Anisotropic medium viscosity wave equation construction and solving method and device

Abstract

The invention belongs to the technical field of geophysical exploration seismic forward modeling, and discloses a method and a device for constructing and solving a viscous wave equation of an anisotropic medium, and the method comprises the steps: 1, constructing a pure acoustic wave equation in the anisotropic medium, and solving the pure acoustic wave equation of the anisotropic medium; step 2, based on a Kelvin-Voigt model, constructing a viscous acoustic wave equation in an isotropic medium; and combining the viscous acoustic wave equation in the isotropic medium with the pure acoustic wave equation in the anisotropic medium to obtain a viscous pure acoustic wave equation in the anisotropic medium. A numerical example shows that the obtained viscous pure acoustic wave equation in the anisotropic medium can effectively eliminate interference and generate high-precision P-wave response; meanwhile, the influence of the anisotropic attenuation medium on seismic wave kinematics and dynamics can be fully displayed, and an efficient and accurate wave field extrapolation tool is provided for subsequent anisotropic attenuation medium migration imaging and waveform inversion.

Description

Technical Field

[0001] This invention belongs to the field of geophysical exploration seismic forward modeling technology, and relates to a method and apparatus for constructing and solving viscous wave equations for anisotropic media. Background Technology

[0002] Extensive seismic exploration field experiments and laboratory tests have shown that the Earth's medium is generally characterized by anisotropy and viscosity. Therefore, when simulating the propagation of seismic waves in the subsurface medium, these two characteristics should be fully considered, which is of great significance for subsequent high-precision seismic wavefield forward modeling, migration imaging, and waveform inversion.

[0003] Compared to the anisotropic elastic wave equation, the anisotropic acoustic wave equation is simpler in form and more computationally efficient, thus gaining preference in practical applications. From a practical perspective, traditional anisotropic acoustic wave equations are mostly based on acoustic assumptions and are therefore collectively referred to as anisotropic pseudo-acoustic wave equations. These equations inevitably produce numerical interference and instability in regions where the medium parameters do not meet the assumptions or where the medium parameters vary significantly. To address the problems of traditional pseudo-acoustic wave equations, anisotropic pure acoustic wave equations have been developed and applied. Currently, there are two commonly used anisotropic pure acoustic wave equations: one uses Taylor series to approximate the dispersion relation of the decoupled pure P-wave, and different numerical algorithms are used to solve the approximate pure P-wave equation; the other uses an optimization algorithm to approximate the dispersion relation of the decoupled pure P-wave, and the solution process for the optimized pure P-wave equation is similar to the first. In comparison, the second optimization algorithm can improve the approximation accuracy to a certain extent, but it increases the specific implementation difficulty and computational load. Therefore, the development of anisotropic pure acoustic wave equations continues to pursue the simultaneous improvement of solution accuracy and efficiency.

[0004] Furthermore, when considering the dielectric absorption attenuation effect, it is often... Q Theorem and standard linear volume theory are currently the two most commonly used theories to describe the decay properties of media. The former uses a power function to describe media decay and points out... Q The factor is independent of frequency. The latter primarily uses a series of standard linear volume models to approximate constants within a fixed frequency band. Q Model. In contrast, the common Q Theoretical methods provide a more accurate description of the absorption attenuation effect of the medium, but the computational complexity is correspondingly higher. To date, various types of methods based on constant... QThe viscous wave equations of theoretical and standard linear body theory have been developed and achieved with satisfactory simulation accuracy, and have been applied and verified in isotropic medium migration imaging and waveform inversion. However, for anisotropic media, especially anisotropic pure acoustic media, there are few viscous pure acoustic wave equations and their high-precision forward modeling algorithms that can be directly used.

[0005] Therefore, in summary, developing viscous pure acoustic wave equations is an important research objective for wave field simulation, migration imaging, and waveform inversion in anisotropic media. Summary of the Invention

[0006] The purpose of this invention is to provide a method and apparatus for constructing and solving the viscous wave equation for anisotropic media, so as to solve the problem that there is no viscous pure acoustic wave equation and its high-precision forward modeling algorithm that can be directly used for anisotropic media in the prior art.

[0007] To achieve the above objectives, the present invention employs the following technical solution: In a first aspect, the present invention provides a method for constructing and solving the viscous wave equation for anisotropic media, comprising the following steps: Step 1: Construct the pure acoustic wave equation in anisotropic media and solve the pure acoustic wave equation in anisotropic media. Step 2: Based on the Kelvin-Voigt model, construct the viscous acoustic wave equation in isotropic media; combine the viscous acoustic wave equation in isotropic media with the pure acoustic wave equation in anisotropic media obtained in Step 1 to obtain the viscous pure acoustic wave equation in anisotropic media.

[0008] Furthermore, step 1 includes the following sub-steps: Step 11, starting from the original pure P-wave dispersion relation in the VTI medium, its three-dimensional form is as follows: (1) in, ω Angular frequency, k x , k y and k z For space wavenumber components, v pz The P-wave velocity along the axis of symmetry. ε and δ These are the Thomsen anisotropy parameters; Step 12, approximate equation (1) as: (2) Transforming equation (2) into the time-space domain, it takes the following form: (3) in, W The pressure wave field symbol is introduced; equation (3) is the pure acoustic wave equation in the anisotropic medium obtained by construction, where the operator , and These are the spatial partial derivatives in different directions; Step 13: Solve the first, second, and third terms of equation (3) using the finite difference method, and solve the fourth term using the pseudospectral method. The specific recursive discrete format is as follows: (4) in, For time step, d The spatial grid step size, For the finite difference discretization scheme of the wave field, where the subscripts are... i , j , l Separate spaces x direction, y direction and z Orientation of grid node index, o For the grid index of the time term; operator , and The solution is obtained using a regular grid finite difference method, in the following form: (5) in, and For higher-order optimization of difference coefficients; Operator The calculation is performed using the pseudospectral method, in the following form: (6) Among them, symbols and These are the forward and inverse Fourier transform operators, respectively. Step 14: Based on the discrete scheme (4), achieve accurate and efficient extrapolation of the pure acoustic wave field in a three-dimensional anisotropic medium; when When the equation (6) degenerates into an extrapolation formula for the pure acoustic wave field in a two-dimensional anisotropic medium, equation (6) degenerates into an extrapolation formula for the pure acoustic wave field in a two-dimensional anisotropic medium.

[0009] Furthermore, step 2 specifically includes the following sub-steps: Step 21, based on the Kelvin-Voigt model, construct the viscous acoustic wave equation in an isotropic medium: (7) In the formula, W Represents an isotropic viscous acoustic wave field. vFor the velocity of sound waves in an isotropic medium, Q Q is a medium quality factor parameter. The Q value is generally a positive integer; a larger value indicates weaker formation absorption and attenuation. x, y, and z represent the coordinates in three spatial directions. The reference angular frequency; Step 22, based on the first-order standard linear body theory, the equation for isotropic viscous acoustic waves is expressed as: (8) Among them, symbols For convolution operators, r For memory variables, Let be a unit step function, and we have: (9) in, For strain relaxation time, For stress relaxation time, It is a relaxation time intermediate variable introduced to simplify the calculation; Transforming the first formula in equation (8) to the frequency-wavenumber domain, we get: (10) Further rearrangement of equation (10) yields: (11) when The above equation simplifies to: (12) in, The imaginary unit is k, and the wave number is k. and The relationship between them can be expressed as follows: (13) Substituting equation (13) into equation (12) and rearranging, we get: (14) Transforming the above equation to the time-space domain and simplifying, we get: (15); The first term on the right side of equation (15) is the original isotropic acoustic wave field, the second term is used to describe the phase dispersion of the medium, and the third term is used to describe the amplitude attenuation of the medium. Step 23, combine equations (7) and (15), that is, introduce the phase dispersion term in equation (15) into equation (7), and improve equation (15) to: (16) Equation (16) is a new viscous acoustic wave equation that simultaneously describes amplitude attenuation and phase dispersion in an isotropic medium. Step 24, the pure acoustic wave equation (3) of the VTI medium obtained in step 12 is rearranged into the following unified form: (17) Where, operator β is the content in parentheses of the right-hand term in equation (3); and the operator in equation (16) Replacing β with β, the equation for viscous pure acoustic waves in anisotropic media is obtained as follows: (18); Step 25: Solve the viscous pure acoustic wave equation in the VTI medium obtained in step 24 using the finite difference method.

[0010] Furthermore, it also includes step 26, which simplifies the viscous pure acoustic wave equation in the VTI medium obtained in step 24 according to different requirements, to obtain the simplified viscous pure acoustic wave equation in anisotropic media. Specifically, if only phase dispersion is considered, equation (18) simplifies to: (19); Similarly, if only amplitude decay is considered, equation (18) simplifies to: (20).

[0011] Secondly, the present invention provides a system for constructing and solving the viscous wave equation for anisotropic media, comprising the following steps: The pure acoustic wave equation construction module is used to construct pure acoustic wave equations in anisotropic media and solve the pure acoustic wave equations in anisotropic media. The viscous pure acoustic wave equation construction module is used to construct the viscous acoustic wave equation in isotropic media based on the Kelvin-Voigt model; and to combine the viscous acoustic wave equation in isotropic media with the pure acoustic wave equation in anisotropic media obtained in step 1 to obtain the viscous pure acoustic wave equation in anisotropic media.

[0012] Thirdly, the present invention provides an electronic device, the electronic device comprising: Memory, used to store executable instructions; A processor, when executing executable instructions or computer programs stored in the memory, implements the method described in this invention.

[0013] Fourthly, the present invention provides a computer-readable storage medium storing executable instructions or a computer program, wherein the executable instructions, when executed by a processor, implement the method described above.

[0014] In summary, to provide an effective wavefield extrapolation tool for migration imaging and waveform inversion in anisotropic attenuated media, this invention proposes a high-precision viscous pure acoustic equation for VTI media and its numerical solution scheme. First, the two-dimensional and three-dimensional VTI media pure acoustic equations based on Taylor series expansion are solved using a combination of the finite difference method and the pseudospectral method, generating high-precision P-wave responses while eliminating interference. Second, a viscous pure acoustic equation suitable for VTI media is derived based on Kelvin-Voigt theory. This equation has a simple form and can be solved efficiently using conventional finite difference methods. Furthermore, it can simultaneously describe the amplitude attenuation and phase dispersion of seismic waves in anisotropic attenuated media, effectively reflecting the influence of the attenuating medium on the kinematics and dynamics of seismic waves. The wave equation and its numerical solution method in this invention provide an effective wavefield extrapolation tool for anisotropic media wavefield simulation and migration imaging. Attached Figure Description

[0015] Figure 1 This is a flowchart of the method of the present invention; Figure 2 These are snapshots of the wave field calculated by two equations in a two-dimensional homogeneous VTI medium: (a) the traditional pseudo-acoustic equation, and (b) the pure acoustic equation. Figure 3 These are snapshots of the wave field calculated using two equations in a three-dimensional homogeneous VTI medium: (ac) is the traditional pseudo-acoustic equation, and (df) is the pure acoustic equation, where (a, d) xoy Planar slice, (b, e) xoz Planar slice, (c, f) yoz Planar slice; Figure 4 (a) Wavefield snapshots and (b) single-channel waveform comparisons calculated by different equations in a two-dimensional uniformly attenuated isotropic medium; Figure 5 (a) Wavefield snapshots and (b) single-channel waveform comparisons calculated by different equations in a two-dimensional uniformly attenuated VTI medium; Figure 6 (a) Calculated by different equations in a three-dimensional uniformly attenuating VTI medium. xoy Planar slice, (b) xoz Planar slice, (c) yoz Planar slices, (d) single-channel waveform comparison; Figure 7 Isotropic decaying medium gas cloud model, (a) velocity model, (b) Q Value model; Figure 8 These are snapshots of the wave field calculated using different equations in an isotropic attenuating medium gas cloud model. Left side: acoustic wave equation; Right side: viscous acoustic wave equation. Figure 9Seismic records calculated using different equations in an isotropic attenuating medium gas cloud model: left side: acoustic wave equation; right side: viscous acoustic wave equation. Figure 10 Comparison of single-channel waveforms calculated by different equations in an isotropic attenuating medium gas cloud model; Figure 11 For the Marmousi model of VTI medium, (a) velocity model, (b) ε Model, (c) δ Model; Figure 12 Wave field snapshots calculated for different equations in the Marmousi model of VTI medium: left side: pure acoustic wave equation; right side: viscous pure acoustic wave equation. Figure 13 Seismic records calculated using different equations in the Marmousi model for VTI medium: left side: pure acoustic equation; right side: viscous pure acoustic equation. Figure 14 Comparison of single-channel waveforms calculated using different equations in the Marmousi model for VTI media.

[0016] The present invention will be further explained and described below with reference to the accompanying drawings and embodiments. Detailed Implementation

[0017] like Figure 1 As shown, the present invention provides a method for constructing and solving the viscous wave equation for anisotropic media, which specifically includes the following steps: Step 1: Construct the pure acoustic wave equation for anisotropic media and solve the pure acoustic wave equation for anisotropic media.

[0018] Step 1 specifically includes the following sub-steps; Step 11: In anisotropic medium wavefield simulation and migration imaging, traditional pseudo-acoustic equations based on acoustic approximations are prone to SV wave interference and numerical instability. Therefore, researchers have developed various types of pure acoustic wave equations to address this issue. Starting from the original pure P-wave dispersion relation in VTI media, its three-dimensional form is as follows: (1) in, ω Angular frequency, k x , k y and k z For space wavenumber components, v pz The P-wave velocity along the axis of symmetry. ε and δ Here, represents the Thomsen anisotropy parameter. εThe value is typically between -0.5 and 0.5. δ The value is generally between -0.5 and 0.5.

[0019] Step 12: The original pure P-wave dispersion relation (1) contains a radical term, which is difficult to solve directly using conventional methods. Therefore, numerical approximation methods are usually used to expand it. Taking the most commonly used first-order Taylor series expansion strategy as an example, equation (1) can be approximated as: (2) Transforming equation (2) into the time-space domain, it takes the following form: (3) in, W For an isotropic viscous acoustic wave field, equation (3) is the pure P-wave equation (i.e., pure acoustic wave equation) in anisotropic (VTI) media, where the operators... , and These are the spatial partial derivatives in different directions.

[0020] Step 13: Based on previous research, for the sake of simplicity, the finite difference method is used to solve the first, second, and third terms of equation (3), and the pseudospectral method is used to solve the fourth term. The specific recursive discrete format is as follows: (4) in, For time step, d The spatial grid step size, For the finite difference discretization scheme of the wave field, where the subscripts are... i , j , l Separate spaces x direction, y direction and z Orientation of grid node index, o For the grid index of the time term. Operator , and The solution is obtained using a regular grid finite difference method, in the following form: (5) in, and For higher-order optimization of the difference coefficients. For example, when M When the value is 5, the corresponding difference coefficients are as follows: , , , , , .

[0021] Operator The calculation is performed using the pseudospectral method, in the following form: (6) Among them, symbols and These are the forward and inverse Fourier transform operators, respectively.

[0022] Step 14, based on the discrete scheme (4), can achieve accurate and efficient extrapolation of the pure acoustic wave field in the three-dimensional VTI medium. Specifically, when... When the equation (6) degenerates into an extrapolation formula for the pure acoustic wave field in a two-dimensional VTI medium, subsequent numerical model examples will verify the effectiveness of the above equation.

[0023] Step 2: Based on the Kelvin-Voigt model, construct the viscous acoustic wave equation in isotropic media; combine the viscous acoustic wave equation in isotropic media with the VTI pure acoustic wave equation obtained in Step 1 to obtain the viscous pure acoustic wave equation in anisotropic (VTI) media.

[0024] Step 2 specifically includes the following sub-steps: Step 21, based on the Kelvin-Voigt model, construct the viscous acoustic wave equation in an isotropic medium: (7) In the formula, W Represents an isotropic viscous acoustic wave field. v For the velocity of sound waves in an isotropic medium, Q Q is a medium quality factor parameter. The Q value is generally a positive integer; a larger value indicates weaker formation absorption and attenuation. x, y, and z represent the coordinates in three spatial directions. Here is the reference angular frequency. Relevant experience shows that the second term on the right-hand side of equation (7) can only reflect the amplitude attenuation, but the equation cannot reflect the phase dispersion in the dielectric absorption attenuation effect.

[0025] Step 22, based on the first-order standard linear body theory, the equation for isotropic viscous acoustic waves is expressed as: (8) Among them, symbols For convolution operators, r For memory variables, Let be a unit step function, and we have: (9) in, For strain relaxation time, For stress relaxation time, It is a relaxation time intermediate variable introduced to simplify the calculation.

[0026] Transforming the first formula in equation (8) to the frequency-wavenumber domain, we get: (10) Further rearrangement of equation (10) yields: (11) when The above formula can be simplified to: (12) in, is the imaginary unit, and k is the wave number.

[0027] and The relationship between them can be expressed as follows: (13) Substituting equation (13) into equation (12) and rearranging, we get: (14) Transforming the above equation to the time-space domain and simplifying, we get: (15) Observing equation (15), we can see that the first term on the right side of the equation is the original isotropic acoustic wave field, the second term is used to describe the phase dispersion of the medium, and the third term is used to describe the amplitude attenuation of the medium.

[0028] Step 23: Since the isotropic viscoacoustic wave equation described in equation (7) only attenuates the amplitude of seismic waves but has no effect on the phase, equation (7) and (15) are combined here. That is, the phase dispersion term in equation (15) is introduced into equation (7), and equation (15) can be improved to: (16) Equation (16) is a new viscous acoustic wave equation that simultaneously describes amplitude attenuation and phase dispersion in isotropic media. Comparing the above equation with equation (7), it is easy to see that equation (16) can not only effectively describe the amplitude attenuation of the seismic wave field, but also describe its phase distortion. In addition, compared with equation (15), equation (16) does not involve complex partial derivative calculations and can be solved efficiently using the conventional time-space domain regular grid finite difference method, thus it has high computational efficiency.

[0029] Step 24: Based on the above, this is extended to anisotropic media. First, the pure acoustic equation (3) for VTI media obtained in step 12 is rearranged into the following unified form: (17) Here, operator β is the content within the parentheses on the right-hand side of equation (3). Observe operator β in equation (17) and operator β in equation (16). It can be observed that both are composed of different spatial partial derivatives and medium parameters, therefore the operators in equation (16) can be... Replacing β with β, the viscous pure acoustic wave equation in the VTI medium is obtained as follows: (18) Step 25: Solve the viscous pure acoustic wave equation in the VTI medium obtained in step 24 using the finite difference method.

[0030] Specifically: The specific solution method has been described above. In the third term on the right side of equation (18) Then, the time derivative can be solved once. Observing the viscous pure acoustic wave equation (18) of VTI medium, it can be seen that the first term on the right side of the above equation is the original pure acoustic wave equation, the second term describes the influence of the medium on the phase of the seismic wave, and the third term describes the influence of the medium on the amplitude of the seismic wave. The above equation (18) has a simple form and can be solved efficiently using the conventional finite difference method.

[0031] In addition, the method of the present invention also includes step 26, which simplifies the viscous pure acoustic wave equation in the VTI medium obtained in step 24 according to different requirements, to obtain a simplified viscous pure acoustic wave equation in the VTI medium.

[0032] Specifically, if only phase dispersion is considered, equation (18) can be decomposed into: (19) Similarly, if only amplitude decay is considered, equation (18) can be simplified to: (20) Equations (18)-(20) are the equations for three types of viscous pure acoustic waves in VTI media. Based on the above equations, accurate and efficient numerical simulation of viscous pure acoustic wave fields in two-dimensional and three-dimensional VTI media can be achieved. Subsequent numerical simulation examples will also verify the effectiveness of the new equations.

[0033] Numerical calculations are performed using the anisotropic medium viscous wave equation construction and solution method of the present invention to numerically simulate the viscous pure acoustic wave field in anisotropic media, thereby obtaining the response of the wave field in VTI medium. Discretization is achieved using the finite difference method, and parallel computation is performed on a GPU cluster to simulate the propagation and attenuation of seismic waves in viscous media, generating a synthetic record. This synthetic record is then used for full waveform inversion to improve the accuracy of velocity modeling, guide oil and gas reservoir identification and fluidity detection, and provide a physical basis for deep seismic data compensation processing.

[0034] Example 1 This embodiment presents a system for constructing and solving the viscous wave equation for anisotropic media, including the following modules: The pure acoustic wave equation construction module is used to construct pure acoustic wave equations in anisotropic media and solve the pure acoustic wave equations in anisotropic media. The viscous pure acoustic wave equation construction module is used to construct the viscous acoustic wave equation in isotropic media based on the Kelvin-Voigt model; and to combine the viscous acoustic wave equation in isotropic media with the pure acoustic wave equation in anisotropic media obtained in step 1 to obtain the viscous pure acoustic wave equation in anisotropic media.

[0035] Example 2 This embodiment provides an electronic device, which includes: Memory, used to store executable instructions; A processor, when executing executable instructions or computer programs stored in the memory, implements the method described in this invention.

[0036] Example 2 This embodiment provides a computer-readable storage medium storing executable instructions or a computer program, characterized in that the executable instructions, when executed by a processor, implement the method described in this invention.

[0037] To verify the effectiveness of the equations obtained by the method of this invention, the present invention employs uniform and complex models to perform trial calculations on the various equations obtained above. The effectiveness of the equations is jointly verified by comparing wavefield snapshots, seismic records, and single-channel waveforms. Simulation results show that the equations obtained by the method of this invention can generate high-precision pure acoustic responses in complex anisotropic media. In addition, they can effectively demonstrate the amplitude dispersion and phase distortion characteristics of seismic waves in attenuating media.

[0038] Figure 2 Wavefield slices calculated using the traditional pseudo-acoustic equation and the pure acoustic equation in a two-dimensional homogeneous VTI medium are presented. Figure 3 Two-dimensional wavefield slices along different directions are given, calculated by the traditional pseudo-acoustic equation and the pure acoustic equation in a three-dimensional homogeneous VTI medium. The relevant anisotropy parameters are as follows: Observation of relevant calculation results shows that while the traditional pseudo-acoustic equation generates a P-wave response, it inevitably produces pseudo-transverse wave interference near the seismic source. In contrast, the pure acoustic equation generates an accurate P-wave response while completely eliminating pseudo-transverse wave interference.

[0039] Figure 4Wavefield slices calculated from different types of wave equations in a two-dimensional homogeneous attenuating isotropic medium are shown. These include the original acoustic wave equation, the viscous acoustic wave equation considering only phase dispersion, the viscous acoustic wave equation considering only amplitude attenuation, and the viscous acoustic wave equation considering both phase dispersion and amplitude attenuation. The relevant parameters are... . Figure 5 and Figure 6 Wavefield slices calculated from different types of wave equations in two-dimensional and three-dimensional homogeneously attenuated VTI media are shown. These include pure acoustic wave equations, viscous pure acoustic wave equations considering only phase dispersion, viscous pure acoustic wave equations considering only amplitude attenuation, and viscous pure acoustic wave equations considering both phase dispersion and amplitude attenuation. The relevant parameters are... Observing the relevant calculation results, it can be seen that the viscous wave equation that only considers phase dispersion can only affect the phase, the viscous wave equation that only considers amplitude attenuation can only affect the amplitude, and the viscous wave equation that considers both phase dispersion and amplitude attenuation can affect both the amplitude and phase information of seismic waves at the same time, and can effectively simulate the propagation of seismic waves in attenuating media.

[0040] To further verify the effectiveness of the method of the present invention, a complex model was used to verify the wave equations of different types in isotropic and anisotropic media. Figure 7 A typical gas cloud model in an isotropic medium, incorporating the medium's attenuation properties, is presented, where the velocity model parameters and Q The parameters of the value model are given in the figure. Figure 8 , Figure 9 and Figure 10 The figure shows instantaneous wavefield snapshots, seismic records, and single-channel waveforms calculated using the acoustic wave equation and the viscous acoustic wave equation in this model. It can be observed from the figure that the viscous acoustic wave equation, which considers the medium absorption and attenuation effect, can significantly influence the amplitude and phase characteristics of seismic wave propagation, thus demonstrating the effectiveness of the method.

[0041] Figure 11 The Marmousi model in VTI medium is presented, and the figure shows the vertical velocity values ​​and Thomsen anisotropy parameters. Q The value parameters are calculated using empirical formulas. Similarly, Figure 12 , Figure 13 and Figure 14The diagram displays instantaneous wavefield snapshots, seismic records, and single-channel waveforms calculated using the pure acoustic equation and the viscous pure acoustic equation in the VTI Marmousi model. Detailed observations of the figures reveal that, in anisotropic media, compared to the simulation results of the pure acoustic equation, the viscous pure acoustic equation, which considers the medium's absorption and attenuation effects, significantly influences the kinematic and dynamic characteristics of seismic wave propagation. It effectively describes the influence of the attenuating medium on the amplitude and phase of seismic waves, thus demonstrating the effectiveness of the viscous pure acoustic equation obtained by the method of this invention.

Claims

1. A method for constructing and solving an anisotropic media viscous wave equation, characterized in that, The method comprises the following steps: Step 1, constructing a pure acoustic wave equation in an anisotropic medium and solving the pure acoustic wave equation in the anisotropic medium; Step 2, constructing a viscous acoustic wave equation in an isotropic medium based on a Kelvin-Voigt model; and combining the viscous acoustic wave equation in the isotropic medium with the pure acoustic wave equation in the anisotropic medium obtained in step 1 to obtain a viscous pure acoustic wave equation in the anisotropic medium.

2. The method of claim 1, wherein, Step 1 comprises the following sub-steps: Step 11, starting from an original pure P-wave dispersion relation in a VTI medium, the three-dimensional form is as follows: (1) where ω is the angular frequency, k x , k y and k z is the spatial wavenumber component, v pz is the P-wave velocity along the symmetry axis direction, ε and δ is the Thomsen anisotropy parameter; Step 12, approximately representing equation (1) as: (2) Converting equation (2) into a time-space domain, and the form is as follows: (3) wherein, W is the introduced pressure wavefield symbol; equation (3) is the constructed pure acoustic wave equation in anisotropic media, where the operator , and are spatial partial derivatives in different directions; Step 13, solving the first term, the second term and the third term in equation (3) by using a finite difference method, and solving the fourth term by using a pseudo-spectral method to obtain a specific recursive discrete format as follows: (4) where is the time step, d is the spatial grid step, is the finite-difference discretization scheme for the wavefield, where the index i , j , l are the grid node indices in the spatial x direction, y direction, and z direction, respectively, o is the grid index for the time term; the operators , and are solved using a regular grid finite-difference method, which is of the form: (5) wherein and are high order optimized difference coefficients; Operator The calculation is performed using the pseudospectral method, which is of the form: (6) where the symbol and are the Fourier forward and inverse transform operators, respectively; Step 14, based on the discrete format (4), the exact and efficient extrapolation of pure acoustic wavefield in 3D anisotropic media is realized; when , equation (6) degenerates into the pure acoustic wavefield extrapolation formula in 2D anisotropic media.

3. The method of claim 2, wherein, Step 2 comprises the following sub-steps: Step 21, constructing a viscous acoustic wave equation in an isotropic medium based on a Kelvin-Voigt model: (7) wherein, W represents an isotropic visco-acoustic wavefield, v is the isotropic medium acoustic velocity, Q is the medium quality factor parameter, the Q value is generally a positive integer, the larger the value represents the weaker the formation absorption attenuation, x, y and z represent the coordinates of three directions in space, is the reference angular frequency; Step 22, representing the isotropic viscous acoustic wave equation based on a first-order standard linear solid theory as: (8) where the symbol is a convolution operator, r is a memory variable, is a unit step function, and has: (9) wherein is the strain relaxation time, is the stress relaxation time, is an intermediate variable for the relaxation time introduced for simplifying the calculation; Converting the first formula in equation (8) into a frequency-wave number domain to obtain: (10) Further, equation (10) is rearranged as: (11) When The above equation simplifies to: (12) wherein is the imaginary unit and k is the wave number; The relationship between the values of the parameters a and b is expressed by the following equation: The relationship between the values of the parameters a and b is expressed by (13) Substituting equation (13) into equation (12) to obtain: (14) Converting the above equation into a time-space domain to obtain: (15)； The first term on the right side of equation (15) is an original isotropic acoustic wave field, the second term is used to describe phase dispersion of the medium, and the third term is used to describe amplitude attenuation of the medium; Step 23, combining equation (7) and (15), that is, introducing the phase dispersion term in equation (15) into equation (7), and improving equation (15) as: (16) Equation (16) is a new viscous acoustic wave equation in the isotropic medium which simultaneously describes amplitude attenuation and phase dispersion; Step 24, rearranging the pure acoustic wave equation (3) of the VTI medium obtained in step 12 into a unified form as follows: (17) where the operator β is the content of the right-hand side bracket in equation (3); and replacing the operator β in equation (16) with β, the pure viscous acoustic wave equation in an anisotropic medium is obtained as follows: where the operator β is the content of the right-hand side bracket in equation (3); and replacing the operator β in equation (16) with β, the pure viscous acoustic wave equation in an anisotropic medium is obtained as follows: (18)； Step 25, solving the viscous pure acoustic wave equation of the VTI medium obtained in step 24 by using a finite difference method.

4. The method of claim 3, wherein, Further comprising step 26, simplifying the viscous pure acoustic wave equation of the VTI medium obtained in step 24 according to different requirements to obtain a simplified viscous pure acoustic wave equation in an anisotropic medium; Specifically, if only phase dispersion is considered, equation (18) is simplified as: (19)； Similarly, if only amplitude attenuation is considered, equation (18) is simplified as: (20)。 5. A system for constructing and solving the viscous wave equation for anisotropic media, characterized in that, The method comprises the following steps: A pure acoustic wave equation construction module is configured to construct a pure acoustic wave equation in an anisotropic medium and solve the pure acoustic wave equation in the anisotropic medium; A viscous pure acoustic wave equation construction module is configured to construct a viscous acoustic wave equation in an isotropic medium based on a Kelvin-Voigt model; and combine the viscous acoustic wave equation in the isotropic medium with the pure acoustic wave equation in the anisotropic medium obtained in step 1 to obtain a viscous pure acoustic wave equation in the anisotropic medium.

6. An electronic device, comprising: The electronic device comprises: a memory configured to store executable instructions; a processor configured to execute the executable instructions or computer programs stored in the memory to implement the method of any one of claims 1-4.

7. A computer-readable storage medium storing executable instructions or a computer program, characterized in that, The executable instructions, when executed by a processor, implement the method of any one of claims 1-4.

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