Seismic wave forward modeling method and device based on viscoelastic medium and electronic equipment

Abstract

The invention relates to a seismic wave forward modeling method and device based on a viscoelastic medium and electronic equipment. The method comprises the following steps: acquiring viscoelastic medium parameters of a stratum to construct a viscoelastic wave fluctuation equation; acquiring a wave equation based on a viscoelastic wave wave equation, and constructing a second-order Green displacement tensor based on the viscoelastic medium density, the angular frequency and a Green function of a scalar wave equation; the method comprises the following steps: acquiring a first coefficient expression of a second-order green displacement tensor based on a geometric model of a viscoelastic medium, introducing a frequency-dependent complex velocity, constructing a green function based on the complex velocity, and acquiring a first solving subitem based on the green function and the first coefficient expression; based on Hooke's law and the first solving subitem, obtaining a second solving subitem; obtaining a frequency domain viscoelastic medium boundary integral equation on the basis of the first solving subitem and the second solving subitem; and performing discrete solution on the frequency domain viscoelastic medium boundary integral equation to obtain the displacement and stress of the seismic wave in the propagation process. And calculation errors can be reduced.

Description

Technical Field

[0001] This invention relates to the field of seismic exploration technology, and in particular to a method, apparatus, and electronic device for forward modeling seismic waves based on viscoelastic media. Background Technology

[0002] The propagation of seismic waves in actual subsurface media is significantly affected by the viscous properties of these media, leading to energy attenuation and phase distortion. For example, viscoelastic absorption near the surface results in energy loss and significantly impacts the interpretation of seismic wave reflection, ground motion, and regional wave phases. To more accurately describe the propagation of seismic waves in subsurface media, the absorption and attenuation effects of the medium need to be considered in wavefield simulations. The finite difference method and the finite element method are used to perform numerical simulations of seismic wave propagation in viscoelastic media, and to simulate seismic wave propagation in multilayer media with irregular interfaces, enabling the study of near-surface velocity dispersion and amplitude attenuation. The finite difference method and the finite element method primarily employ time-domain methods based on the quality factor Q and frequency-domain methods based on complex velocities for various viscoelastic numerical simulations. The time-domain methods based on the quality factor Q mainly use various phenomenological models, such as the Kelvin-Voigt, Maxwell, and standard linear solid models, to describe the viscosity of the medium, while the frequency-domain methods based on complex velocities characterize the attenuation characteristics through frequency-dependent complex velocities. However, this numerical simulation method for viscoelastic media earthquakes suffers from significant calculation errors when simulating the reflection and transmission of seismic waves at irregular interfaces, as both the finite difference method and the finite element method implicitly use boundary conditions when dealing with irregular boundaries. Consequently, the accuracy of the interpretation of seismic wave reflection, ground motion, and regional wave phases is relatively low. Summary of the Invention

[0003] In view of this, the present invention provides a method, apparatus and electronic device for forward modeling of seismic waves based on viscoelastic media.

[0004] Specifically, the present invention is achieved through the following technical solution: According to a first aspect of the present invention, a method for forward modeling seismic waves based on viscoelastic media is provided, the method comprising: Obtain the viscoelastic medium parameters of the formation, and construct a viscoelastic wave equation based on the seismic wave displacement vector based on the viscoelastic medium parameters. The viscoelastic medium parameters include: P-wave velocity, S-wave velocity, viscoelastic medium density, source angular frequency, first Lamé constant, second Lamé constant, P-wave quality factor, and S-wave quality factor. Based on the viscoelastic wave equation, the wave equation for the field integration point is obtained. Based on the viscoelastic medium density, angular frequency and Green's function of the scalar wave equation, a second-order Green's displacement tensor is constructed to obtain the solution of the wave equation. Based on the geometric model of viscoelastic medium, the first coefficient expression of the second-order Green's displacement tensor is obtained. Frequency-dependent complex velocity is introduced to construct the Green's function based on the complex velocity. Based on the Green's function based on the complex velocity and the first coefficient expression, the first solution term corresponding to the first coefficient expression of the second-order Green's displacement tensor is obtained. Based on Hooke's law and the first solution term, the second solution term corresponding to the second coefficient expression of the second-order Green's displacement tensor is obtained; Based on the first and second partial solutions, the frequency domain boundary integral equation of the viscoelastic medium corresponding to the viscoelastic wave equation is obtained. Discretely solve the boundary integral equation of the viscoelastic medium in the frequency domain to obtain the displacement and stress of the seismic wave during propagation.

[0005] Optionally, the step of discretizing and solving the boundary integral equation of the viscoelastic medium in the frequency domain to obtain the displacement and stress of the seismic wave during propagation includes: The free surfaces and irregular interfaces in the geometric model are discretized into nodes, and node-type functions are constructed based on the discretized nodes. Based on nodal functions, the discrete nodal expressions of the first solution terms of the boundary integral equation of the viscoelastic medium in the frequency domain are obtained. Based on discrete node expressions, the frequency domain viscoelastic medium boundary integral equation is transformed into a matrix equation; Based on the continuity boundary conditions of the free surface and irregular interface in the geometric model, the coefficient matrix of the matrix equation is obtained; By acquiring the coefficient matrix values ​​from the seismic data of the target seismic wave, the matrix equation is solved to obtain the displacement and stress during the propagation of the target seismic wave.

[0006] Optionally, the viscoelastic wave equation is as follows: ; in, For P-wave velocity, For S-wave velocity, For the density of a viscoelastic medium, The first Lamé constant, For the second Lamé constant, For P-wave quality factor, For S-wave quality factor, This represents the seismic wave displacement vector during its propagation. This is a physical activity item.

[0007] Optionally, the wave equation for the field integral point is as follows: ; in, The coordinates of the earthquake source are... Here are the coordinates of the field integration point, which is a point in the geometric model. It is a second-order Green's displacement tensor.

[0008] Optionally, the second-order Green's displacement tensor can be obtained using the following formula:

[0009] Where I is the identity matrix, , .

[0010] Optionally, the method further includes: Obtain the geometric dimension parameter matrix of the non-smooth medium in the geometric model; The boundary integral equation of the viscoelastic medium in the frequency domain is simplified based on the geometric dimension parameter matrix.

[0011] Optionally, the geometric dimension parameter matrix is: ; Where C(r) is the geometric dimension parameter matrix, It is Poisson's ratio. and It is the angle between the boundary corner point and the boundary tangent.

[0012] The seismic wave forward modeling method based on viscoelastic media in this technical solution obtains the viscoelastic medium parameters of the formation, and constructs a viscoelastic wave equation based on the seismic wave displacement vector based on these parameters. The viscoelastic medium parameters include: P-wave velocity, S-wave velocity, viscoelastic medium density, source angular frequency, first Lamé constant, second Lamé constant, P-wave quality factor, and S-wave quality factor. Based on the viscoelastic wave equation, the wave equation for the field integration point is obtained. Based on the viscoelastic medium density, angular frequency, and the Green's function of the scalar wave equation, a second-order Green's displacement tensor is constructed to obtain the solution to the wave equation. Based on the geometric model of the viscoelastic medium, a second-order Green's displacement tensor is obtained. The first coefficient expression of the second-order Green's displacement tensor is used to introduce a frequency-dependent complex velocity, constructing a Green's function based on the complex velocity. Based on the Green's function and the first coefficient expression, the first solution term corresponding to the first coefficient expression of the second-order Green's displacement tensor is obtained. Based on Hooke's law and the first solution term, the second solution term corresponding to the second coefficient expression of the second-order Green's displacement tensor is obtained. Based on the first and second solution terms, the frequency-domain viscoelastic medium boundary integral equation corresponding to the viscoelastic wave equation is obtained. The frequency-domain viscoelastic medium boundary integral equation is discretized and solved to obtain the displacement and stress of the seismic wave during propagation. Thus, based on the quality factor related to the viscoelastic medium, the complex velocity of the medium is obtained and introduced into the viscoelastic wave equation. Transformation based on the second-order Green's displacement tensor yields the frequency-domain viscoelastic medium boundary integral equation. The geometric model is then discretized and solved using this equation to obtain the displacement and stress of the seismic wave during propagation, effectively improving computational accuracy and thus enhancing the interpretation of seismic wave reflection, ground motion, and regional wave phases.

[0013] According to a second aspect of the present invention, a seismic wave forward modeling apparatus based on a viscoelastic medium is provided, the seismic wave forward modeling apparatus based on a viscoelastic medium comprising: The first equation construction module is used to obtain the viscoelastic medium parameters of the strata and construct a viscoelastic wave equation based on the seismic wave displacement vector based on the viscoelastic medium parameters. The viscoelastic medium parameters include: P-wave velocity, S-wave velocity, viscoelastic medium density, source angular frequency, first Lamé constant, second Lamé constant, P-wave quality factor and S-wave quality factor. The displacement tensor construction module is used to obtain the wave equation for the field integration point based on the viscoelastic wave equation. Based on the viscoelastic medium density, angular frequency and Green's function of the scalar wave equation, a second-order Green's displacement tensor is constructed to obtain the solution of the wave equation. The first coefficient analysis module is used to obtain the first coefficient expression of the second-order Green's displacement tensor based on the geometric model of the viscoelastic medium, introduce frequency-dependent complex velocity, construct the Green's function based on complex velocity, and obtain the first solution term corresponding to the first coefficient expression of the second-order Green's displacement tensor based on the Green's function of complex velocity and the first coefficient expression. The second coefficient analysis module is used to obtain the second solution term corresponding to the second coefficient expression of the second-order Green's displacement tensor based on Hooke's law and the first solution term; The second equation construction module is used to obtain the frequency domain viscoelastic medium boundary integral equation corresponding to the viscoelastic wave equation based on the first solution partial equation and the second solution partial equation. The discrete solution module is used to discretely solve the boundary integral equation of the viscoelastic medium in the frequency domain to obtain the displacement and stress of the seismic wave during propagation.

[0014] According to a third aspect of the invention, a storage medium is provided that stores a computer program thereon, which, when executed by a processor, implements the steps of the viscoelastic medium-based seismic wave forward modeling method in any possible implementation of the first aspect.

[0015] According to a fourth aspect of the present invention, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the viscoelastic medium-based seismic wave forward modeling method in any possible implementation of the first aspect. Attached Figure Description

[0016] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0018] Figure 1 A flowchart illustrating a seismic wave forward modeling method based on viscoelastic media, provided for an embodiment of the present invention; Figure 2 A schematic diagram of the geometric model of a two-dimensional viscoelastic medium in a seismic wave forward modeling method based on viscoelastic medium provided in an embodiment of the present invention; Figure 3 A schematic diagram of zero-shot-receiver distance data at a focal depth of 1000m in a seismic wave forward modeling method based on viscoelastic media provided in an embodiment of the present invention; Figure 4 A schematic diagram of three-layer velocities based on a geometric model in a seismic wave forward modeling method based on viscoelastic media provided in an embodiment of the present invention; Figure 5 A schematic diagram of the synthetic seismic record (vertical component) obtained by using the boundary integral equation of the viscoelastic medium in the frequency domain in a forward modeling method for seismic waves based on viscoelastic medium provided in an embodiment of the present invention; Figure 6 A schematic diagram of the synthetic seismic record (horizontal component) obtained by using the boundary integral equation of the viscoelastic medium in the frequency domain in a forward modeling method for seismic waves based on viscoelastic medium provided in an embodiment of the present invention; Figure 7 A velocity diagram of a viscoelastic graben model in a seismic wave forward modeling method based on viscoelastic media provided in an embodiment of the present invention; Figure 8 A schematic diagram of the synthetic seismic record (vertical component) obtained by solving the viscoelastic graben model using the frequency domain viscoelastic medium boundary integral equation in a seismic wave forward modeling method based on viscoelastic medium provided in an embodiment of the present invention; Figure 9 A schematic diagram of the synthetic seismic record (horizontal component) obtained by solving the viscoelastic graben model using the frequency domain viscoelastic medium boundary integral equation in a seismic wave forward modeling method based on viscoelastic medium provided in an embodiment of the present invention; Figure 10 A schematic diagram of a seismic wave forward modeling device based on a viscoelastic medium provided in an embodiment of the present invention; Figure 11 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] In related technologies, the numerical simulation methods for seismic events in viscoelastic media, such as the finite difference method and the finite element method, implicitly use boundary conditions when dealing with irregular boundaries. As a result, there are large calculation errors when simulating reflection and transmission at irregular interfaces, leading to low accuracy in interpreting seismic wave reflection, ground motion, and regional wave phases.

[0021] Unlike the finite difference method and finite element method, which implicitly use boundary conditions, methods that explicitly use boundary conditions belong to the semi-analytical methods based on boundary integral equations. These semi-analytical methods are widely used as accurate tools for simulating reflection and transmission at irregular interfaces. Common semi-analytical methods include: the traditional boundary element method, the Aki–Larner method, the Bouchon–Campillo method, the global generalized reflection / transmission matrix method, and the boundary element-volume element method. These semi-analytical methods are widely used to study terrain scattering effects due to their flexibility in handling multi-scale terrain roughness; for example, near-surface complexity and rugged terrain can be directly analyzed using the boundary integral matrix. However, semi-analytical (full-waveform numerical) methods, which involve numerous matrix operations, are computationally extremely expensive for high-frequency and large-scale problems, and the frequency-dependent amplitude / phase fluctuations caused by near-surface scattering attenuation are significantly affected by the near-surface viscous properties.

[0022] In this embodiment, frequency-dependent complex velocities are introduced into the frequency-domain elastic wave boundary element method (Frequency Domain Elastic Boundary Element Method) to simulate numerical wave propagation in viscoelastic media. Boundary conditions are explicitly used at irregular interfaces to ensure simulation accuracy. First, frequency-dependent complex velocities are introduced to represent viscous properties in the scalar Helmholtz equation (elastic wave equation), and the corresponding viscoelastic integral equation (viscoelastic wave equation) is obtained based on the Green's function of the complex velocities. Second, for multilayer viscoelastic media, the Frequency Domain Elastic Boundary Element Method is applied to the viscoelastic integral equation, and each subdomain in the entire computational domain is processed separately. Finally, the numerical matrix of the current computational domain is assembled with the boundary conditions at the shared boundaries of adjacent subdomains to form a global matrix. Because this global coefficient matrix is ​​sparse and narrowband, solving the equations is more efficient when dealing with large models. Thus, this embodiment provides a forward modeling method for seismic waves in near-surface viscous media. By introducing frequency-dependent complex velocities into the elastic wave equation, the conventional elastic wave equation is improved into a viscoelastic wave equation. By explicitly applying boundary conditions at irregular interfaces, this method is a semi-analytical approach. Compared with traditional pure numerical methods, it can effectively reduce calculation errors and has significant advantages when dealing with models containing irregular interfaces.

[0023] See Figure 1 This invention provides a method for forward modeling seismic waves based on viscoelastic media, which may include the following steps: S101. Obtain the viscoelastic medium parameters of the formation, and construct a viscoelastic wave equation based on the seismic wave displacement vector based on the viscoelastic medium parameters. The viscoelastic medium parameters include: P-wave velocity, S-wave velocity, viscoelastic medium density, source angular frequency, first Lamé constant, second Lamé constant, P-wave quality factor, and S-wave quality factor. Figure 2 This is a schematic diagram of the geometric model of a two-dimensional viscoelastic medium in a seismic wave forward modeling method based on viscoelastic media, provided as an embodiment of the present invention. Figure 2 As shown, the geometric model is located in half-space, with its left, right, and bottom boundaries extending to infinity. At this point, the geometric model is free surface and irregular interfaces The model is divided into a first subdomain and a second subdomain. The first subdomain is the subdomain formed along the direction from the irregular interface to the free surface, and the seismic source point is located within the first subdomain of the geometric model. Place.

[0024] In this embodiment, as an optional implementation, the source spectrum of the seismic source point can be characterized using the following formula: , in: For the source spectrum, Angular frequency, source spectrum It is angular frequency The function, This is the Dirac function.

[0025] In this embodiment, the seismic wave displacement vector based on the geometric model satisfies the following viscoelastic wave equation: (1) in, For P-wave velocity, For S-wave velocity, For the density of a viscoelastic medium, The first Lamé constant, For the second Lamé constant, For P-wave quality factor, For S-wave quality factor, This represents the seismic wave displacement vector during its propagation. This is a physical activity item.

[0026] S102. Based on the viscoelastic wave equation, obtain the wave equation for the field integration point. Based on the viscoelastic medium density, angular frequency and the Green's function of the scalar wave equation, construct the second-order Green's displacement tensor to obtain the solution of the wave equation. In this embodiment, the wave equation for the field integral point obtained based on the elastic wave equation is as follows: (2) in, The coordinates of the earthquake source are... Let be the coordinates of the field integration point, which is a point in the geometric model.

[0027] It is a second-order Green's displacement tensor, which characterizes the displacement and stress of the seismic wave during propagation, and is a solution to the wave equation.

[0028] In this embodiment, as an optional implementation, the expression for the second-order Green's displacement tensor, based on the viscoelastic medium density, angular frequency, and Green's function of the scalar wave equation, is as follows: (3) Where I is the identity matrix, , . S103. Based on the geometric model of the viscoelastic medium, obtain the first coefficient expression of the second-order Green's displacement tensor, introduce the frequency-dependent complex velocity, construct the Green's function based on the complex velocity, and obtain the first solution term corresponding to the first coefficient expression of the second-order Green's displacement tensor based on the Green's function based on the complex velocity and the first coefficient expression. In this embodiment, in equation 3 The preceding part is the expression for the first coefficient, and the following part is the expression for the second coefficient.

[0029] In this embodiment, the scalar wave equation is the vectorless equation corresponding to the wave equation, and the expression for the second-order Green's displacement tensor is as follows: and Let be the Green's functions (first Green's function and second Green's function) of the scalar wave equation, respectively, and satisfy the following relationship: (4) In the formula, For P-wave number, For S-wave number, ;or, .

[0030] For example, Equation 4 includes:

[0031] In this embodiment, for a two-dimensional problem, in the above formula, and It can be represented in the following form: (5) in, , This is a Hankel function of the first kind.

[0032] In this embodiment, the attenuation properties of any viscoelastic model can be expressed in the frequency domain through complex velocity in the following form, i.e., the Green's function based on complex velocity is: (6) in For spatial coordinates, ;or, .

[0033] Based on Equation 6, replacing the wavenumber in Equation 5 with the complex wavenumber yields the first solution term corresponding to the first coefficient expression of the second-order Green's displacement tensor: (7) (8)

[0034] S104. Based on Hooke's law and the first solution term, obtain the second solution term corresponding to the second coefficient expression of the second-order Green's displacement tensor. In this embodiment, the second solution term is the Green's stress tensor. Based on Hooke's law, the Green's stress tensor... The partial terms can be solved by first solving the problem. The expression is: (9) S105. Based on the first and second partial equations, obtain the frequency domain viscoelastic medium boundary integral equation corresponding to the viscoelastic wave equation. In this embodiment, based on equations 7 to 9, the boundary integral equation of the viscoelastic medium in the frequency domain can be expressed as: (10) in, For boundary integrals, Let C(r) be the volume integral, and C(r) be the parameter matrix related to the geometric dimensions of the geometric model.

[0035] In this embodiment, as an optional embodiment, the method further includes: Obtain the geometric dimension parameter matrix of the non-smooth medium in the geometric model; The boundary integral equation of the viscoelastic medium in the frequency domain is simplified based on the geometric dimension parameter matrix.

[0036] In this embodiment, for non-smooth media, C(r) can be expressed as: (11) in It is Poisson's ratio. and It is the angle between the boundary corner point and the boundary tangent.

[0037] Based on Equation 11, the frequency domain boundary integral equation for viscoelastic media can be further simplified to the following form: (12) (13) S106. Discretely solve the boundary integral equation of the viscoelastic medium in the frequency domain to obtain the displacement and stress of the seismic wave during propagation.

[0038] In this embodiment, the frequency domain viscoelastic medium boundary integral equation obtained based on the viscoelastic wave equation is discretely solved.

[0039] In this embodiment, as an optional implementation, the boundary integral equation of the viscoelastic medium in the frequency domain is discretized and solved to obtain the displacement and stress of the seismic wave during propagation, including: A11, the free surfaces and irregular interfaces in the geometric model are discretized into nodes respectively, and node-type functions are constructed based on the discretized nodes; In this embodiment, as an optional implementation, the free surface of the geometric model is used. and irregular interfaces Discretize into having and The number of elements in each node is denoted as . and Through adjacent nodes and Between units Linear fitting of the node values ​​to construct a nodal function To approximate variables: (14) in and , respectively, are the node coordinates and numbers of the element, and l2 is the field integral point contained within the element.

[0040] A12, based on nodal functions, obtain the discrete nodal expression of the first solution term of the boundary integral equation of the viscoelastic medium in the frequency domain; In this embodiment, based on nodal functions, Equation 10 (frequency domain viscoelastic medium boundary integral equation) can be calculated for each element. Let: (15) (16) A13, based on discrete node expressions, transforms the frequency domain viscoelastic medium boundary integral equation into a matrix equation; In this embodiment, based on the simplified frequency-domain viscoelastic medium boundary integral equations, namely Equations 13 and 14, further simplification is achieved using discrete nodal expressions, resulting in the following discrete equations: (17) (18) in , which is the number of boundary elements in the entire geometric model.

[0041] A14. Based on the continuity boundary conditions of the free surface and irregular interface in the geometric model, obtain the coefficient matrix of the matrix equation. In this embodiment, the continuity boundary condition is expressed as follows: (19) in, The symbol represents stress, with - indicating the upper interface and + indicating the lower interface. Based on the continuity boundary conditions, the discrete equations (Equations 18 and 19) can be transformed into the following matrix equations: (20) in , representing the displacement and stress of each boundary element. Wherein,

[0042] A15: Based on the seismic data of the target seismic wave, obtain the coefficient matrix value, solve the matrix equation, and obtain the displacement and stress during the propagation process of the target seismic wave.

[0043] In this embodiment, the unknowns (displacement, stress) at any field integration point within the solution region of the geometric model can be solved using Equation 20. As an optional embodiment, Gaussian elimination can be used to solve the above matrix equations, which can further improve computational efficiency.

[0044] In this embodiment, in order to study the dispersion and amplitude attenuation effects of viscoelastic media, the frequency domain viscoelastic wave equation is transformed and discretized to obtain the displacement and stress of seismic waves during propagation. Unlike numerical simulation methods in related technologies, such as the finite difference method and the finite element method, this embodiment is based on the elastic wave boundary element method for numerical simulation. By introducing complex velocity into the viscoelastic wave equation, it is extended to viscoelastic media, providing a new semi-numerical-semi-analytical method for studying scattering and attenuation caused by viscoelastic media. It has higher computational accuracy when dealing with undulating interfaces and free surface problems.

[0045] This embodiment is based on numerical simulation of a geometric model. To verify the correctness of the method in this embodiment, the simulation results of the method in this embodiment are compared with the simulation results of the finite difference method in related technologies.

[0046] Figure 3 This is a schematic diagram of zero-shot-receiver offset data at a source depth of 1000m in a seismic wave forward modeling method based on viscoelastic media provided in an embodiment of the present invention. Figure 3 The image shows zero-shot-receiver distance data from a single stratum at a focal depth of 1000m, illustrating the influence of different viscosity coefficients on elastic wave propagation. The left half represents the spectra of models with different viscosity coefficients, while the right half represents the synthetic seismic record.

[0047] Figure 4 This is a schematic diagram of three-layer velocities based on a geometric model in a seismic wave forward modeling method based on viscoelastic media, provided as an embodiment of the present invention. Figure 4 As shown, the velocities include P-wave velocities and S-wave velocities, with the second layer being a viscous layer and the coordinates of the source point being (0, 0).

[0048] Figure 5 This diagram illustrates the synthetic seismic record (vertical component) obtained using the frequency-domain viscoelastic medium boundary integral equation in a forward modeling method for seismic waves based on viscoelastic media, as provided in an embodiment of the present invention. Figure 5 As shown, in Figure (a), In Figure (b), In Figure (c), In Figure (d), .

[0049] Figure 6 This diagram illustrates the synthetic seismic record (horizontal component) obtained using the frequency-domain viscoelastic medium boundary integral equation in a seismic wave forward modeling method based on viscoelastic media, as provided in an embodiment of the present invention. Figure 6 As shown, in Figure (a), In Figure (b), In Figure (c), In Figure (d), . Figure 5 and Figure 6 In this embodiment, the geometric model parameters are consistent with those in the 2015 book "Seismic Exploration of Hydrocarbons in Heterogeneous Reservoirs: New Theories, Methods and Applications" by Ba Jing et al. The synthetic seismic records obtained using the method in this embodiment are consistent with those in that article, verifying the reliability of the method in this embodiment.

[0050] Figure 7 This is a velocity diagram illustrating a viscoelastic graben model as the geometric model in a seismic wave forward modeling method based on viscoelastic media provided in an embodiment of the present invention. Figure 7 As shown, the graben model is used to verify the applicability of the boundary integral equation of the viscoelastic medium in the frequency domain. The source coordinates are (1500, 50).

[0051] Figure 8 This diagram illustrates the synthetic seismic record (vertical component) obtained by solving the viscoelastic graben model using the frequency-domain viscoelastic medium boundary integral equation in a seismic wave forward modeling method based on viscoelastic media, as provided in an embodiment of the present invention. Figure 8 As shown in Figure (a), In Figure (b), .

[0052] Figure 9 This diagram illustrates the synthetic seismic record (horizontal component) obtained by solving the viscoelastic graben model using the frequency-domain viscoelastic medium boundary integral equation in a seismic wave forward modeling method based on viscoelastic media, as provided in an embodiment of the present invention. Figure 9 As shown in Figure (a), In Figure (b), .like Figure 8 and Figure 9 As shown, the results of the synthetic seismic record demonstrate the effectiveness of the method in this embodiment.

[0053] In this embodiment, the complex velocity of the medium is obtained based on the quality factor related to the viscosity of the medium, and further converted into the complex wave number. This is then introduced into the viscoelastic wave equation, ultimately transforming it into a frequency-domain viscoelastic medium boundary integral equation. The geometric model is then discretized using this frequency-domain viscoelastic medium boundary integral equation, and the seismic wave field at the detector is calculated. By adaptively discretizing the geometric model subdomain by subdomain and boundary, a discrete wave equation is obtained and finally assembled into a matrix equation form. This matrix equation applies infinite elements to absorb reflected waves from the left and right interfaces. Furthermore, by combining the advantages of the boundary element method, it is suitable for handling undulating interfaces and free surfaces, resulting in higher accuracy in the calculation results.

[0054] Based on the same inventive concept, such as Figure 10 As shown, this embodiment of the invention also provides a seismic wave forward modeling device based on viscoelastic media, the device comprising: The first equation construction module 11 is used to obtain the viscoelastic medium parameters of the strata and construct a viscoelastic wave equation based on the seismic wave displacement vector based on the viscoelastic medium parameters. The viscoelastic medium parameters include: P-wave velocity, S-wave velocity, viscoelastic medium density, source angular frequency, first Lamé constant, second Lamé constant, P-wave quality factor and S-wave quality factor. In this embodiment, as an optional implementation, the viscoelastic wave equation is as follows: ; in, For P-wave velocity, For S-wave velocity, For the density of a viscoelastic medium, The first Lamé constant, For the second Lamé constant, For P-wave quality factor, For S-wave quality factor, This represents the seismic wave displacement vector during its propagation. This is a physical activity item.

[0055] The displacement tensor construction module 12 is used to obtain the wave equation for the field integration point based on the viscoelastic wave equation, and to construct a second-order Green's displacement tensor based on the viscoelastic medium density, angular frequency and Green's function of the scalar wave equation to obtain the solution of the wave equation. In this embodiment, as an optional implementation, the wave equation for the field integral point is as follows: ; in, The coordinates of the earthquake source are... Here are the coordinates of the field integration point, which is a point in the geometric model. It is a second-order Green's displacement tensor.

[0056] In this embodiment, the second-order Green's displacement tensor is obtained using the following formula:

[0057] Where I is the identity matrix, , .

[0058] The first coefficient analysis module 13 is used to obtain the first coefficient expression of the second-order Green's displacement tensor based on the geometric model of the viscoelastic medium, introduce frequency-dependent complex velocity, construct Green's function based on complex velocity, and obtain the first solution term corresponding to the first coefficient expression of the second-order Green's displacement tensor based on the Green's function of complex velocity and the first coefficient expression. The second coefficient analysis module 14 is used to obtain the second solution term corresponding to the second coefficient expression of the second-order Green's displacement tensor based on Hooke's law and the first solution term; In this embodiment, the second solution term is the Green's stress tensor. Based on Hooke's law, the Green's stress tensor... The partial terms can be solved by first solving the problem. The expression is: .

[0059] The second equation construction module 15 is used to obtain the frequency domain viscoelastic medium boundary integral equation corresponding to the viscoelastic wave equation based on the first solution partial equation and the second solution partial equation. In this embodiment, as an optional embodiment, the second equation construction module 15 is further configured to: Obtain the geometric dimension parameter matrix of the non-smooth medium in the geometric model; The boundary integral equation of the viscoelastic medium in the frequency domain is simplified based on the geometric dimension parameter matrix.

[0060] In this embodiment, as an optional embodiment, the geometric dimension parameter matrix is: ; Where C(r) is the geometric dimension parameter matrix, It is Poisson's ratio. and It is the angle between the boundary corner point and the boundary tangent.

[0061] Discrete solution module 16 is used to discretely solve the boundary integral equation of the viscoelastic medium in the frequency domain to obtain the displacement and stress of the seismic wave during propagation.

[0062] In this embodiment, as an optional implementation, the discrete solution module 16 is specifically used for: The free surfaces and irregular interfaces in the geometric model are discretized into nodes, and node-type functions are constructed based on the discretized nodes. Based on nodal functions, the discrete nodal expressions of the first solution terms of the boundary integral equation of the viscoelastic medium in the frequency domain are obtained. Based on discrete node expressions, the frequency domain viscoelastic medium boundary integral equation is transformed into a matrix equation; Based on the continuity boundary conditions of the free surface and irregular interface in the geometric model, the coefficient matrix of the matrix equation is obtained; By acquiring the coefficient matrix values ​​from the seismic data of the target seismic wave, the matrix equation is solved to obtain the displacement and stress during the propagation of the target seismic wave.

[0063] Based on the same inventive concept, embodiments of the present invention also provide a storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the viscoelastic medium-based seismic wave forward modeling method in any of the above possible implementations.

[0064] Optionally, the storage medium may be a non-transitory computer-readable storage medium, such as a ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk, and optical data storage device.

[0065] Based on the same inventive concept, see [link to inventive concept] Figure 11 This invention also provides an electronic device, including a memory 101 (e.g., non-volatile memory), a processor 102, and a computer program stored in the memory 101 and executable on the processor 102. When the processor 102 executes the program, it implements the steps of the viscoelastic medium-based seismic wave forward modeling method described in any of the above possible implementations, which is equivalent to the previously mentioned viscoelastic medium-based seismic wave forward modeling device. Of course, the processor can also be used to process other data or perform calculations. This electronic device can be a PC, server, terminal, or other similar device.

[0066] like Figure 11 As shown, the electronic device may also include: memory 103, network interface 104, and internal bus 105. In addition to these components, other hardware may also be included, which will not be described in detail here.

[0067] It should be noted that the above-mentioned seismic wave forward modeling device based on viscoelastic medium can be implemented by software. As a device in a logical sense, it is formed by the processor 102 of the electronic device in which it is located reading the computer program instructions stored in the non-volatile memory into the memory 103 for execution.

[0068] The embodiments of the subject matter and functional operation described in this specification can be implemented in the following ways: digital electronic circuits, tangibly embodied computer software or firmware, computer hardware including the structures disclosed in this specification and their structural equivalents, or combinations thereof. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible, non-transitory program carrier for execution by a data processing apparatus or for controlling the operation of a data processing apparatus. Alternatively or additionally, the program instructions may be encoded on artificially generated propagation signals, such as machine-generated electrical, optical, or electromagnetic signals, which are generated to encode information and transmit it to a suitable receiving device for execution by the data processing apparatus. The computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or combinations thereof.

[0069] The processing and logic flow described in this specification can be executed by one or more programmable computers that execute one or more computer programs to perform corresponding functions by operating on input data and generating output. The processing and logic flow can also be executed by special-purpose logic circuitry—such as FPGA (Field Programmable Gate Array) or ASIC (Application-Specific Integrated Circuit), and the device can also be implemented as special-purpose logic circuitry.

[0070] Suitable computers for executing computer programs include, for example, general-purpose and / or special-purpose microprocessors, or any other type of central processing unit. Typically, the central processing unit receives instructions and data from read-only memory and / or random access memory. The basic components of a computer include a central processing unit for implementing or executing instructions and one or more memory devices for storing instructions and data. Typically, a computer will also include one or more mass storage devices for storing data, such as disks, magneto-optical disks, or optical disks, or the computer will be operatively coupled to such mass storage devices to receive data from or transfer data to them, or both. However, a computer is not required to have such devices. Furthermore, a computer can be embedded in another device, such as a mobile phone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a global positioning system (GPS) receiver, or a portable storage device such as a universal serial bus (USB) flash drive, to name a few.

[0071] Computer-readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media, and memory devices, such as semiconductor memory devices (e.g., EPROM, EEPROM, and flash memory devices), magnetic disks (e.g., internal hard disks or removable disks), magneto-optical disks, and CD-ROM and DVD-ROM disks. Processors and memory may be supplemented by or incorporated into dedicated logic circuitry.

[0072] While this specification contains numerous specific implementation details, these should not be construed as limiting the scope of any invention or the scope of the claims, but rather are primarily used to describe features of specific embodiments of a particular invention. Certain features described in the various embodiments herein may also be implemented in combination in a single embodiment. Conversely, various features described in a single embodiment may also be implemented separately in various embodiments or in any suitable sub-combination. Furthermore, while features may function in certain combinations as described above and even initially claimed in this way, one or more features from a claimed combination may be removed from that combination in some cases, and a claimed combination may refer to a sub-combination or a variation thereof.

[0073] Similarly, although the operations are depicted in a specific order in the accompanying drawings, this should not be construed as requiring these operations to be performed in the specific order shown or sequentially, or requiring all illustrated operations to be performed to achieve the desired result. In some cases, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system modules and components in the above embodiments should not be construed as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0074] Thus, specific embodiments of the subject matter have been described. Other embodiments are within the scope of the appended claims. In some cases, the actions recited in the claims may be performed in a different order and still achieve the desired result. Furthermore, the processes depicted in the drawings are not necessarily shown in a specific order or sequence to achieve the desired result. In some implementations, multitasking and parallel processing may be advantageous.

[0075] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0076] The above are merely specific embodiments of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A forward modeling method for seismic waves based on viscoelastic media, characterized in that, include: Obtain the viscoelastic medium parameters of the formation, and construct a viscoelastic wave equation based on the seismic wave displacement vector based on the viscoelastic medium parameters. The viscoelastic medium parameters include: P-wave velocity, S-wave velocity, viscoelastic medium density, source angular frequency, first Lamé constant, second Lamé constant, P-wave quality factor, and S-wave quality factor. Based on the viscoelastic wave equation, the wave equation for the field integration point is obtained. Based on the viscoelastic medium density, angular frequency and Green's function of the scalar wave equation, a second-order Green's displacement tensor is constructed to obtain the solution of the wave equation. Based on the geometric model of viscoelastic medium, the first coefficient expression of the second-order Green's displacement tensor is obtained. Frequency-dependent complex velocity is introduced to construct the Green's function based on the complex velocity. Based on the Green's function based on the complex velocity and the first coefficient expression, the first solution term corresponding to the first coefficient expression of the second-order Green's displacement tensor is obtained. Based on Hooke's law and the first solution term, the second solution term corresponding to the second coefficient expression of the second-order Green's displacement tensor is obtained; Based on the first and second partial solutions, the frequency domain boundary integral equation of the viscoelastic medium corresponding to the viscoelastic wave equation is obtained. Discretely solve the boundary integral equation of the viscoelastic medium in the frequency domain to obtain the displacement and stress of the seismic wave during propagation.

2. The seismic wave forward modeling method based on viscoelastic media according to claim 1, characterized in that, The discrete solution of the boundary integral equation of the viscoelastic medium in the frequency domain to obtain the displacement and stress of the seismic wave during propagation includes: The free surfaces and irregular interfaces in the geometric model are discretized into nodes, and node-type functions are constructed based on the discretized nodes. Based on nodal functions, the discrete nodal expressions of the first solution terms of the boundary integral equation of the viscoelastic medium in the frequency domain are obtained. Based on discrete node expressions, the frequency domain viscoelastic medium boundary integral equation is transformed into a matrix equation; Based on the continuity boundary conditions of the free surface and irregular interface in the geometric model, the coefficient matrix of the matrix equation is obtained; By acquiring the coefficient matrix values ​​from the seismic data of the target seismic wave, the matrix equation is solved to obtain the displacement and stress during the propagation of the target seismic wave.

3. The seismic wave forward modeling method based on viscoelastic media according to claim 1, characterized in that, The viscoelastic wave equation is as follows: ； in, For P-wave velocity, For S-wave velocity, For the density of a viscoelastic medium, The first Lamé constant, For the second Lamé constant, For P-wave quality factor, For S-wave quality factor, This represents the seismic wave displacement vector during its propagation. This is a physical activity item.

4. The seismic wave forward modeling method based on viscoelastic media according to claim 3, characterized in that, The wave equation for the field integral point is as follows: ； in, The coordinates of the earthquake source are... Here are the coordinates of the field integration point, which is a point in the geometric model. It is a second-order Green's displacement tensor.

5. The seismic wave forward modeling method based on viscoelastic media according to claim 4, characterized in that, The second-order Green's displacement tensor is obtained using the following formula: Where I is the identity matrix, , .

6. The seismic wave forward modeling method based on viscoelastic media according to any one of claims 1 to 5, characterized in that, The method further includes: Obtain the geometric dimension parameter matrix of the non-smooth medium in the geometric model; The boundary integral equation of the viscoelastic medium in the frequency domain is simplified based on the geometric dimension parameter matrix.

7. The seismic wave forward modeling method based on viscoelastic media according to claim 6, characterized in that, The geometric dimension parameter matrix is ​​as follows: ； Where C(r) is the geometric dimension parameter matrix, It is Poisson's ratio. and It is the angle between the boundary corner point and the boundary tangent.

8. A seismic wave forward modeling device based on viscoelastic media, characterized in that, The seismic wave forward modeling device based on viscoelastic media includes: The first equation construction module is used to obtain the viscoelastic medium parameters of the strata and construct a viscoelastic wave equation based on the seismic wave displacement vector based on the viscoelastic medium parameters. The viscoelastic medium parameters include: P-wave velocity, S-wave velocity, viscoelastic medium density, source angular frequency, first Lamé constant, second Lamé constant, P-wave quality factor and S-wave quality factor. The displacement tensor construction module is used to obtain the wave equation for the field integration point based on the viscoelastic wave equation. Based on the viscoelastic medium density, angular frequency and Green's function of the scalar wave equation, a second-order Green's displacement tensor is constructed to obtain the solution of the wave equation. The first coefficient analysis module is used to obtain the first coefficient expression of the second-order Green's displacement tensor based on the geometric model of the viscoelastic medium, introduce frequency-dependent complex velocity, construct the Green's function based on complex velocity, and obtain the first solution term corresponding to the first coefficient expression of the second-order Green's displacement tensor based on the Green's function of complex velocity and the first coefficient expression. The second coefficient analysis module is used to obtain the second solution term corresponding to the second coefficient expression of the second-order Green's displacement tensor based on Hooke's law and the first solution term; The second equation construction module is used to obtain the frequency domain viscoelastic medium boundary integral equation corresponding to the viscoelastic wave equation based on the first solution partial equation and the second solution partial equation. The discrete solution module is used to discretely solve the boundary integral equation of the viscoelastic medium in the frequency domain to obtain the displacement and stress of the seismic wave during propagation.

9. A storage medium, characterized in that, A program or instruction is stored on a storage medium, and the program or instruction is executed by a processor to implement the steps of the seismic wave forward modeling method based on viscoelastic medium as described in any one of claims 1 to 7.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the seismic wave forward modeling method based on viscoelastic media as described in any one of claims 1 to 7.

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