solving the Christoffel equation; constructing an anisotropic wavefield separation operator according to the polarization properties, and approximating it by combining polynomial expansion and optimization strategies to obtain an approximate wavefield separation operator; applying the approximate wavefield separation operator to the original elastic wavefield to obtain decoupled P-wave and S-wave data; based on the decoupled P-wave and S-wave data, guiding seismic exploration data acquisition, performing seismic exploration processing and interpretation, and obtaining exploration results.

[0007] In one possible implementation, the Christoffel equation is expressed as: ;in, is the identity matrix, , is the eigenvalue of matrix A, , , is the total wave number, is the phase velocity, is the angular frequency, is the Fourier response of the displacement wave field component in the horizontal direction, is the Fourier response of the displacement wave field component in the vertical direction, is the wave number component in the horizontal direction, is the wave number component in the vertical direction, is the density, , , and is the stiffness matrix parameter in VTI medium; , , , ;in, is the speed of the P wave, is the speed of the S wave, To describe the Thomsen parameter of rock elastic anisotropy, is the Thomsen parameter describing the inelastic effect of rock.

[0008] In a possible implementation, obtaining the polarization properties of the P wave and the S wave by solving the Christoffel equation includes: solving the Christoffel equation to obtain two eigenvalues ​​representing the phase velocities of the P wave and the S wave in the VTI medium, and respectively calculating the two eigenvalues ​​by a first-order Taylor series expansion; the first-order Taylor series expansion considers non-elliptic anisotropy; and calculating the two eigenvalues ​​by the first-order Taylor series expansion is: , .

[0009] In a possible implementation, obtaining the P-wave and S-wave polarization properties by solving the Christoffel equation further includes: using expressions of two eigenvectors corresponding to the two eigenvalues ​​to obtain the P-wave and S-wave polarization properties; the expressions of the two eigenvectors corresponding to the two eigenvalues ​​are: , ;in, is used to describe the polarization vector of the P wave and is used as the polarization attribute of the P wave. It is used to describe the polarization vector of the S wave and take it as the polarization attribute of the S wave. is a unit vector.

[0010] In a possible implementation, the anisotropic wavefield separation operator is constructed according to the polarization attribute, and the approximate wavefield separation operator is processed by combining the polynomial expansion and the optimization strategy to obtain the approximate wavefield separation operator, including: defining a vector wavefield in the wavenumber domain, and projecting the vector wavefield onto the polarization vector to obtain the corresponding projection equation to construct the anisotropic wavefield separation operator, and obtaining the rewritten projection equation based on the anisotropic wavefield separation operator; the vector wavefield in the wavenumber domain is: ;in, is the Fourier response of the displacement wave field in the spatial domain, is the vector P wave field in the wavenumber domain, is the vector S wave field in the wave number domain; the rewritten projection equation is: , , , ;in, is the anisotropic wave field separation operator.

[0011] In a possible implementation, the anisotropic wavefield separation operator is constructed according to the polarization attribute, and the anisotropic wavefield separation operator is approximated by combining the polynomial expansion and optimization strategy to obtain the approximate wavefield separation operator, and further includes: solving the rewritten projection equations simultaneously to obtain the expressions of the components of the P wave and the S wave in the wavenumber domain, and arranging the expressions of the components of the P wave and the S wave in the wavenumber domain into a vector form introducing imaginary numbers to obtain the approximate wavefield separation operator; the expressions of the components of the P wave and the S wave in the wavenumber domain are: , , , ;in, is the horizontal component of the P wave, is the component of the P wave in the vertical direction, is the horizontal component of the S wave, is the component of the S wave in the vertical direction; the vector form of the imaginary number is: , ;in, is the introduced imaginary number, , , is an approximate wavefield separation operator.

[0012] In a possible implementation, the method further includes: using polynomial expansion and optimization strategies to approximate the approximate wavefield separation operator in the vector form of the introduced imaginary number to obtain an approximate expansion equation, and calculating the combination operators of the three wavenumber domains based on the approximate expansion equation, performing inverse Fourier transform on the combination operators of the three wavenumber domains to convert the combination operators of the three wavenumber domains back to the space domain to obtain the combination operators of the three space domains; the approximate expansion equation is: ;in, , and are the coefficients of the right-hand side expanded polynomial, which are related to the wave number and anisotropy parameter, is a parameter related to anisotropy; the combination operators in the three wavenumber domains are , and , , , ; The combinatorial operators of the three spatial domains are , and , , , ;in, is the inverse Fourier transform.

[0013] In a possible implementation, an approximate wavefield separation operator is applied to the original elastic wavefield to obtain decoupled P-wave and S-wave data, including: based on the obtained spatial domain combination operator, applying the spatial domain wavefield separation formula to obtain three intermediate wavefields of the P wave and three intermediate wavefields of the S wave respectively, performing weighted combination on the obtained three intermediate wavefields of the P wave and three intermediate wavefields of the S wave to obtain decoupled P-wave and S-wave data; the spatial domain wavefield separation formula is: , ;in, is the vector P wave field in the spatial domain, is the vector S wave field in the spatial domain, for The inverse Fourier transform of is the pseudo-Helmholtz decomposition operator in the spatial domain, , is the partial derivative with respect to the horizontal direction, is the partial derivative in the vertical direction, , is the vector field; the three intermediate wave fields of the P wave are , and , , , ; The three intermediate wave fields of S wave are , and , , , ; The expression of the decoupled P-wave data is: ; The expression of the decoupled S-wave data is: .

[0014] In a second aspect, an embodiment of the present application provides an anisotropic elastic medium seismic exploration wave field separation device, which includes: an acquisition module, used to obtain anisotropic elastic medium seismic exploration model parameters; an equation solving module, used to convert the time domain VTI elastic medium seismic wave equation into the wave number domain, and obtain the P-wave and S-wave polarization properties by solving the Christoffel equation; an approximate wave field separation operator acquisition module, used to construct an anisotropic wave field separation operator according to the polarization property, and approximate it by combining polynomial expansion and optimization strategy to obtain the approximate wave field separation operator; a decoupled P-wave and S-wave data acquisition module, used to apply the approximate wave field separation operator to the original elastic wave field to obtain decoupled P-wave and S-wave data; an exploration result acquisition module, used to guide seismic exploration data acquisition, perform seismic exploration processing and interpretation, and obtain exploration results based on the decoupled P-wave and S-wave data.

[0015] One or more technical solutions provided in the embodiments of the present application have at least the following technical effects:

[0016] The embodiment of the present application provides a method for wave field separation of seismic exploration of anisotropic elastic medium, obtains the parameters of the seismic exploration model of anisotropic elastic medium, and realizes the conversion to the wave number domain based on the seismic wave equation of VTI elastic medium in the time domain. By solving the Christoffel equation, the polarization properties of P wave and S wave can be accurately obtained, which is very important for understanding the anisotropic characteristics of underground media. Further, the anisotropic wave field separation operator constructed according to the polarization property is approximated by combining the polynomial expansion and optimization strategy to obtain the approximate wave field separation operator, so that the wave field separation process is more efficient and stable. This step not only reduces the computational complexity, but also improves the accuracy and reliability of wave field separation. By processing the original elastic wave field with the approximate wave field separation operator, the decoupling of P wave and S wave can be effectively realized, and high-quality decoupled P wave and S wave data can be obtained. This provides a solid foundation for the subsequent processing and interpretation of seismic exploration data, making the exploration results more accurate and reliable. Based on the decoupled P-wave and S-wave data, the acquisition and processing of seismic exploration data can be guided more accurately, improving the efficiency and success rate of exploration. It solves the problem of how to separate the wave field of anisotropic elastic media more efficiently and accurately. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments of the present application or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0018] Figure 1 A flow chart of a method for wave field separation in seismic exploration of anisotropic elastic media provided in an embodiment of the present application;

[0019] Figure 2 A comparison diagram of the original wavefield separation operator constructed based on the eigenvalues ​​obtained by the first-order Taylor expansion provided in an embodiment of the present application, the form of approximating the wavefield separation operator by the existing method, and the approximate expansion equation of the present application;

[0020] Figure 3 A schematic diagram of vector elastic wave fields of different components calculated by the existing method and the separated vector P wave fields and S wave fields provided in an embodiment of the present application;

[0021] Figure 4 A schematic diagram of vector elastic wave fields of different components and separated vector P wave fields and S wave fields calculated by the method of the present application provided in an embodiment of the present application;

[0022] Figure 5 A waveform recording diagram of the x component at the target point calculated by the existing method and the method of the present application provided in the embodiment of the present application;

[0023] Figure 6 Parameter diagram of the anisotropic Marmousi model provided in the embodiment of the present application;

[0024] Figure 7 A schematic diagram of a wave field separation result obtained by applying the method of the present application to an anisotropic Marmousi model provided in an embodiment of the present application;

[0025] Figure 8 A schematic diagram of an anisotropic elastic medium seismic exploration wave field separation device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0026] The technical solutions in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0027] The following describes some of the techniques involved in the embodiments of the present application to facilitate understanding, and they should be considered as merely exemplary. Therefore, it should be appreciated by those of ordinary skill in the art that various changes and modifications may be made to the embodiments described herein without departing from the scope and spirit of the present application. Similarly, for the sake of clarity and conciseness, some descriptions of well-known functions and structures are omitted in the following description.

[0028] The present application embodiment provides a method for separating wave fields in seismic exploration of anisotropic elastic media. Figure 1 As shown, the method includes steps S101 to S105. Among them, Figure 1 This is only an execution order shown in the embodiment of the present application, and does not represent the only execution order of a method for wave field separation in seismic exploration of anisotropic elastic media. In the case where the final result can be achieved, Figure 1 The steps shown may be performed in parallel or reversed.

[0029] S101: Obtaining parameters of anisotropic elastic medium seismic exploration model.

[0030] The parameters of the anisotropic elastic medium seismic exploration model include the velocity parameters of P waves, the velocity parameters of S waves, the density parameters, and the Thomsen anisotropy parameters used in the anisotropic seismic exploration wave field simulation. and .

[0031] S102: Based on the VTI elastic medium seismic wave equation in the time domain, it is converted to the wave number domain, and the polarization properties of P waves and S waves are obtained by solving the Christoffel equation.

[0032] It should be noted that the seismic wave equation of VTI elastic medium in the time domain and the Christoffel equation in the wave number domain are equivalent. VTI elastic medium is a transversely isotropic medium. P waves are longitudinal waves, and S waves are transverse waves.

[0033] In VTI media, the Christoffel equation can accurately represent the characteristics of elastic wave propagation. The expression of the Christoffel equation is: .in, is the identity matrix, , is the eigenvalue of matrix A, , , is the total wave number, is the phase velocity, is the angular frequency, is the Fourier response of the displacement wave field component in the horizontal direction, is the Fourier response of the displacement wave field component in the vertical direction, is the wave number component in the horizontal direction, is the wave number component in the vertical direction, is the density, , , and is the stiffness matrix parameter in VTI medium. , , , .in, is the speed of the P wave, is the speed of the S wave, To describe the Thomsen parameter of rock elastic anisotropy, is the Thomsen parameter describing the inelastic effect of rock.

[0034] By solving the Christoffel equation, the polarization properties of the P wave and the S wave are obtained, including: solving the Christoffel equation to obtain two eigenvalues ​​representing the phase velocity of the P wave and the S wave in the VTI medium, and calculating the two eigenvalues ​​respectively by the first-order Taylor series expansion. The first-order Taylor series expansion takes into account the non-elliptic anisotropy. The two eigenvalues ​​calculated by the first-order Taylor series expansion are: , .

[0035] Furthermore, in VTI media, the matrix A describes the relationship between the displacement wave field components of elastic waves in the horizontal and vertical directions, and its determinant form can be expressed as: . Solve the eigenvalue when the above determinant is equal to zero and . The eigenvalues ​​represent the phase velocities of P and S waves in VTI media. To simplify the calculation, the stiffness matrix parameters are replaced by Thomsen anisotropy parameters to obtain a further simplified form of the eigenvalues. . and The expression of contains radical terms and complex fractional forms, which describe the propagation characteristics of waves in VTI media. These expressions are difficult to solve and apply directly, so approximate methods are needed to deal with them.

[0036] It should be noted that It can also indicate the eigenvalue and The expression of Pick When , it represents the eigenvalue ; When the formula Pick When , it represents the eigenvalue .

[0037] Exact eigenvalues and It contains a square root term, which is difficult to solve directly, so the first-order Taylor expansion is used to approximate it. Based on the first-order Taylor expansion, we can get: , .

[0038] By solving the Christoffel equation, the P-wave and S-wave polarization properties are obtained, and the method further includes: using expressions of two eigenvectors corresponding to the two eigenvalues ​​to obtain the P-wave and S-wave polarization properties. The expressions of the two eigenvectors corresponding to the two eigenvalues ​​are: , .in, is used to describe the polarization vector of the P wave and is used as the polarization attribute of the P wave. It is used to describe the polarization vector of the S wave and take it as the polarization attribute of the S wave. is a unit vector.

[0039] Specifically, in anisotropic media, the polarization properties of seismic waves become particularly complex and critical. In order to accurately describe the polarization properties of these waves, two eigenvectors corresponding to the two eigenvalues ​​are introduced. These two eigenvectors, namely and , which are used to describe the polarization characteristics of P waves and S waves respectively. During the propagation of P waves, their vibration direction is consistent with the propagation direction, so their polarization vector, that is, the vibration direction, is closely related to the propagation direction of the wave. The vibration direction of S waves is perpendicular to the propagation direction, so there is an obvious orthogonal relationship between their polarization vector and the propagation direction of the wave. It is important to note that in anisotropic media, these two eigenvectors and are perpendicular to each other. This characteristic provides an important basis for separating P waves and S waves in actual seismic data processing. In order to achieve the separation of P waves and S waves, the projection principle of vector wave fields can be used. Specifically, the displacement or velocity component wave field can be projected onto the eigenvector and In the direction of. Since the polarization vectors of P-wave and S-wave are respectively and Therefore, by projecting the wave field into the direction of these eigenvectors, the P-wave and S-wave components can be effectively separated.

[0040] Furthermore, the derivation process of the two eigenvectors is as follows. and Uniformly marked as , and mark the corresponding feature vector as , which describes the relationship between the eigenvalues ​​and eigenvectors of matrix A. The following system of equations is obtained: In this system of equations, there are two unknowns and , which represent the two components of the eigenvector. By solving this system of equations, we can find the eigenvalue The corresponding eigenvector In particular, In ( is the wave number component in the vertical direction), , the known eigenvalues Substituting this into the equation, the eigenvector The expression is: . Eigenvector With eigenvalue correspond. is the speed of the P wave and the speed of the S wave as well as and The unit vector involved. To describe the Thomsen parameter of rock elastic anisotropy, is the Thomsen parameter describing the inelastic effect of rock.

[0041] for There are two cases for the expression of : one is to expand it through the zero-order Taylor series expansion, and the other is to expand it through the first-order Taylor series expansion. When expanded through the zero-order Taylor series expansion: . When expanded by a first-order Taylor expansion: , , , , .

[0042] Similarly, when we order In ( is the horizontal wave number component), we can solve , and then get the feature vector The expression This feature vector With eigenvalue correspond.

[0043] S103: construct an anisotropic wavefield separation operator according to the polarization attribute, perform approximate processing on it by combining polynomial expansion and optimization strategy, and obtain an approximate wavefield separation operator.

[0044] According to the polarization attribute, an anisotropic wavefield separation operator is constructed, and it is approximated by combining polynomial expansion and optimization strategy to obtain an approximate wavefield separation operator, including: defining the vector wavefield in the wavenumber domain, and projecting the vector wavefield onto the polarization vector to obtain the corresponding projection equation to construct the anisotropic wavefield separation operator, and obtaining the rewritten projection equation based on the anisotropic wavefield separation operator. The vector wavefield in the wavenumber domain is: .in, is the Fourier response of the displacement wave field in the spatial domain, is the vector P wave field in the wavenumber domain, is the vector S wave field in the wave number domain. The rewritten projection equation is: , , , .in, is the anisotropic wave field separation operator.

[0045] Specifically, is the displacement wave field in the spatial domain The Fourier response of . Among them, is the displacement wave field The component in the x direction, is the displacement wave field Component in the z direction. The component in the x direction, Component in the z direction. is the vector P wave field in the wavenumber domain, is the wave field of vector S in the wave number domain. Among them, The component in the x direction, The component in the z direction, The component in the x direction, Component in the z direction.

[0046] It should be noted that the x direction in the present application is the horizontal direction, and the z direction is the vertical direction.

[0047] Specifically, in VTI media, the separation of elastic wave fields is a key step that helps to gain a deeper understanding of the wave propagation characteristics and the properties of the medium. Based on the theory of vector wave field separation, a specific method can be used to project the elastic wave fields onto their respective polarization directions to achieve wave field separation. However, traditional separation methods, such as non-stationary filtering or low-rank approximation methods, require multiple Fourier transforms in each time iteration step, which results in a large amount of computation.

[0048] In order to improve the computational efficiency and ensure the separation accuracy, this application proposes a new method: the pseudo-Helmholtz decomposition operator and the optimization expansion strategy are combined to effectively separate the VTI elastic wave field. , which consists of and composition. is the vector P wave field in the wavenumber domain, is the vector S wave field in the wave number domain. Based on the Helmholtz decomposition theory, the vector wave field , and Projection onto the known polarization vector and To obtain the projection equation, we define an anisotropic wave field separation operator , which is related to the polarization vector The form is consistent and orthogonal to the polarization vector This operator can be regarded as a pseudo-Helmholtz decomposition operator in the wave number domain, which can more effectively separate P waves and S waves. and is the feature vector and .

[0049] According to the polarization attribute, an anisotropic wavefield separation operator is constructed, and it is approximated by combining polynomial expansion and optimization strategy to obtain an approximate wavefield separation operator, which also includes: solving the rewritten projection equations to obtain the expressions of the P-wave and S-wave components in the wavenumber domain, and organizing the expressions of the P-wave and S-wave components in the wavenumber domain into a vector form with the introduction of imaginary numbers to obtain the approximate wavefield separation operator. The expressions of the P-wave and S-wave components in the wavenumber domain are: , , , .in, is the horizontal component of the P wave, is the component of the P wave in the vertical direction, is the horizontal component of the S wave, is the component of the S wave in the vertical direction. The vector form of the introduced imaginary number is: , .in, is the introduced imaginary number, , , is an approximate wavefield separation operator.

[0050] Specifically, in the process of wave field separation, a core problem is to effectively solve the wave field separation operator . Since it is very difficult to directly calculate the operator, the existing technology uses a method that combines the weak anisotropy assumption and the Taylor series expansion for approximate processing. This approximate equation simplifies the calculation of the original operator to a certain extent, allowing the wavefield separation process to proceed. However, an in-depth analysis of this approximate method reveals that it has two main problems. 1. Taylor expansion is essentially a low-frequency / low-wavenumber approximation method. As the frequency or wavenumber increases, the accuracy of the approximation will gradually decrease, making it difficult to obtain accurate results under high-frequency or high-wavenumber conditions. 2. This approximate equation is constructed based on the assumption of elliptical anisotropy. Therefore, in non-elliptical anisotropy ( ) parameter conditions, its approximate accuracy is difficult to guarantee. This limits the application of this technology in a wider range of anisotropic media.

[0051] Furthermore, in order to further improve the calculation accuracy, this application proposes a method combining polynomial expansion and optimization strategy, which is specifically used for approximate wave field separation operator This method uses polynomial expansion and optimization strategies to approximate the wave field separation operator. Make an approximation.

[0052] The approximate wavefield separation operator in the vector form with the introduction of imaginary numbers is approximated by polynomial expansion and optimization strategy to obtain the approximate expansion equation. The combination operators in the three wavenumber domains are calculated based on the approximate expansion equation. The combination operators in the three wavenumber domains are subjected to inverse Fourier transform to convert the combination operators in the three wavenumber domains back to the space domain to obtain the combination operators in the three space domains.

[0053] The wave field separation operator in the vector form of the introduced imaginary number is approximated by using polynomial expansion and optimization strategy to obtain the approximate expansion equation, and the combination operators of the three wave number domains are calculated based on the approximate expansion equation. The combination operators of the three wave number domains are subjected to inverse Fourier transform to convert the combination operators of the three wave number domains back to the space domain to obtain the combination operators of the three space domains, including: The approximate expansion equation is: .in, , and are the coefficients of the right-hand side expanded polynomial, which are related to the wave number and anisotropy parameter, is a parameter related to anisotropy. The combination operators in the three wavenumber domains are , and , , , The combinatorial operators of the three spatial domains are , and , , , .in, is the inverse Fourier transform.

[0054] Specifically, further observation of the approximate expansion equation shows that, compared with the form of the wavefield separation operator using the first-order Taylor expansion, the form of the approximate expansion equation of the present application is actually a linear equation. Therefore, the solution can be obtained by minimizing the error between the original operator and the expansion polynomial. , and To this end, this application constructs the following objective function. The objective function is: .in, is the objective function, is the wave number component in the horizontal direction, is the wave number component in the vertical direction, In the wave number domain To perform integration, In the wave number domain By using the optimization algorithm to solve the above equation, the coefficients of the optimized polynomial can be obtained. , and These coefficients will make the expansion polynomial approximate the original operator as accurately as possible in the wave number domain, thereby significantly improving the accuracy of the approximate processing while ensuring the computational efficiency.

[0055] S104: Apply an approximate wave field separation operator to the original elastic wave field to obtain decoupled P-wave and S-wave data.

[0056] Applying an approximate wavefield separation operator to the original elastic wavefield to obtain decoupled P-wave and S-wave data, including: based on the obtained spatial domain combination operator, applying the spatial domain wavefield separation formula to obtain three intermediate wavefields of the P wave and three intermediate wavefields of the S wave respectively, performing weighted combination on the obtained three intermediate wavefields of the P wave and the three intermediate wavefields of the S wave to obtain the decoupled P-wave and S-wave data.

[0057] The formula for wave field separation in the spatial domain is: , .in, is the vector P wave field in the spatial domain, is the vector S wave field in the spatial domain, for The inverse Fourier transform of is the pseudo-Helmholtz decomposition operator in the spatial domain, , is the partial derivative with respect to the horizontal direction, is the partial derivative in the vertical direction, , is a vector field. The three intermediate wave fields of the P wave are , and , , , The three intermediate wave fields of S waves are , and , , , The expression of the decoupled P-wave data is: The expression of the decoupled S-wave data is: .

[0058] S105: Based on the decoupled P-wave and S-wave data, guide seismic exploration data acquisition, perform seismic exploration processing and interpretation, and obtain exploration results.

[0059] Based on the decoupled P-wave and S-wave data, we can more accurately understand the propagation characteristics of different seismic wave types in underground media, guide the optimization and design of the observation system during the seismic exploration data acquisition process, and effectively verify the seismic exploration processing methods and interpretation results, thereby obtaining higher-precision exploration results.

[0060] Specifically, the spatial domain wave field separation formula is obtained by and Substitution At the same time, , and Converted to the spatial domain. and .in, for The component in the x direction, for The component in the z direction, for The component in the x direction, for Component in the z direction.

[0061] When using the existing approximation scheme, The expression in the spatial domain is: When the solution of this application is adopted, The expression in the spatial domain is .

[0062] Compute the pseudo-Helmholtz decomposition operator in the spatial domain and consider the form of the parameter r. When the Christoffel equation is expanded by the zero-order Taylor series expansion, the parameter r in the spatial domain is: When the Christoffel equation is expanded by a first-order Taylor series expansion, the parameter r in the spatial domain is: , , , , .in, Represents the phase direction vector. In the wave number domain, the phase direction vector is calculated using the wave number vector: , .in, is the wave number vector in the horizontal direction, is the wave number vector in the vertical direction. In the spatial domain, the phase direction vector is calculated using the wave field gradient operator: .in, is the wavefield gradient operator, is a vector field.

[0063] This application uses a uniform anisotropic model to obtain the eigenvalues ​​obtained using the first-order Taylor expansion , And the further simplified form of the eigenvalue is , The further simplified form of the eigenvalue is taken as the exact eigenvalue. The background parameters of the model are , , , the Thomsen anisotropy parameter is , The purpose of this study is to compare the differences between the eigenvalues ​​obtained by the first-order Taylor expansion and the exact eigenvalues. ) on the eigenvalues. Evaluate the performance of the Taylor expansion strategy in terms of computational efficiency and approximation accuracy.

[0064] Figure 2 A comparison chart of the original wavefield separation operator constructed based on the eigenvalues ​​obtained from the first-order Taylor expansion provided in the embodiment of the present application, the form of the wavefield separation operator approximated by the existing method, and the approximate expansion equation of the present application. The specific parameters of the anisotropic model are , . Figure 2 (a) in the figure is the original wave field separation operator. Figure 2 (b) in the existing method is to Schematic diagram of the absolute error between the approximated form and the original wavefield separation operator. Figure 2(c) is a schematic diagram of the absolute error between the wavefield separation operator calculated using the approximate expansion equation of the present application and the original wavefield separation operator.

[0065] Existing methods all have significant errors. Compared with existing methods, the approximate expansion equations of this application show higher approximate accuracy under different parameter conditions. This discovery lays a solid foundation for the development and application of wave field separation technology for seismic exploration of complex anisotropic elastic media.

[0066] This application uses a uniform anisotropic elastic model to test the effectiveness of existing methods and the method of this application in wave field separation. The model size is 4000m×4000m, and the horizontal and vertical grid spacing is 10m. A Ricker wavelet with a main frequency of 25Hz is selected and placed in the center of the model to generate a P-wave source. The time sampling interval is 1ms. The background parameters of the uniform anisotropic elastic model are , , , Thomsen anisotropy parameters are , The related equations are numerically discretized using the staggered grid finite difference method with second-order accuracy in time and twelfth-order accuracy in space.

[0067] Figure 3 A schematic diagram of vector elastic wave fields of different components calculated using the existing method and the separated vector P wave fields and S wave fields provided in the embodiment of the present application. Figure 3 (a) in the figure is the full wave field of the x component. Figure 3 (b) is the decoupled x-component P wave field. Figure 3 (c) in the figure is the decoupled x-component S wave field. Figure 3 (d) in the figure is the full wave field of the z component. Figure 3 (e) in the figure is the decoupled z-component P wave field. Figure 3 (f) in the figure is the decoupled z-component S wave field.

[0068] Figure 4 A schematic diagram of vector elastic wave fields of different components and separated vector P wave fields and S wave fields calculated by the method of the present application provided in the embodiment of the present application. Figure 4 (a) in the figure is the full wave field of the x component. Figure 4 (b) is the decoupled x-component P wave field. Figure 4 (c) in the figure is the decoupled x-component S wave field. Figure 4 (d) in the figure is the full wave field of the z component. Figure 4 (e) in the figure is the decoupled z-component P wave field. Figure 4 (f) in the figure is the decoupled z-component S wave field. Figure 3 and Figure 4It can be seen that the residual amount calculated by the method of the present application is smaller.

[0069] Figure 5 The waveform recording diagram of the x component at the target point calculated by the existing method and the method of the present application is provided in the embodiment of the present application. The target point is (1500m, 1500m). Figure 5 (a) in the figure is the existing method. Figure 5 (b) in the figure is the method of this application. The black solid line in the figure is the original full elastic wave field, the red dotted line is the decoupled P wave field, and the green dotted line is the decoupled S wave field. Figure 5 The matching degree of the colored dashed lines (red and green) with the black solid line, Figure 5 The matching degree of (a) is poor. Figure 5 (b) in the figure has a higher match.

[0070] By comparing the separation results of the two methods, it can be seen that the method in the present application can produce a higher precision separation effect, and the single-channel waveform after separation has a higher matching degree with the original waveform, as shown by the black arrow in the figure.

[0071] Figure 6 Parameter diagram of the anisotropic Marmousi model provided in the embodiment of the present application. Including the velocity of the P wave , Thomsen anisotropy parameter and . Figure 6 (a) is the velocity of the P wave picture. Figure 6 (b) is the Thomsen anisotropy parameter picture. Figure 6 (c) is the Thomsen anisotropy parameter Fig. In this model, the ratio of S-wave to P-wave velocities is set to 1:1.7, and the density is given by the empirical formula The calculation area of ​​the anisotropic model is 5000m×3500m, and the length of the discrete grid unit is 10m. In order to generate the P-wave source, a Ricker wavelet with a main frequency of 18Hz is placed in the shallow position.

[0072] Figure 7 The present application provides a schematic diagram of the wavefield separation results obtained by applying the method of the present application to the anisotropic Marmousi model, which clearly shows the high-precision vector P wavefield and vector S wavefield. The method of the present application can show excellent performance when processing complex anisotropic models and generate high-precision wavefield separation results. These results provide effective wavefield continuation algorithms and tools for subsequent imaging and inversion research of elastic anisotropic media, and have important practical application value. Among them, Figure 7 (a) in the figure is the full wave field of the x component. Figure 7 (b) is the decoupled x-component P wave field. Figure 7 (c) in the figure is the decoupled x-component S wave field. Figure 7 (d) in the figure is the full wave field of the z component. Figure 7 (e) in the figure is the decoupled z-component P wave field. Figure 7 (f) in the figure is the decoupled z-component S wave field.

[0073] The present application also provides an anisotropic elastic medium seismic exploration wave field separation device 800, such as Figure 8 As shown, the device includes: an acquisition module 801, an equation solving module 802, an approximate wave field separation operator acquisition module 803, a decoupled P-wave and S-wave data acquisition module 804, and an exploration result acquisition module 805.

[0074] The acquisition module 801 is used to acquire the parameters of the anisotropic elastic medium seismic exploration model.

[0075] The equation solving module 802 is used to convert the VTI elastic medium seismic wave equation in the time domain into the wave number domain, and obtain the polarization properties of the P wave and the S wave by solving the Christoffel equation.

[0076] The module 803 for obtaining an approximate wavefield separation operator is used to construct an anisotropic wavefield separation operator according to polarization attributes, and perform approximate processing on the anisotropic wavefield separation operator in combination with polynomial expansion and optimization strategy to obtain an approximate wavefield separation operator.

[0077] The module 804 for obtaining decoupled P-wave and S-wave data is used to apply the approximate wavefield separation operator to the original elastic wavefield to obtain decoupled P-wave and S-wave data.

[0078] The exploration result obtaining module 805 is used to guide seismic exploration data acquisition, perform seismic exploration processing and interpretation, and obtain exploration results based on the decoupled P-wave and S-wave data.

[0079] Some modules in the apparatus described in the present application can be described in the general context of computer executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, classes, etc. that perform specific tasks or implement specific abstract data types. The present application can also be practiced in distributed computing environments, in which tasks are performed by remote processing devices connected through a communication network. In a distributed computing environment, program modules can be located in local and remote computer storage media including storage devices.

[0080] The devices or modules described in the above application embodiments can be implemented by computer chips or entities, or by products with certain functions. For the convenience of description, the above devices are described in various modules according to their functions. When implementing the embodiments of the present application, the functions of each module can be implemented in the same or multiple software and / or hardware. Of course, the module that implements a certain function can also be implemented by combining multiple sub-modules or sub-units.

[0081] The methods, devices or modules described in this application can be implemented in the form of computer-readable program codes. The controller can be implemented in any appropriate manner. For example, the controller can take the form of a microprocessor or processor and a computer-readable medium storing computer-readable program codes (such as software or firmware) that can be executed by the (micro)processor, logic gates, switches, application-specific integrated circuits (English: Application Specific Integrated Circuit, referred to as: ASIC), programmable logic controllers and embedded microcontrollers. Examples of controllers include but are not limited to the following microcontrollers: ARC 625D, Atmel AT91SAM, Microchip PIC18F26K20 and Silicone Labs C8051F320. The memory controller can also be implemented as part of the control logic of the memory. Those skilled in the art also know that in addition to implementing the controller in the form of pure computer-readable program codes, the controller can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers and embedded microcontrollers by logically programming the method steps. Therefore, this controller can be considered as a hardware component, and the devices included in it for implementing various functions can also be regarded as structures within the hardware component. Or even, the means for realizing various functions may be regarded as both a software module for realizing the method and a structure within a hardware component.

[0082] It can be seen from the description of the above implementation methods that those skilled in the art can clearly understand that the present application can be implemented by means of software plus necessary hardware. Based on this understanding, the technical solution of the present application can be essentially or partly contributed to the prior art in the form of a software product, or it can be reflected in the implementation process of data migration. The computer software product can be stored in a storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a mobile terminal, a server, or a network device, etc.) to execute the method described in the embodiment of the present application.

[0083] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. All or part of this application can be used in many general or special computer system environments or configurations.

[0084] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit the present application. Although the present application has been described in detail with reference to the aforementioned embodiments, a person of ordinary skill in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present application.

Claims

1. A method for wave field separation in seismic exploration of anisotropic elastic media, characterized in that: include: Obtaining parameters of anisotropic elastic medium seismic exploration model; According to the VTI elastic medium seismic wave equation in the time domain, it is converted into the wave number domain, and the polarization properties of P waves and S waves are obtained by solving the Christoffel equation; The method of obtaining the polarization properties of P waves and S waves by solving the Christoffel equation includes: solving the Christoffel equation to obtain two eigenvalues ​​representing the phase velocities of P waves and S waves in the VTI medium, and respectively calculating the two eigenvalues ​​by a first-order Taylor series expansion; the first-order Taylor series expansion considers non-elliptic anisotropy; and calculating the two eigenvalues ​​by the first-order Taylor series expansion is: , ;in, To describe the Thomsen parameter of rock elastic anisotropy, is the Thomsen parameter describing the inelastic effect of rock, is the speed of the P wave, is the speed of the S wave, is the wave number component in the horizontal direction, is the wave number component in the vertical direction, is the density; according to the polarization attribute, an anisotropic wave field separation operator is constructed, and it is approximated by combining polynomial expansion and optimization strategy to obtain an approximate wave field separation operator; Apply the approximate wave field separation operator to the original elastic wave field to obtain the decoupled P-wave and S-wave data; The approximate wavefield separation operator in the vector form of the introduced imaginary number is approximated by using polynomial expansion and optimization strategy to obtain the approximate expansion equation, and the combination operators in the three wavenumber domains are calculated based on the approximate expansion equation. The combination operators in the three wavenumber domains are subjected to inverse Fourier transformation to convert the combination operators in the three wavenumber domains back to the space domain to obtain the combination operators in the three space domains. The method of applying the approximate wavefield separation operator to the original elastic wavefield to obtain the decoupled P-wave and S-wave data comprises: applying the spatial domain wavefield separation formula based on the obtained spatial domain combination operator to obtain three intermediate wavefields of the P-wave and three intermediate wavefields of the S-wave respectively, and performing weighted combination on the obtained three intermediate wavefields of the P-wave and three intermediate wavefields of the S-wave to obtain the decoupled P-wave and S-wave data; Based on the decoupled P-wave and S-wave data, seismic exploration data acquisition is guided, and seismic exploration processing and interpretation are carried out to obtain exploration results.

2. The anisotropic elastic medium seismic exploration wave field separation method according to claim 1, characterized in that: The expression of Christoffel equation is: ;in, is the identity matrix, , is the eigenvalue of matrix A, , , is the total wave number, is the phase velocity, is the angular frequency, is the Fourier response of the displacement wave field component in the horizontal direction, is the Fourier response of the displacement wave field component in the vertical direction, is the wave number component in the horizontal direction, is the wave number component in the vertical direction, is the density, , , and is the stiffness matrix parameter in VTI medium; , , , ;in, is the speed of the P wave, is the speed of the S wave, To describe the Thomsen parameter of rock elastic anisotropy, is the Thomsen parameter describing the inelastic effect of rock.

3. The anisotropic elastic medium seismic exploration wave field separation method according to claim 2, characterized in that: The method of obtaining the polarization properties of P-wave and S-wave by solving the Christoffel equation also includes: Use expressions for the two eigenvectors corresponding to the two eigenvalues ​​to obtain P-wave and S-wave polarization properties; The expressions for the two eigenvectors corresponding to the two eigenvalues ​​are: , ;in, is used to describe the polarization vector of the P wave and is used as the polarization attribute of the P wave. It is used to describe the polarization vector of the S wave and take it as the polarization attribute of the S wave. is a unit vector.

4. The anisotropic elastic medium seismic exploration wave field separation method according to claim 3, characterized in that: The anisotropic wave field separation operator is constructed according to the polarization attribute, and is approximated by combining polynomial expansion and optimization strategy to obtain an approximate wave field separation operator, including: A vector wave field in the wave number domain is defined, and the vector wave field is projected onto the polarization vector to obtain the corresponding projection equation, so as to construct an anisotropic wave field separation operator, and a rewritten projection equation is obtained based on the anisotropic wave field separation operator; The vector wave field in the wavenumber domain is: ;in, is the Fourier response of the displacement wave field in the spatial domain, is the vector P wave field in the wavenumber domain, is the vector S wave field in the wave number domain; The rewritten projection equation is: , , , ;in, is the anisotropic wave field separation operator.

5. The anisotropic elastic medium seismic exploration wave field separation method according to claim 4, characterized in that: The method further includes: constructing an anisotropic wave field separation operator according to the polarization attribute, performing approximate processing on the anisotropic wave field separation operator by combining polynomial expansion and optimization strategy to obtain an approximate wave field separation operator; The rewritten projection equations are solved simultaneously to obtain the expressions of the components of the P wave and the S wave in the wave number domain, and the expressions of the components of the P wave and the S wave in the wave number domain are organized into vector forms with the introduction of imaginary numbers to obtain an approximate wave field separation operator; The expressions for the components of P and S waves in the wavenumber domain are: , , , ;in, is the horizontal component of the P wave, is the component of the P wave in the vertical direction, is the horizontal component of the S wave, is the component of the S wave in the vertical direction; The vector form of the introduced imaginary number is: , ;in, is the introduced imaginary number, , , is an approximate wavefield separation operator.

6. The anisotropic elastic medium seismic exploration wave field separation method according to claim 5, characterized in that: Also includes: The approximate wavefield separation operator in the vector form of the introduced imaginary number is approximated by using polynomial expansion and optimization strategy to obtain the approximate expansion equation, and the combination operators in the three wavenumber domains are calculated based on the approximate expansion equation. The combination operators in the three wavenumber domains are subjected to inverse Fourier transformation to convert the combination operators in the three wavenumber domains back to the space domain to obtain the combination operators in the three space domains. The approximate expanded equation is: ;in, , and are the coefficients of the right-hand side expanded polynomial, which are related to the wave number and anisotropy parameter, is a parameter related to anisotropy; The three wavenumber domain combination operators are , and , , , ; The combinatorial operators of the three spatial domains are , and , , , ;in, is the inverse Fourier transform.

7. The method for separating wave fields in seismic exploration of anisotropic elastic media according to claim 6, characterized in that: Apply the approximate wave field separation operator to the original elastic wave field to obtain the decoupled P-wave and S-wave data, including: Based on the obtained combination operator in the space domain, the space domain wave field separation formula is applied to obtain three intermediate wave fields of the P wave and three intermediate wave fields of the S wave respectively, and the obtained three intermediate wave fields of the P wave and three intermediate wave fields of the S wave are weightedly combined to obtain the decoupled P wave and S wave data; The formula for wave field separation in the spatial domain is: , ;in, is the vector P wave field in the spatial domain, is the vector S wave field in the spatial domain, for The inverse Fourier transform of is the pseudo-Helmholtz decomposition operator in the spatial domain, , is the partial derivative with respect to the horizontal direction, is the partial derivative in the vertical direction, , is a vector field; The three intermediate wave fields of the P wave are , and , , , ; The three intermediate wave fields of S waves are , and , , , ; The expression of the decoupled P-wave data is: ; The expression of the decoupled S-wave data is: .

8. An anisotropic elastic medium seismic exploration wave field separation device, characterized in that: include: An acquisition module, used for acquiring parameters of anisotropic elastic medium seismic exploration model; The equation solving module is used to convert the time domain VTI elastic medium seismic wave equation into the wave number domain, and obtain the polarization properties of P waves and S waves by solving the Christoffel equation; the obtaining of the polarization properties of P waves and S waves by solving the Christoffel equation includes: solving the Christoffel equation to obtain two eigenvalues ​​representing the phase velocity of P waves and S waves in the VTI medium, and respectively calculating the two eigenvalues ​​by a first-order Taylor series expansion; the first-order Taylor series expansion considers non-elliptic anisotropy; the two eigenvalues ​​are calculated by the first-order Taylor series expansion as follows: , ;in, To describe the Thomsen parameter of rock elastic anisotropy, is the Thomsen parameter describing the inelastic effect of rock, is the speed of the P wave, is the speed of the S wave, is the wave number component in the horizontal direction, is the wave number component in the vertical direction, is the density; An approximate wavefield separation operator module is obtained, which is used to construct an anisotropic wavefield separation operator according to polarization attributes, and approximate it by combining polynomial expansion and optimization strategy to obtain an approximate wavefield separation operator; A module for obtaining decoupled P-wave and S-wave data is provided, which is used to apply an approximate wavefield separation operator to the original elastic wavefield to obtain decoupled P-wave and S-wave data; a polynomial expansion and optimization strategy is used to approximate the approximate wavefield separation operator in the vector form of an imaginary number to obtain an approximate expansion equation, and based on the approximate expansion equation, combination operators in three wavenumber domains are calculated, and an inverse Fourier transform is performed on the combination operators in the three wavenumber domains to convert the combination operators in the three wavenumber domains back to the space domain to obtain combination operators in three space domains; the application of the approximate wavefield separation operator to the original elastic wavefield to obtain decoupled P-wave and S-wave data comprises: based on the obtained space domain combination operator, applying the space domain wavefield separation formula to respectively obtain three intermediate wavefields of the P wave and three intermediate wavefields of the S wave, and weighted combination of the obtained three intermediate wavefields of the P wave and three intermediate wavefields of the S wave to obtain decoupled P-wave and S-wave data; The exploration result obtaining module is used to guide seismic exploration data acquisition, perform seismic exploration processing and interpretation, and obtain exploration results based on the decoupled P-wave and S-wave data.

Images