Three-dimensional anisotropic medium seismic wave field simulation method, device and equipment and medium

Abstract

The invention relates to a three-dimensional anisotropic medium seismic wave field simulation method, device and equipment and a medium, and belongs to the technical field of geophysical exploration numerical simulation. Comprising the following steps: introducing a speed attenuation damping term for carrying out seismic wave attenuation in a boundary region on the basis of double factors of time and space into an initial elastic wave equation set which is used for describing seismic wave propagation in a three-dimensional anisotropic medium and is based on an EAL boundary, and obtaining a target anisotropic elastic wave equation set; constructing an expression of a speed attenuation damping item according to the target wave field weighting function; the target wave field weighting function simulates and controls wave field change rates at an inner boundary and an outer boundary corresponding to a wave field absorption boundary based on a Gaussian weighting coefficient; and based on the target anisotropic elastic wave equation set and the expression of the speed attenuation damping term, numerical simulation of the seismic wave propagation process in the three-dimensional anisotropic medium is carried out. Calculation efficiency is considered, calculation resources are saved, and three-dimensional complex earth medium high-precision seismic wave field simulation is achieved.

Description

Technical Field

[0001] The present disclosure relates to the technical field of geophysical exploration numerical simulation, and in particular to a three-dimensional anisotropic medium seismic wave field simulation method, device, equipment and medium. Background Art

[0002] Wave equation forward modeling is widely used in the field of seismic exploration, and one of its core research contents is to use different numerical algorithms to discretely solve various types of seismic wave equations.

[0003] When numerically solving wave equations on a computer platform, the computational domain is necessarily limited due to computing power and memory limitations. Consequently, strong truncation boundary reflections are generated at the model's boundaries, severely interfering with the internal effective wavefield and reducing the accuracy of the seismic wavefield simulation. To address this issue, artificial boundary conditions are currently commonly used to process and suppress the reflections caused by truncation boundaries.

[0004] In the process of implementing the concepts disclosed herein, the inventors discovered at least the following technical problems in the related art: Artificial boundary conditions currently include: attenuation-type absorbing boundaries, one-way wave-type absorbing boundaries, hybrid absorbing boundaries, and PML (Perfectly Matched Layer) absorbing boundaries. However, the numerical simulation results corresponding to existing artificial boundary conditions either fail to achieve comprehensive advantages in terms of performance and computational resource consumption. Some boundary conditions correspond to wave equations constructed with these conditions, requiring a large amount of computation and consuming a lot of memory during solution, resulting in relatively low energy efficiency. Some artificial boundary conditions improve computational complexity and memory consumption by reducing some boundary absorption effects, but only have good results for two-dimensional acoustic and elastic wave numerical simulations, and are not effective in three-dimensional anisotropic elastic wave numerical simulations. Therefore, there is an urgent need to provide a solution that is applicable to three-dimensional seismic wave field simulations in anisotropic media and is both energy-efficient (providing good simulation results and reasonable resource consumption, etc.). Summary of the Invention

[0005] In order to solve the above technical problems or at least partially solve the above technical problems, embodiments of the present disclosure provide a three-dimensional anisotropic medium seismic wave field simulation method, device, equipment and medium.

[0006] In a first aspect, an embodiment of the present disclosure provides a method for simulating a seismic wave field in a three-dimensional anisotropic medium. The method is applied to an electronic device and includes: introducing a velocity attenuation damping term into an initial elastic wave equation group used to describe seismic wave propagation in a three-dimensional anisotropic medium to obtain a target anisotropic elastic wave equation group; wherein the initial elastic wave equation group is an elastic seismic wave equation based on an EAL boundary condition; the velocity attenuation damping term attenuates seismic waves in the boundary region based on both time and space factors; constructing an expression for the velocity attenuation damping term based on a target wave field weighting function; the target wave field weighting function simulates and controls the wave field change rate at the inner and outer boundaries corresponding to the wave field absorption boundary based on a Gaussian weighting coefficient, so that a relatively smooth transition is generated in the wave field within the boundary region; and performing a numerical simulation of the seismic wave propagation process in the three-dimensional anisotropic medium on the electronic device based on the target anisotropic elastic wave equation group and the expression for the velocity attenuation damping term.

[0007] In some embodiments, the velocity attenuation damping term is set in the wave field absorption boundary condition as an attenuation factor, which prolongs the propagation time of the seismic wave in the boundary area by reducing the propagation velocity of the seismic wave.

[0008] In some embodiments, based on the above-mentioned target anisotropic elastic wave equation group and the expression of the above-mentioned velocity attenuation damping term, a numerical simulation of the seismic wave propagation process in the three-dimensional anisotropic medium is performed in the above-mentioned electronic device, including: based on the staggered grid finite difference method, the target anisotropic elastic wave equation group with the above-mentioned velocity attenuation damping term expression is numerically discretized and solved, and the solution process realizes the numerical simulation of the seismic wave propagation process in the three-dimensional anisotropic medium.

[0009] In some embodiments, the three-dimensional anisotropic medium includes a three-dimensional vertically symmetric transversely isotropic (VTI) elastic medium.

[0010] In some embodiments, the velocity decay damping term is expressed as follows: +1, in, represents the velocity decay damping term; express x The velocity attenuation component corresponding to the direction; express y The velocity attenuation component corresponding to the direction; express z The velocity attenuation component corresponding to the direction; The velocity attenuation components in each direction satisfy the following expressions: , in, nIndicates the distance from the computation node to the boundary of the absorption layer; represents the speed reduction damping factor of the construction; represents the target wavefield weighting function; represents the vertical S-wave velocity; represents the spatial discrete grid step size; Indicates the dominant frequency of the source wavelet used.

[0011] In some embodiments, the target wavefield weighting function satisfies the following expression: , in, Indicates the order, which is used to control the rate of change of the wave field at the inner and outer boundaries; Represents the total number of absorbing boundaries, which is a positive integer. N The larger the value, the thicker the absorption layer. represents the e-exponential function; It is the logarithm to the base of e, 2.

[0012] In some embodiments, the target anisotropic elastic wave equations satisfy the following expressions: , in, Corresponding to along x 、 y 、 z Directional velocity wave field component; 、 、 are all normal stress wave field components, corresponding to x As the normal line corresponds to the plane along x The axial normal stress component, y As the normal line corresponds to the plane along y The axial normal stress component, z As the normal line corresponds to the plane along z Axial normal stress component; 、 、 are all shear stress wave field components, corresponding to y As normal correspondence xoz Along the plane z The axial shear stress component, x As normal correspondence yoz Along the plane z The axial shear stress component, x As normal correspondence yoz Along the plane y Axial stress component; E represents the damping attenuation term in the boundary conditions; Represents the velocity decay damping term introduced; Indicates the density of the medium; 、 、 、 、 It is the three-dimensional VTI medium elastic coefficient matrix, which depends on different media.

[0013] In a second aspect, embodiments of the present disclosure provide a device for simulating seismic wavefields in three-dimensional anisotropic media. The device comprises a wave equation construction module, an expression construction module, and a processing module. The wave equation construction module is configured to introduce a velocity attenuation damping term into an initial set of elastic wave equations describing seismic wave propagation in a three-dimensional anisotropic medium, thereby obtaining a target set of anisotropic elastic wave equations. The initial set of elastic wave equations is an elastic seismic wave equation based on EAL boundary conditions. The velocity attenuation damping term attenuates seismic waves in boundary regions based on both temporal and spatial factors. The expression construction module is configured to construct an expression for the velocity attenuation damping term based on a target wavefield weighting function. The target wavefield weighting function uses a Gaussian weighting coefficient to simulate and control the wavefield change rate at the inner and outer boundaries corresponding to the wavefield absorption boundary, thereby producing a smoother transition of the wavefield within the boundary region. The processing module is configured to numerically simulate seismic wave propagation in a three-dimensional anisotropic medium based on the target set of anisotropic elastic wave equations and the expression for the velocity attenuation damping term.

[0014] In a third aspect, embodiments of the present disclosure provide an electronic device. The electronic device includes a processor, a communication interface, a memory, and a communication bus. The processor, communication interface, and memory communicate with each other via the communication bus. The memory is configured to store a computer program. The processor is configured to implement the aforementioned method for simulating three-dimensional seismic wavefields in anisotropic media when executing the program stored in the memory.

[0015] In a fourth aspect, embodiments of the present disclosure provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method for simulating seismic wavefields in three-dimensional anisotropic media.

[0016] The above technical solutions provided by the embodiments of the present disclosure have at least some or all of the following advantages: The above technical solution is suitable for simulating seismic wave fields in three-dimensional anisotropic media and has both energy efficiency and good simulation effect (with reasonable resource consumption and high computational efficiency). By introducing a velocity attenuation damping term into the initial elastic wave equations based on the EAL boundary conditions, the velocity attenuation damping term attenuates seismic waves in the boundary area based on the dual factors of time and space. Based on the addition of the dual factors of time and space and the attenuation of velocity, in the boundary area, the longer the propagation time of the wave, the more fully the energy of the seismic wave will be absorbed. This can more accurately simulate the propagation process of seismic waves in three-dimensional anisotropic media, which reflects the transmission process closely related to the spatial position coordinates and time. At the same time, according to the target wave field, The weighting function is constructed to obtain the expression of the above-mentioned velocity attenuation damping term; since the above-mentioned target wave field weighting function is based on a Gaussian weighting coefficient to simulate and control the wave field change rate at the inner and outer boundaries corresponding to the wave field absorption boundary, a relatively smooth transition of the wave field is produced in the boundary area; thus, in the subsequent numerical simulation of the seismic wave propagation process in the three-dimensional anisotropic medium in electronic equipment based on the above-mentioned target anisotropic elastic wave equation group and the expression of the above-mentioned velocity attenuation damping term, the truncated boundary reflection interference in the three-dimensional elastic wave numerical simulation can be effectively suppressed on the basis of taking into account the computational efficiency and saving the computational resources, the internal wave field is effectively protected, and the high-precision seismic wave field simulation results of the three-dimensional complex earth medium are obtained.

[0017] Compared to numerical simulations using the elastic wave equations with PML absorbing boundary conditions, the proposed solution saves significant computing resources and improves processing time. Compared to numerical simulations using the initial elastic wave equations with EAL boundary conditions, the computational complexity and additional computational effort are roughly the same, but with increased application scenarios for three-dimensional media and high-precision simulation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and, together with the description, serve to explain the principles of the present disclosure.

[0019] In order to more clearly illustrate the embodiments of the present disclosure or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or related technical descriptions. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0020] Figure 1 The flowchart of the three-dimensional anisotropic medium seismic wave field simulation method applied to electronic equipment according to one embodiment of the present disclosure is schematically shown.

[0021] Figure 2The wave field slices along the xoy plane simulated under different boundary conditions in a three-dimensional uniform VTI elastic medium I are schematically shown. (a) is a wave field slice obtained by simulation without applying the absorbing boundary condition, (b) is a wave field slice obtained by simulation using the traditional EAL boundary condition, and (c) is a wave field slice obtained by simulation using the improved IEAL boundary condition according to an embodiment of the present disclosure.

[0022] Figure 3 The wave field slices along the xoz plane simulated under different boundary conditions in a three-dimensional uniform VTI elastic medium I are schematically shown. (a) is a wave field slice obtained by simulation without applying the absorbing boundary condition, (b) is a wave field slice obtained by simulation using the traditional EAL boundary condition, and (c) is a wave field slice obtained by simulation using the improved IEAL boundary condition according to an embodiment of the present disclosure.

[0023] Figure 4 The wave field slices along the yoz plane simulated under different boundary conditions in a three-dimensional uniform VTI elastic medium I are schematically shown. (a) is a wave field slice obtained by simulation without applying the absorbing boundary condition, (b) is a wave field slice obtained by simulation using the traditional EAL boundary condition, and (c) is a wave field slice obtained by simulation using the improved IEAL boundary condition according to an embodiment of the present disclosure.

[0024] Figure 5 The wave field slices along the xoy plane simulated under different boundary conditions in a three-dimensional uniform VTI elastic medium II are schematically shown. (a) is a wave field slice obtained by simulation without applying the absorbing boundary condition, (b) is a wave field slice obtained by simulation using the traditional EAL boundary condition, and (c) is a wave field slice obtained by simulation using the improved IEAL boundary condition according to an embodiment of the present disclosure.

[0025] Figure 6 The wave field slices along the xoz plane simulated under different boundary conditions in a three-dimensional uniform VTI elastic medium II are schematically shown. (a) is a wave field slice obtained by simulation without applying the absorbing boundary condition, (b) is a wave field slice obtained by simulation using the traditional EAL boundary condition, and (c) is a wave field slice obtained by simulation using the improved IEAL boundary condition according to an embodiment of the present disclosure.

[0026] Figure 7 The wave field slices along the yoz plane simulated under different boundary conditions in a three-dimensional uniform VTI elastic medium II are schematically shown. (a) is a wave field slice obtained by simulation without applying the absorbing boundary condition, (b) is a wave field slice obtained by simulation using the traditional EAL boundary condition, and (c) is a wave field slice obtained by simulation using the improved IEAL boundary condition according to an embodiment of the present disclosure.

[0027] Figure 8Schematic diagram of the modified three-dimensional anisotropic Marmousi model, where (a) is the P-wave velocity model, (b) is the anisotropy parameter ε model, and (c) is the anisotropy parameter δ model.

[0028] Figure 9 The diagram schematically shows the single-shot records calculated using the three-dimensional VTI elastic wave equation in the modified three-dimensional anisotropic Marmousi model when no absorbing boundary conditions are applied, where (a) is the single-shot record result corresponding to xy, (b) is the single-shot record result corresponding to xt, and (c) is the single-shot record result corresponding to yt.

[0029] Figure 10 Schematic diagram showing the single-shot records calculated using the 3D VTI elastic wave equation when applying 15-layer traditional EAL boundary conditions in the modified 3D anisotropic Marmousi model, where (a) is the single-shot record result corresponding to xy, (b) is the single-shot record result corresponding to xt, and (c) is the single-shot record result corresponding to yt.

[0030] Figure 11 Schematically illustrates the single-shot records calculated by the three-dimensional VTI elastic wave equation when the EAL boundary conditions of the 15-layer embodiment of the present disclosure are applied in the modified three-dimensional anisotropic Marmousi model, where (a) is the single-shot record result corresponding to xy, (b) is the single-shot record result corresponding to xt, and (c) is the single-shot record result corresponding to yt.

[0031] Figure 12 The structural block diagram of the electronic device provided by the embodiment of the present disclosure is schematically shown. DETAILED DESCRIPTION

[0032] The embodiments of the present disclosure provide a method, apparatus, device and medium for simulating seismic wave fields in three-dimensional anisotropic media. The above scheme is applicable to the simulation of seismic wave fields in three-dimensional anisotropic media and has both energy efficiency and good simulation effect (good simulation effect, reasonable resource consumption and high computational efficiency). By introducing a velocity attenuation damping term into the initial elastic wave equations based on the EAL boundary conditions, the above velocity attenuation damping term attenuates seismic waves in the boundary area based on the dual factors of time and space. Based on the addition of the dual factors of time and space and the attenuation of velocity, in the boundary area, the longer the propagation time of the wave, the more fully the energy of the seismic wave will be absorbed. This can more accurately simulate the propagation process of seismic waves in three-dimensional anisotropic media, which reflects a transmission process that is closely related to the spatial position coordinates and time. At the same time, the expression of the above velocity attenuation damping term is constructed according to the target wave field weighting function; by The target wave field weighting function is based on a Gaussian weighting coefficient to simulate and control the wave field change rate at the inner and outer boundaries corresponding to the wave field absorption boundary, so that a relatively smooth transition of the wave field is produced in the boundary area; in this way, in the subsequent numerical simulation of the seismic wave propagation process in the three-dimensional anisotropic medium in the electronic device based on the target anisotropic elastic wave equation group and the expression of the velocity attenuation damping term, the truncated boundary reflection interference in the three-dimensional elastic wave numerical simulation can be effectively suppressed on the basis of taking into account the computational efficiency and saving the computational resources, the internal wave field is effectively protected, and a high-precision wave field simulation result is obtained.

[0033] Compared to numerical simulations using the elastic wave equations with PML absorbing boundary conditions, the proposed solution saves significant computing resources and improves processing time. Compared to numerical simulations using the initial elastic wave equations with EAL boundary conditions, the computational complexity and additional computational effort are roughly the same, but with increased application scenarios for three-dimensional media and high-precision simulation results.

[0034] To make the objectives, technical solutions, and advantages of the embodiments of the present disclosure more clear, the technical solutions in the embodiments of the present disclosure will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present disclosure, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present disclosure without making any creative efforts shall fall within the scope of protection of the present disclosure.

[0035] The embodiments of the present disclosure are described in detail below with reference to the accompanying drawings.

[0036] A first exemplary embodiment of the present disclosure provides a three-dimensional anisotropic medium seismic wave field simulation method, which is applied to electronic equipment.

[0037] In theory, the goal of solving elastic wave problems is to find an exact solution to the wave function under given boundary conditions. The wave equation, a second-order linear partial differential equation with constant coefficients, can be solved analytically using methods such as the superposition principle, mathematical transformations, and separation of variables. However, when faced with complex geometries and dielectric properties, precise calculations often require the use of numerical computer methods.

[0038] Figure 1 The flowchart of the three-dimensional anisotropic medium seismic wave field simulation method applied to electronic equipment according to one embodiment of the present disclosure is schematically shown.

[0039] Reference Figure 1 As shown, the three-dimensional anisotropic medium seismic wave field simulation method applied to electronic equipment provided by the embodiment of the present disclosure includes the following steps: S110, S120 and S130.

[0040] In step S110, a velocity attenuation damping term is introduced into the initial elastic wave equation group used to describe the propagation of seismic waves in a three-dimensional anisotropic medium to obtain a target anisotropic elastic wave equation group; wherein the above-mentioned initial elastic wave equation group is an elastic seismic wave equation based on the EAL boundary condition; the above-mentioned velocity attenuation damping term attenuates the seismic wave in the boundary area based on the dual factors of time and space.

[0041] The above target anisotropic elastic wave equations are described based on a three-dimensional space coordinate system (xyz).

[0042] In some embodiments, the three-dimensional anisotropic medium includes a hexagonal anisotropic medium (TI medium). For example, a TI medium having a vertical symmetry axis is called a vertical transverse isotropic (VTI) medium.

[0043] A transversely isotropic medium is a medium with a vertical axis of symmetry, which is usually found in complex geological structures, such as rocks with a large number of cracks. In such a medium, the speed of seismic waves will vary with the direction of the wave movement, which is called anisotropy.

[0044] The embodiment of the present disclosure improves the boundary conditions on the basis of the elastic seismic wave equation based on the EAL boundary condition, and describes the elastic seismic wave equation based on the EAL boundary condition as an initial elastic wave equation group. In this field, the elastic seismic wave equation based on the EAL boundary condition has been successfully applied in two-dimensional acoustic wave and elastic wave numerical simulation, but its application effect in three-dimensional seismic wave field simulation, especially three-dimensional anisotropic elastic wave numerical simulation, needs to be improved, and the numerical simulation effect is not good.

[0045] Therefore, in the embodiment of the present disclosure, a velocity attenuation damping term is introduced into the initial elastic wave equation group. The above-mentioned velocity attenuation damping term attenuates the seismic wave in the boundary area based on the dual factors of time and space. Based on the addition of the dual factors of time and space and the attenuation of the velocity, in the boundary area, the propagation time of the wave becomes longer, and the energy of the seismic wave will be absorbed more fully. This can more accurately simulate the propagation process of seismic waves in three-dimensional anisotropic media, which reflects the transmission process closely related to the spatial position coordinates and time.

[0046] In some embodiments, the velocity attenuation damping term is set in the wave field absorption boundary condition as an attenuation factor, which prolongs the propagation time of the seismic wave in the boundary area by reducing the propagation velocity of the seismic wave.

[0047] For example, the velocity decay damping term is expressed as , In particular, when When , this item will not affect the wave field propagation characteristics; when This will cause the seismic wave propagation speed to decrease, thereby extending its propagation time in the boundary area.

[0048] In some embodiments, the velocity decay damping term is expressed as: +1, (1) in, represents the velocity decay damping term; express x The velocity attenuation component corresponding to the direction; express y The velocity attenuation component corresponding to the direction; express z The velocity attenuation component corresponding to the direction; The velocity attenuation components in each direction satisfy the following expressions: , (2) in, n Indicates the distance from the computation node to the boundary of the absorption layer; represents the speed reduction damping factor of the construction; represents the target wavefield weighting function; represents the vertical S-wave velocity; represents the spatial discrete grid step size; Indicates the dominant frequency of the source wavelet used.

[0049] In some embodiments, the target anisotropic elastic wave equations satisfy the following expressions: , (3) in, Corresponding to along x 、 y 、 z Directional velocity wave field component; 、 、 are all normal stress wave field components, corresponding to x As the normal line corresponds to the plane along x The axial normal stress component, y As the normal line corresponds to the plane along y The axial normal stress component, z As the normal line corresponds to the plane along z Axial normal stress component; 、 、 are all shear stress wave field components, corresponding to y As normal correspondence xoz Along the plane z The axial shear stress component, x As normal correspondence yoz Along the plane z The axial shear stress component, x As normal correspondence yoz Along the plane y Axial stress component; E represents the damping attenuation term in the boundary conditions; Represents the velocity decay damping term introduced; Indicates the density of the medium; 、 、 、 、 It is the three-dimensional VTI medium elastic coefficient matrix, which depends on different media.

[0050] In the above formula (3), the form is Represents any variable (For specific variables, see the specific expression of formula (4). Here is the explanation of the general expression method.) t The partial derivative of 、 、 Represents any variable Partial derivatives in the direction of the corresponding coordinate axis.

[0051] In some embodiments, when the medium is a VTI medium, the specific expression of each VTI medium elastic coefficient matrix is ​​as follows: , (4) in, 、 They correspond to the velocities of vertical P waves (P waves are longitudinal waves) and S waves (S waves are transverse waves); 、 、 is the Thomsen anisotropy parameter (a parameter in the Thomsen model, which is a commonly used model to describe the anisotropy of rocks or media).

[0052] In step S120, an expression for the velocity attenuation damping term is constructed based on a target wavefield weighting function. The target wavefield weighting function simulates and controls the wavefield change rate at the inner and outer boundaries corresponding to the wavefield absorption boundary based on a Gaussian weighting coefficient, so as to produce a smoother transition of the wavefield within the boundary region.

[0053] Based on the construction of the above formula (2), it can be seen that the speed reduction damping term The effect depends on the wavefield weighting function. If the weighting factor changes too drastically in the boundary area, it will cause a strong reflection wave inside the truncation boundary. Conversely, the reflection wave inside the truncation boundary will be better controlled. Therefore, in the embodiment of the present disclosure, the wavefield weighting function is improved to construct a target wavefield weighting function that produces a smoother transition of the wavefield in the boundary area. It is a Gaussian hybrid weighting coefficient.

[0054] In some embodiments, the target wavefield weighting function satisfies the following expression: , (5) in, Indicates the order, which is used to control the rate of change of the wave field at the inner and outer boundaries; Represents the total number of absorbing boundaries, which is a positive integer. N The larger the value, the thicker the absorption layer. represents the e-exponential function; It is the logarithm to the base of e, 2.

[0055] In some embodiments, when β When the value is 2.5, the Gaussian boundary condition can produce a good absorption effect on boundary reflection while taking into account stability.

[0056] Substituting the expression of the above velocity attenuation damping term into the target anisotropic elastic wave equations, the medium first-order velocity-stress elastic wave equations of the improved effective absorbing boundary condition (IEAL) proposed in the embodiment of the present disclosure are obtained.

[0057] In step S130, based on the target anisotropic elastic wave equations and the expression of the velocity attenuation damping term, a numerical simulation of the seismic wave propagation process in the three-dimensional anisotropic medium is performed in an electronic device.

[0058] In some embodiments, based on the above-mentioned target anisotropic elastic wave equation group and the expression of the above-mentioned velocity attenuation damping term, a numerical simulation of the seismic wave propagation process in the three-dimensional anisotropic medium is performed in the above-mentioned electronic device, including: based on the staggered grid finite difference method, the target anisotropic elastic wave equation group with the above-mentioned velocity attenuation damping term expression is numerically discretized and solved, and the solution process realizes the numerical simulation of the seismic wave propagation process in the three-dimensional anisotropic medium.

[0059] This disclosed embodiment improves the EAL boundary, resulting in a numerical simulation scheme based on the IEAL boundary. This approach broadens the application of traditional EAL boundary simulations from two-dimensional isotropic media to three-dimensional complex VTI media. Key improvements include improvements to the boundary condition's velocity reduction damping attenuation term and wavefield weighting coefficient. While maintaining computational efficiency and conserving computing resources, the IEAL boundary condition in this disclosed embodiment effectively suppresses truncated boundary reflection interference in three-dimensional VTI elastic wave numerical simulations, effectively protecting the internal wavefield.

[0060] In order to illustrate the effect comparison between this case and the existing boundary conditions, the wave equations based on the traditional EAL boundary are used as an example.

[0061] The elastic seismic wave equation using the EAL boundary condition can be expressed as follows: , (6) In order to clearly indicate the differences, the same parameters are indicated in the same way, and the specific meanings are not repeated. Subscripts are used to indicate different parameters, such as represents the damping attenuation term in the EAL boundary condition, and in formula (3), E represents the damping attenuation term in the boundary condition (i.e., the improved effective absorbing boundary condition provided by the embodiment of the present disclosure), wherein E and The relationship between them is: .

[0062] The damping attenuation term in the EAL boundary condition satisfies the following expression: , (7) in, Indicates along x The damping attenuation component of the axis; Indicates along y The damping attenuation component of the axis; Represents the damping attenuation component along the x-axis.

[0063] The damping attenuation components in each direction satisfy the following expressions: , (8) in, is the vertical P-wave velocity; parameter R is the theoretical reflection coefficient; Represents the wavefield weighting function based on the EAL boundary.

[0064] Wavefield weighting function based on EAL boundary satisfies the following expression: . (9) When the number of absorption layers is 10, 20 and 40 respectively, the parameters R Corresponding to 0.001, 0.0001 and 0.00001 respectively. The range of variation is 0~1. When the computing node is located in the absorption layer, the corresponding parameter value range is , at this time, the EAL boundary will absorb and attenuate the wave field in the absorption layer. When the node is located in the calculation area, the corresponding parameter value range is , attenuation term parameter , at this time the elastic wave equation (6) degenerates into the original equation, and the attenuation term has no effect on the wave field in the calculation area.

[0065] In some embodiments, the particle x Directional velocity component Taking the equation as an example, the high-order staggered grid discretization format without any artificial boundary conditions, with EAL artificial boundary conditions, and with IEAL artificial boundary conditions can be expressed as the following expressions (10), (11), and (12), respectively: , (10) , (11) . (12) in, A , B , C are high-order staggered grid discretization operators for different normal stress components, in the following form: . (13) by x Directional particle normal stress component Taking the equation as an example, the high-order staggered grid discretization formats without any artificial boundary conditions, with EAL artificial boundary conditions, and with IEAL artificial boundary conditions correspond to the following expressions (14), (15), and (16), respectively: , (14) , (15) , (16) in, D , E , F are high-order staggered grid discretization operators for different velocity components, respectively, and their expressions are as follows: , (17) in, i , j , k and o The spatial coordinates x , y , z and time coordinates t The grid node index, h is the spatial grid step size, is the optimized spatial high-order staggered grid difference coefficient, M It is half the length of the staggered grid difference operator.

[0066] A comparative analysis based on the above formulas shows that, without the use of artificial boundaries, the discretization formats for loading traditional EAL boundaries and the improved IEAL boundaries provided by the embodiments of this disclosure are essentially identical, differing only in the coefficient terms in the difference equations. Since the coefficient terms in the discrete equations can be calculated in advance, they remain unchanged during wavefield iterative updates. Therefore, overall, the computational complexity and memory requirements for implementing IEAL boundaries in the solution provided by the embodiments of this disclosure are comparable to those for implementing EAL boundaries, effectively controlling computational efficiency and cost.

[0067] The uniform model and the complex model are used to calculate the three-dimensional VTI elastic wave equation without absorbing boundary conditions, with EAL boundary conditions and with IEAL boundary conditions, and the effects of the two boundary conditions are analyzed and compared.

[0068] First, two three-dimensional uniform VTI elastic models were used to test the EAL boundary conditions and IEAL boundary conditions. In order to compare the results, the three-dimensional VTI elastic wave equation without artificial absorbing boundary conditions was calculated at the same time. The extrapolation format is shown in formulas (10), (13), (14) and (17). The size of the three-dimensional model is 2000 m×2000 m×2000 m, the cubic discrete grid spacing is 10 m, and the time sampling interval is 0.001 s. A Ricker wavelet with a main frequency of 30 Hz is placed in the center of the model to generate vibration. The parameters of the uniform VTI medium model I are , , , , and The parameters of the uniform VTI medium model II are , , , , and .

[0069] Figure 2 The wave field slices along the xoy plane simulated under different boundary conditions in a three-dimensional uniform VTI elastic medium I are schematically shown. (a) is a wave field slice obtained by simulation without applying the absorbing boundary condition, (b) is a wave field slice obtained by simulation using the traditional EAL boundary condition, and (c) is a wave field slice obtained by simulation using the improved IEAL boundary condition according to an embodiment of the present disclosure. Figure 3 The wave field slices along the xoz plane simulated under different boundary conditions in a three-dimensional uniform VTI elastic medium I are schematically shown. (a) is a wave field slice obtained by simulation without applying the absorbing boundary condition, (b) is a wave field slice obtained by simulation using the traditional EAL boundary condition, and (c) is a wave field slice obtained by simulation using the improved IEAL boundary condition according to an embodiment of the present disclosure. Figure 4 The wave field slices along the yoz plane simulated under different boundary conditions in a three-dimensional uniform VTI elastic medium I are schematically shown. (a) is a wave field slice obtained by simulation without applying the absorbing boundary condition, (b) is a wave field slice obtained by simulation using the traditional EAL boundary condition, and (c) is a wave field slice obtained by simulation using the improved IEAL boundary condition according to an embodiment of the present disclosure. Figure 5 The wave field slices along the xoy plane simulated under different boundary conditions in a three-dimensional uniform VTI elastic medium II are schematically shown. (a) is a wave field slice obtained by simulation without applying the absorbing boundary condition, (b) is a wave field slice obtained by simulation using the traditional EAL boundary condition, and (c) is a wave field slice obtained by simulation using the improved IEAL boundary condition according to an embodiment of the present disclosure. Figure 6The wave field slices along the xoz plane simulated under different boundary conditions in a three-dimensional uniform VTI elastic medium II are schematically shown. (a) is a wave field slice obtained by simulation without applying the absorbing boundary condition, (b) is a wave field slice obtained by simulation using the traditional EAL boundary condition, and (c) is a wave field slice obtained by simulation using the improved IEAL boundary condition according to an embodiment of the present disclosure. Figure 7 The wave field slices along the yoz plane simulated under different boundary conditions in a three-dimensional uniform VTI elastic medium II are schematically shown. (a) is a wave field slice obtained by simulation without applying the absorbing boundary condition, (b) is a wave field slice obtained by simulation using the traditional EAL boundary condition, and (c) is a wave field slice obtained by simulation using the improved IEAL boundary condition according to an embodiment of the present disclosure.

[0070] Figures 2 to 7 The results of two 3D uniform VTI elastic models (elastic medium I and elastic medium II) without artificial boundary conditions, with EAL boundary conditions with 20 layers, and with IEAL boundary conditions with 20 layers are presented. xoy flat, xoz Plane and yoz Plane wavefield snapshot slice. The corresponding propagation time of each wavefield slice increases from left to right. Figure 2 (a) to (c) Figure 7 From (a) to (c), we can see that when no artificial boundary conditions are applied, strong truncated boundary reflection waves are generated in the boundary region of the model, interfering with the internal effective wave field. When the EAL boundary conditions and IEAL boundary conditions are applied, the truncated boundary reflection waves are effectively suppressed and absorbed. In addition, compared with the simulation results of the EAL boundary conditions, the IEAL boundary conditions can produce a better absorption effect on the truncated boundary reflection without increasing the computational complexity and additional computational cost.

[0071] Figure 8 Schematic diagram of the modified three-dimensional anisotropic Marmousi model, (a) is the P-wave velocity model, (b) is the anisotropy parameter ε model, and (c) is the anisotropy parameter δ model. Figure 9 The diagram schematically shows the single-shot records calculated using the three-dimensional VTI elastic wave equation in the modified three-dimensional anisotropic Marmousi model when no absorbing boundary conditions are applied, where (a) is the single-shot record result corresponding to xy, (b) is the single-shot record result corresponding to xt, and (c) is the single-shot record result corresponding to yt. Figure 10 Schematic diagram showing the single-shot records calculated using the 3D VTI elastic wave equation when applying 15-layer traditional EAL boundary conditions in the modified 3D anisotropic Marmousi model, where (a) is the single-shot record result corresponding to xy, (b) is the single-shot record result corresponding to xt, and (c) is the single-shot record result corresponding to yt. Figure 11 Schematically illustrates the single-shot records calculated by the three-dimensional VTI elastic wave equation when the EAL boundary conditions of the 15-layer embodiment of the present disclosure are applied in the modified three-dimensional anisotropic Marmousi model, where (a) is the single-shot record result corresponding to xy, (b) is the single-shot record result corresponding to xt, and (c) is the single-shot record result corresponding to yt. Figure 9 (a) to (c) Figure 10 (a) to (c) and Figure 11 In (a) to (c), in order to simplify the illustration, the schematic method of the three-view drawing is used. The coordinate axes at the same position in a certain figure follow the coordinate axes of the corresponding figure, for example Figure 9 The horizontal y-axis corresponding to (a) and (b) is the same, only one is shown; similarly, Figure 9 The vertical axes t corresponding to (b) and (c) are the same, and only one is shown.

[0072] The effectiveness of different boundary conditions was further tested using a complex anisotropic elastic model. Figure 8 A modified 3D Marmousi VTI anisotropic model is proposed, including the vertical P-wave velocity and Thomsen anisotropy parameter ε and δ , shear wave velocity Set to , and the remaining parameters are set as constants, namely: and The three-dimensional model has dimensions of 3000 m × 3000 m × 2100 m, a discrete grid spacing of 12 m, and a time sampling interval of 0.0008 s. A Ricker wavelet with a dominant frequency of 12.5 Hz is placed in the shallow layer of the model to generate vibrations. Figure 9 (a)~(c)~ Figure 11 (a) to (c) show the seismic records of the modified 3D Marmousi VTI anisotropic elastic model without artificial boundary conditions, with EAL boundary conditions of 15 layers, and with IEAL boundary conditions of 15 layers. Figure 9 (a)~(c)~ Figure 11 As can be seen in Figures (a) through (c), when no treatment is applied to the truncation boundary, strong truncation boundary reflection waves are generated at the model boundary region, interfering with the effective wavefield within. Applying the EAL boundary condition and the IEAL boundary effectively suppresses these truncation boundary reflection waves. In particular, compared with the EAL boundary treatment results, the IEAL boundary provides a better absorption effect on the truncation boundary without increasing complexity or computational cost.

[0073] Overall, from the calculation examples of uniform models and complex models, it can be seen that the improved effective boundary conditions provided by the method for simulating three-dimensional anisotropic media seismic wavefields provided in the embodiments of the present disclosure can provide an effective wavefield extension tool for three-dimensional anisotropic media wavefield simulation and subsequent inversion imaging.

[0074] In summary, in the embodiment including steps S110 to S130, by introducing the velocity attenuation damping term into the initial elastic wave equations based on the EAL boundary conditions, the velocity attenuation damping term attenuates the seismic wave in the boundary area based on the dual factors of time and space. Based on the addition of the dual factors of time and space and the attenuation of the velocity, in the boundary area, the longer the propagation time of the wave becomes, the more fully the energy of the seismic wave will be absorbed. In this way, the propagation process of the seismic wave in the three-dimensional anisotropic medium can be simulated more accurately, and this process reflects the transmission process that is closely related to the spatial position coordinates and time. At the same time, the above-mentioned The expression of the velocity attenuation damping term; since the above-mentioned target wave field weighting function is based on a Gaussian weighting coefficient to simulate and control the wave field change rate at the inner and outer boundaries corresponding to the wave field absorption boundary, a relatively smooth transition of the wave field is produced in the boundary area; thus, in the subsequent numerical simulation of the seismic wave propagation process in the three-dimensional anisotropic medium in the electronic equipment based on the above-mentioned target anisotropic elastic wave equation group and the expression of the above-mentioned velocity attenuation damping term, the truncated boundary reflection interference in the three-dimensional elastic wave numerical simulation can be effectively suppressed on the basis of taking into account the computational efficiency and saving the computational resources, the internal wave field is effectively protected, and the high-precision wave field simulation result is obtained.

[0075] The disclosed embodiments are suitable for simulating seismic wavefields in three-dimensional anisotropic media and offer both energy efficiency and performance (excellent simulation results, reasonable resource consumption, and high computational efficiency). Compared to numerical simulations using the elastic wave equations with PML absorbing boundary conditions, this approach significantly saves computing resources and improves processing time. Compared to numerical simulations using the initial elastic wave equations with EAL boundary conditions, this approach maintains similar computational complexity and additional computational effort, but adds application scenarios specific to three-dimensional media and achieves highly accurate simulation results.

[0076] A second exemplary embodiment of the present disclosure provides a three-dimensional anisotropic medium seismic wave field simulation device, which includes a wave equation building module, an expression building module, and a processing module.

[0077] The above-mentioned wave equation construction module is used to introduce a velocity attenuation damping term into the initial elastic wave equation group used to describe the propagation of seismic waves in three-dimensional anisotropic media, so as to obtain a target anisotropic elastic wave equation group; wherein, the above-mentioned initial elastic wave equation group is an elastic seismic wave equation based on the EAL boundary condition; the above-mentioned velocity attenuation damping term attenuates the seismic wave in the boundary area based on the dual factors of time and space.

[0078] The expression construction module is used to construct an expression for the velocity attenuation damping term based on a target wavefield weighting function. The target wavefield weighting function simulates and controls the wavefield change rate at the inner and outer boundaries corresponding to the wavefield absorption boundary based on a Gaussian weighting coefficient, so that a relatively smooth transition of the wavefield occurs in the boundary region.

[0079] The processing module is used to perform numerical simulation of the seismic wave propagation process in a three-dimensional anisotropic medium based on the target anisotropic elastic wave equation group and the expression of the velocity attenuation damping term.

[0080] For more details of this embodiment, please refer to the relevant description of the first embodiment, which will not be repeated here.

[0081] Any number of the aforementioned wave equation building blocks, expression building blocks, and processing blocks can be combined into a single module, or any one of these blocks can be split into multiple modules. Alternatively, at least part of the functionality of one or more of these blocks can be combined with at least part of the functionality of other blocks and implemented in a single module. At least one of the aforementioned wave equation building blocks, expression building blocks, and processing blocks can be at least partially implemented as a hardware circuit, such as a field programmable gate array (FPGA), a programmable logic array (PLA), a system on a chip, a system on a substrate, a system on a package, an application-specific integrated circuit (ASIC), or can be implemented in hardware or firmware through any other reasonable means of circuit integration or packaging, or can be implemented in any one of the three implementation methods of software, hardware, and firmware, or any suitable combination of any of these. Alternatively, at least one of the aforementioned wave equation building blocks, expression building blocks, and processing blocks can be at least partially implemented as a computer program module that, when executed, performs the corresponding functionality.

[0082] A third exemplary embodiment of the present disclosure provides an electronic device.

[0083] Figure 12 The structural block diagram of the electronic device provided by the embodiment of the present disclosure is schematically shown.

[0084] Reference Figure 12As shown, the electronic device 1200 provided in the embodiment of the present disclosure includes a processor 1201, a communication interface 1202, a memory 1203 and a communication bus 1204, wherein the processor 1201, the communication interface 1202 and the memory 1203 communicate with each other through the communication bus 1204; the memory 1203 is used to store computer programs; the processor 1201 is used to implement the three-dimensional anisotropic medium seismic wave field simulation method as described above when executing the program stored in the memory.

[0085] A fourth exemplary embodiment of the present disclosure further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned method for simulating a three-dimensional seismic wave field in anisotropic media.

[0086] The computer-readable storage medium may be included in the device or apparatus described in the above embodiments, or may exist independently without being incorporated into the device or apparatus. The computer-readable storage medium carries one or more programs, and when the one or more programs are executed, the method according to the embodiments of the present disclosure is implemented.

[0087] According to embodiments of the present disclosure, a computer-readable storage medium may be a non-volatile computer-readable storage medium, such as, but not limited to, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In the present disclosure, a computer-readable storage medium may be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0088] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or device comprising the element.

[0089] The foregoing description is intended only to provide specific embodiments of the present disclosure, intended to enable those skilled in the art to understand and implement the present disclosure. 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 present disclosure. Therefore, the present disclosure is not to be limited to the embodiments shown herein, but is to be construed in the broadest manner consistent with the principles and novel features claimed herein.

Claims

1. A three-dimensional anisotropic medium seismic wave field simulation method, characterized in that: Applied to electronic equipment, the method includes: A velocity attenuation damping term is introduced into an initial elastic wave equation group used to describe seismic wave propagation in a three-dimensional anisotropic medium to obtain a target anisotropic elastic wave equation group; wherein the initial elastic wave equation group is an elastic seismic wave equation based on an EAL boundary condition; and the velocity attenuation damping term attenuates seismic waves in the boundary region based on both time and space factors; An expression for the velocity attenuation damping term is constructed based on a target wavefield weighting function; the target wavefield weighting function simulates and controls the wavefield change rate at the inner and outer boundaries corresponding to the wavefield absorption boundary based on a Gaussian weighting coefficient, so as to produce a smoother transition of the wavefield within the boundary region; Based on the target anisotropic elastic wave equation group and the expression of the velocity attenuation damping term, a numerical simulation of the seismic wave propagation process in the three-dimensional anisotropic medium is performed on the electronic device.

2. The method according to claim 1, characterized in that The velocity attenuation damping term is set in the wave field absorption boundary condition as an attenuation factor, which prolongs the propagation time of the seismic wave in the boundary area by reducing the propagation velocity of the seismic wave.

3. The method according to claim 2, characterized in that Based on the target anisotropic elastic wave equation group and the expression of the velocity attenuation damping term, a numerical simulation of a seismic wave propagation process in a three-dimensional anisotropic medium is performed on the electronic device, including: Based on the staggered grid finite difference method, the target anisotropic elastic wave equations with the velocity attenuation damping term expression are numerically discretized and solved, and the solution process realizes the numerical simulation of the seismic wave propagation process in three-dimensional anisotropic media.

4. The method according to claim 1, wherein The three-dimensional anisotropic medium includes: a three-dimensional vertical symmetry axis transversely isotropic VTI elastic medium.

5. The method according to any one of claims 1 to 4, characterized in that The expression of the velocity decay damping term is: +1， in, represents the velocity decay damping term; express x The velocity attenuation component corresponding to the direction; express y The velocity attenuation component corresponding to the direction; express z The velocity attenuation component corresponding to the direction; The velocity attenuation components in each direction satisfy the following expressions: ， in, n Indicates the distance from the computation node to the boundary of the absorption layer; represents the speed reduction damping factor of the construction; represents the target wavefield weighting function; represents the vertical S-wave velocity; represents the spatial discrete grid step size; Indicates the dominant frequency of the source wavelet used.

6. The method according to any one of claims 1 to 4, characterized in that The target wavefield weighting function satisfies the following expression: ， in, Indicates the order, which is used to control the rate of change of the wave field at the inner and outer boundaries; Represents the total number of absorbing boundaries, which is a positive integer. N The larger the value, the thicker the absorption layer. represents the e-exponential function; It is the logarithm to the base of e, 2.

7. The method according to any one of claims 1 to 4, characterized in that The target anisotropic elastic wave equations satisfy the following expressions: ， in, Corresponding to along x 、 y 、 z Directional velocity wave field component; 、 、 are all normal stress wave field components, corresponding to x As the normal line corresponds to the plane along x The axial normal stress component, y As the normal line corresponds to the plane along y The axial normal stress component, z As the normal line corresponds to the plane along z Axial normal stress component; 、 、 are all shear stress wave field components, corresponding to y As normal correspondence xoz Along the plane z The axial shear stress component, x As normal correspondence yoz Along the plane z The axial shear stress component, x As normal correspondence yoz Along the plane y Axial stress component; E represents the damping attenuation term in the boundary conditions; Represents the velocity decay damping term introduced; Indicates the density of the medium; 、 、 、 、 It is the three-dimensional VTI medium elastic coefficient matrix, which depends on different media.

8. A three-dimensional anisotropic medium seismic wave field simulation device, characterized in that: include: A wave equation construction module is used to introduce a velocity attenuation damping term into an initial elastic wave equation system used to describe seismic wave propagation in a three-dimensional anisotropic medium, thereby obtaining a target anisotropic elastic wave equation system; wherein the initial elastic wave equation system is an elastic seismic wave equation based on an EAL boundary condition; and the velocity attenuation damping term attenuates seismic waves in the boundary region based on both time and space factors; An expression construction module is used to construct an expression for the velocity attenuation damping term based on a target wavefield weighting function; the target wavefield weighting function simulates and controls the wavefield change rate at the inner and outer boundaries corresponding to the wavefield absorption boundary based on a Gaussian weighting coefficient, so as to produce a relatively smooth transition of the wavefield in the boundary region; A processing module is used to perform numerical simulation of the seismic wave propagation process in a three-dimensional anisotropic medium based on the target anisotropic elastic wave equation group and the expression of the velocity attenuation damping term.

9. An electronic device, characterized in that: The processor, the communication interface, the memory and the communication bus are connected to each other via the communication bus. Memory for storing computer programs; A processor, configured to implement the method according to any one of claims 1 to 7 when executing a program stored in a memory.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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