High-precision seismic elastic wave field forward modeling method, device and equipment and storage medium

Abstract

The embodiment of the invention provides a high-precision seismic elastic wave field forward modeling method, device and equipment and a storage medium, and the method comprises the steps: carrying out the discretization of a wave equation in an elastic medium through the combined application of an improved time high-order implicit staggered grid difference method, and obtaining two types of time-space domain frequency dispersion relationships related to a P wave and an S wave based on the plane wave arrangement and simplification; solving the two types of time-space domain dispersion relations of the P wave and the S wave by combining a least square method and a Taylor series expansion method to obtain high-order difference coefficients corresponding to the P wave and the S wave; based on a wave field separation technology, a P wave field component is calculated by using a high-order difference coefficient corresponding to a P wave, an S wave field component is calculated by using a high-order difference coefficient corresponding to an S wave, and the components are superposed to obtain a high-precision full-elastic wave field. According to the technical scheme, under the same parameter condition, better simulation precision can be generated, so that an effective wave field continuation scheme is provided for subsequent elastic wave migration imaging and waveform inversion.

Description

Technical Field

[0001] This application relates to the field of seismic forward modeling in geophysical exploration, specifically to high-precision seismic elastic wave field forward modeling methods, apparatus, equipment, and storage media. Background Technology

[0002] High-precision seismic wavefield extrapolation technology is the foundation and key to seismic migration imaging and waveform inversion. The core of seismic wavefield extrapolation is to use numerical algorithms to discretize and solve the wave equation. Among the many numerical solutions for seismic wavefields, the finite difference method is widely favored due to its simplicity, ease of implementation, and computational efficiency.

[0003] Improving the accuracy, stability, and flexibility of numerical discretization has been a long-term research goal of the finite difference method. Increasing the length of the finite difference operator can achieve higher-order simulation accuracy in the spatial domain (Dablain, 1986; Virieux, 1986; Dong et al., 2000; Pei et al., 2004; Du et al., 2010; Liu et al., 2014; Yin et al., 2015), but its simulation accuracy in the time domain remains second-order. The idea of ​​replacing higher-order time derivatives with combinations of spatial derivatives can effectively improve time accuracy (Dablain, 1986; Chen, 2011), but this scheme belongs to the spatial domain and its accuracy still needs further improvement. Liu and Sen (2009) developed a spatiotemporal finite difference method. The difference coefficients calculated by this method depend on the wave field propagation parameters, effectively improving the time simulation accuracy while ensuring spatial simulation accuracy. Furthermore, Liu and Sen (2013) developed a spatiotemporal finite difference scheme based on the diamond difference method. This scheme introduces paraxial nodes to achieve high-order temporal and spatial simulation accuracy simultaneously, building upon the traditional cross-difference method. Based on this idea, by introducing additional grid nodes to the traditional finite difference method to jointly approximate different partial derivatives in the wave equation, and using Taylor expansion or optimization algorithms to solve the corresponding spatiotemporal dispersion relations, the new combined difference method can achieve high-order spatial and temporal simulation accuracy (Tan and Huang, 2014; Wang et al., 2016; Zhang et al., 2016; Chen et al., 2017; Ren et al., 2017).

[0004] However, existing high-order time-difference methods mainly employ explicit finite difference methods to discretize the partial derivatives in the wave equation. Compared to explicit finite differences, implicit finite differences can achieve higher simulation accuracy when the operator length is consistent. Therefore, in order to further improve the temporal and spatial accuracy of finite difference methods in solving wave equations, it is necessary to develop high-order time-implicit finite difference methods for wave equations in elastic media. This is also of significant research importance for elastic wave reverse-time migration and waveform inversion. Summary of the Invention

[0005] In view of this, in order to improve the accuracy of seismic wavefield forward modeling numerical simulation, this application provides a high-precision seismic elastic wavefield forward modeling method, apparatus, equipment and storage medium based on the improved implicit scheme time high-order difference method. This enables elastic wave numerical simulation to obtain higher temporal and spatial accuracy at the same time, generate more accurate seismic wavefield response, and thus provide a more effective seismic wavefield extrapolation tool for seismic wavefield migration imaging and full waveform inversion.

[0006] In a first aspect, embodiments of this application provide a high-precision forward modeling method for seismic elastic wave fields, including:

[0007] An improved time-order implicit staggered grid difference method is used to discretize the wave equation in elastic media, and two types of spatiotemporal dispersion relations for P-waves and S-waves are obtained by simplification based on plane waves.

[0008] By combining the least squares method and the Taylor series expansion method, two types of spatiotemporal dispersion relations of P-waves and S-waves are solved, and the higher-order difference coefficients corresponding to P-waves and S-waves are obtained.

[0009] Based on wave field separation technology, the P-wave wave field component is calculated using the higher-order difference coefficients corresponding to the P-wave, and the S-wave wave field component is calculated using the higher-order difference coefficients corresponding to the S-wave. The components are then superimposed to obtain a high-precision fully elastic wave field.

[0010] In one possible implementation, the wave equation in the elastic medium is as follows:

[0011]

[0012] Among them, v x and v z For the velocity component, τ xx τ zz and τ xz Let ρ be the stress component and ρ be the density. Let v be Lamé constant. p and v s Let be the longitudinal wave velocity and the transverse wave velocity, respectively; t be the time term; x be the horizontal coordinate in space; and z be the vertical coordinate in space.

[0013] In one possible implementation, an improved time-order implicit staggered grid difference method is jointly applied to discretize the wave equation in the elastic medium, resulting in the following discretized form of the wave equation in the elastic medium:

[0014]

[0015] In the above formula, Δt is the time sampling interval; In the table, the subscripts i and j are the grid indices in the spatial x and z directions, and the superscript o is the time grid index; f1, f3, g1, g3, p1, q1, w1, w3 are implicit scheme finite difference solutions; f2, f4, g2, g4, p2, q2, w2, w4 are explicit scheme finite difference solutions, and their specific forms are as follows:

[0016]

[0017] Where h is the spatial grid step size; d m d m,n To improve the higher-order difference coefficients involved in the discrete scheme; M is half the length of the spatial difference operator, N is half the length of the temporal difference operator, m is the grid index of the spatial difference operator M, n is the grid index of the temporal difference operator N; b is the difference coefficient in the implicit scheme; and has

[0018]

[0019] Where X is an arbitrary wave field component; Let be the wave field value at any time, where the subscripts i and j are the grid indices in the spatial x and z directions, and the superscript o is the time grid index; Find the sign of the second-order partial derivative along the x-direction.

[0020] In one possible implementation, the two types of spatiotemporal dispersion relations concerning P-waves and S-waves are as follows:

[0021]

[0022] in,

[0023]

[0024]

[0025] ω is the angular frequency; Δt is the time sampling interval; r p =v p Δt / h is the Courand number of the P-wave, v p r is the longitudinal wave velocity, h is the spatial grid step size; s =v s Δt / h is the S-wave Courland number, v s d represents the transverse wave velocity. m d m,n To improve the higher-order difference coefficients involved in the discrete scheme; M is half the length of the spatial difference operator, N is half the length of the temporal difference operator, m is the index of the spatial difference operator M, and n is the index of the temporal difference operator N; k x is the wavenumber in the x-direction; b is the difference coefficient in the implicit scheme; k zLet be the wave number in the z-direction.

[0026] In one possible implementation, the formulas for calculating the higher-order difference coefficients corresponding to the P-wave and S-wave are as follows:

[0027]

[0028] By solving equations (34)-(37), the corresponding P-wave differential coefficients in the improved time-high-order implicit staggered grid differential method can be obtained; by solving equations (34)-(38), the corresponding S-wave differential coefficients in the improved time-high-order implicit staggered grid differential method can be obtained; where ε, δ, f ε,δ f δ,ε w ε+δ , γ, w γ , w γ-ζ+1 All of these are intermediate variables.

[0029] In one possible implementation, the P-wave field component is:

[0030]

[0031] in, For the velocity components associated with the P-wave, The stress component associated with the P-wave, ρ is the density, and v is the stress component associated with the P-wave. p Let v be the longitudinal wave velocity. x and v z Let t be the velocity component, t be the time term, x be the horizontal coordinate in space, and z be the vertical coordinate in space.

[0032] In one possible implementation, the S-wave field components are:

[0033]

[0034] in, For the velocity components associated with the S-wave, The stress component is associated with the S-wave, ρ is the density, and v is the stress component associated with the S-wave. s v is the transverse wave velocity. x and v z Let t be the velocity component, t be the time term, x be the horizontal coordinate in space, and z be the vertical coordinate in space.

[0035] Secondly, embodiments of this application provide a high-precision seismic elastic wavefield forward modeling apparatus, including:

[0036] Two types of spatiotemporal dispersion relation construction modules are used to jointly apply the improved temporal high-order implicit staggered grid difference method to discretize the wave equation in the elastic medium, and obtain two types of spatiotemporal dispersion relations for P-wave and S-wave based on plane wave simplification.

[0037] The higher-order difference coefficient acquisition module is used to solve the spatiotemporal dispersion relation by combining the least squares method and the Taylor series expansion method to obtain the higher-order difference coefficients corresponding to the P-wave and S-wave.

[0038] The high-precision fully elastic wavefield acquisition module is used to calculate the P-wave wavefield component based on wavefield separation technology, using the higher-order difference coefficients corresponding to the P-wave and the higher-order difference coefficients corresponding to the S-wave to calculate the S-wave wavefield component. The high-precision fully elastic wavefield can be obtained by superimposing the components.

[0039] Thirdly, embodiments of this application provide an electronic device, including:

[0040] processor;

[0041] Memory;

[0042] And a computer program, wherein the computer program is stored in the memory, the computer program including instructions that, when executed by the processor, cause the electronic device to perform the method described in any one of the first aspects.

[0043] Fourthly, embodiments of this application provide a computer-readable storage medium including a stored program, wherein, when the program is executed, it controls the device where the computer-readable storage medium is located to perform the method described in any one of the first aspects.

[0044] In this embodiment, the partial derivatives in the wave equation of the elastic medium are first approximated by combining implicit finite difference and rhombic finite difference methods. Then, two types of spatiotemporal dispersion relations for P-waves and S-waves are derived. The higher-order difference coefficients involved in the improved temporal higher-order implicit staggered grid finite difference method are solved with high precision using the least squares method and Taylor expansion method. Finally, based on wavefield separation technology, the calculated P-wave wavefield components are calculated using the calculated P-wave spatiotemporal difference coefficients, and the S-wave wavefield components are calculated using the S-wave spatiotemporal difference coefficients. Summing the component wavefields yields a high-precision elastic wavefield. This improved seismic wavefield forward modeling method can simultaneously achieve higher temporal and spatial simulation accuracy in elastic wavefield simulation, obtaining a more accurate elastic wavefield response. This provides an accurate wavefield extrapolation scheme for subsequent elastic wavefield migration imaging and full waveform inversion. Attached Figure Description

[0045] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 A schematic flowchart of the high-precision seismic elastic wave field forward modeling method provided in the embodiments of this application;

[0047] Figure 2 The figures show a comparison of the P-wave dispersion curves of the staggered grid finite difference method calculated at different angles using the improved temporal high-order implicit staggered grid finite difference method and the traditional implicit finite difference method provided in the embodiments of this application. Figure (a) shows the traditional Taylor expansion implicit staggered grid finite difference scheme with M=4; Figure (b) shows the improved temporal high-order implicit staggered grid finite difference method with M=4 and N=2; Figure (c) shows the improved temporal high-order implicit staggered grid finite difference method with M=4, N=3, and rp=0.45.

[0048] Figure 3 The figures show a comparison of the S-wave dispersion curves of the staggered grid finite difference method calculated at different angles using the improved temporal high-order implicit staggered grid finite difference method and the traditional implicit finite difference method provided in the embodiments of this application. Figure (a) shows the traditional Taylor expansion implicit staggered grid finite difference scheme with M=4; Figure (b) shows the improved temporal high-order implicit staggered grid finite difference method with M=4 and N=2; Figure (c) shows the improved temporal high-order implicit staggered grid finite difference method with M=4, N=3, and rs=0.225.

[0049] Figure 4 A comparison of wave field snapshots calculated in a uniform elastic model using the improved temporal high-order implicit staggered grid difference method and the traditional implicit difference method provided in the embodiments of this application; wherein, Figure (a) is the traditional implicit staggered grid difference scheme, and Figure (b) is the improved temporal high-order implicit staggered grid difference method, N=2;

[0050] Figure 5 The non-standard Marmousi velocity model provided for the embodiments of this application;

[0051] Figure 6 Comparison of wavefield snapshots calculated in a non-standard Marmousi velocity model using the improved temporal high-order implicit staggered grid difference method and the traditional implicit difference method provided in the embodiments of this application; wherein, Figure (a) is the traditional implicit staggered grid difference scheme, and Figure (b) is the improved temporal high-order implicit staggered grid difference method, N=2;

[0052] Figure 7 A structural block diagram of the high-precision seismic elastic wave field forward modeling device provided in the embodiments of this application;

[0053] Figure 8 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0054] To better understand the technical solution of this application, the embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0055] It should be understood that the described embodiments are merely some, not all, of the embodiments in this application. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application.

[0056] The terminology used in the embodiments of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of this application. The singular forms “a,” “the,” and “the” used in the embodiments of this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0057] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0058] See Figure 1 This is a flowchart illustrating the high-precision seismic elastic wave field forward modeling method provided in this application embodiment. Figure 1 As shown, it mainly includes the following steps.

[0059] Step S1: The improved temporal high-order implicit staggered grid difference method is jointly applied to discretize the wave equation in the elastic medium. Based on the plane wave, the spatiotemporal dispersion relations for P-waves and S-waves are simplified to obtain two types. Specifically, as follows:

[0060] Step S101: Construct the wave equation in the elastic medium. The wave equation in the elastic medium is as follows:

[0061]

[0062] Among them, v x and v z For the velocity component, τ xx τ zz and τ xz Let ρ be the stress component and ρ be the density. Let v be Lamé constant. p and v s Let be the longitudinal wave velocity and the transverse wave velocity, respectively; t be the time term; x be the horizontal coordinate in space; and z be the vertical coordinate in space.

[0063] Step S102: Discretize the wave equation in the elastic medium using the improved time-order implicit staggered grid difference method.

[0064] In existing technologies, the traditional time-second and spatial high-order staggered grid finite difference method can be used to numerically solve equations (1)-(5). The corresponding spatial simulation accuracy can reach any even order, but the time accuracy is only second order. In order to further improve the numerical accuracy of the traditional staggered grid finite difference method in solving the wave equation in elastic media, this embodiment provides an improved time-high-order implicit staggered grid finite difference method, which can achieve higher simulation accuracy in both the time and spatial domains. The wave equation in elastic media is discretized based on the improved time-high-order implicit staggered grid finite difference method. Then the discretized form of equations (1)-(5) is:

[0065]

[0066]

[0067] In the above formula, Δt is the time sampling interval; In the table, the subscripts i and j are the grid indices in the spatial x and z directions, and the superscript o is the time grid index; f1, f3, g1, g3, p1, q1, w1, w3 are implicit scheme finite difference solutions; f2, f4, g2, g4, p2, q2, w2, w4 are explicit scheme finite difference solutions, and their specific forms are as follows:

[0068]

[0069]

[0070] Where h is the spatial grid step size; d m d m,n To improve the higher-order difference coefficients involved in the discrete scheme; M is half the length of the spatial difference operator, N is half the length of the temporal difference operator, m is the grid index of the spatial difference operator M, n is the grid index of the temporal difference operator N; b is the difference coefficient in the implicit scheme; and has

[0071]

[0072] Where X is an arbitrary wave field component; Let be the wave field value at any time, where the subscripts i and j are the grid indices in the spatial x and z directions, and the superscript o is the time grid index; Find the sign of the second-order partial derivative along the x-direction.

[0073] Step 103: Based on the plane wave, simplify and obtain two types of spatiotemporal dispersion relations for P-waves and S-waves.

[0074] Substituting the improved implicit staggered grid discretization scheme into equations (1)-(5), and simplifying based on plane wave theory, we can derive two types of spatiotemporal dispersion relations for P-waves and S-waves, as shown below:

[0075]

[0076] in,

[0077]

[0078]

[0079] ω is the angular frequency; Δt is the time sampling interval; r p =v p Δt / h is the Courand number of the P-wave, v p r is the longitudinal wave velocity, h is the spatial grid step size; s =v s Δt / h is the S-wave Courland number, v s d represents the transverse wave velocity. m d m,n To improve the higher-order difference coefficients involved in the discrete scheme; M is half the length of the spatial difference operator, N is half the length of the temporal difference operator, m is the index of the spatial difference operator M, and n is the index of the temporal difference operator N; k x is the wavenumber in the x-direction; b is the difference coefficient in the implicit scheme; k z Let be the wave number in the z-direction.

[0080] Step S2: Solve the spatiotemporal dispersion relation by combining the least squares method and the Taylor series expansion method to obtain the higher-order difference coefficients corresponding to the P-wave and S-wave.

[0081] Formulas (28) and (29) relative to the difference coefficient d m d m,n Since b is nonlinear, directly solving for the difference coefficients is difficult. To address this issue, this application employs a combination of the least squares method and the Taylor series expansion method to solve for the difference coefficients. In formulas (28) and (29), let k... z =0 (or k can be set) x Simplify the expression (=0) to obtain the simplified formula:

[0082]

[0083] The above two formulas are still nonlinear with respect to the difference coefficients; here, we assume d... m,n Since this is known, the two formulas above can be further simplified as follows:

[0084]

[0085] in,

[0086]

[0087] Observing the two formulas above, we can see that it is relative to the difference coefficient d. m Since b and are linear, the optimized difference coefficients can be obtained by minimizing the errors at both ends of the above two formulas. Based on this, the following objective function needs to be constructed first:

[0088]

[0089] in,

[0090]

[0091] c m (m∈[1,2,…,M+1])=[d1,d2,…,d M [b] T

[0092] Where β is k r The upper limit of h.

[0093] Solving the above objective function equation using the least squares method yields:

[0094]

[0095] The difference coefficient d in the simplified formula m,n The solution can be obtained using Taylor series expansion. The core idea is to use Taylor series to expand the trigonometric functions in the dispersion relation of P-wave and S-wave (28)-(29), and obtain the difference coefficients by comparing the polynomial coefficients. The difference coefficients d m,n The solution can be found using coefficient equations:

[0096]

[0097]

[0098] Where ε, δ, f ε,δ f δ,ε w ε+δ , γ, w γ w These are all intermediate variables introduced for the convenience of mathematical calculations and have no clear physical meaning.

[0099] By solving equations (34)-(37), the corresponding P-wave differential coefficients in the improved time-high-order implicit staggered grid differential method can be obtained; by solving equations (34)-(38), the corresponding S-wave differential coefficients in the improved time-high-order implicit staggered grid differential method can be obtained.

[0100] Step S3: Based on wave field separation technology, calculate the P-wave wave field component using the higher-order difference coefficients corresponding to the P-wave, calculate the S-wave wave field component using the higher-order difference coefficients corresponding to the S-wave, and superimpose the components to obtain a high-precision fully elastic wave field.

[0101] Since two sets of difference coefficients for P-waves and S-waves were obtained, this application embodiment combined wavefield separation technology to solve the problem in order to obtain more accurate elastic wave simulation results. Based on the vector separation algorithm, the wavefield sum in equations (1)-(5) can be expressed as the sum of the wavefields of the P-wave component and the S-wave component, as follows:

[0102]

[0103] in, These represent the component wave fields of P-wave and S-wave along different directions, respectively.

[0104] The P-wave field is represented as:

[0105]

[0106] in, For the velocity components associated with the P-wave, The stress component associated with the P-wave, ρ is the density, and v is the stress component associated with the P-wave. p Let v be the longitudinal wave velocity. x and v z Let t be the velocity component, t be the time term, x be the horizontal coordinate in space, and z be the vertical coordinate in space.

[0107] The S-wave field is represented as:

[0108]

[0109] in, For the velocity components associated with the S-wave, The stress component is associated with the S-wave, ρ is the density, and v is the stress component associated with the S-wave. s v is the transverse wave velocity. x and v z Let t be the velocity component, t be the time term, x be the horizontal coordinate in space, and z be the vertical coordinate in space.

[0110] To verify the accuracy of the improved time-order implicit staggered grid difference method proposed in this application, phase velocity analysis is first used to compare the traditional scheme and the improved method. Based on formulas (28) and (29), the following formula is defined to measure the phase velocity error of P-wave and S-wave:

[0111]

[0112] Among them, D x D z G xz and G zx The values ​​are given in equations (30)-(33). In these two equations, the closer the sum of the parameters is to 1, the higher the accuracy; the further the values ​​deviate from 1, the lower the accuracy. See also Figure 2 Figure 1 shows a comparison of the P-wave dispersion curves of the staggered grid finite difference method at different angles calculated by the improved temporal high-order implicit staggered grid finite difference method and the traditional implicit finite difference method provided in the embodiments of this application. Figure 2(a) shows the traditional Taylor expansion implicit staggered grid finite difference scheme with M=4; Figure 3(b) shows the improved temporal high-order implicit staggered grid finite difference method with M=4 and N=2; Figure 4(c) shows the improved temporal high-order implicit staggered grid finite difference method with M=4, N=3, and rp=0.45. See also... Figure 3 Figure 1 shows a comparison of the S-wave dispersion curves of the staggered grid finite difference method calculated at different angles using the improved temporal high-order implicit staggered grid finite difference method and the traditional implicit finite difference method provided in the embodiments of this application. Figure 2 shows the traditional Taylor expansion implicit staggered grid finite difference scheme with M=4; Figure 3 shows the improved temporal high-order implicit staggered grid finite difference method with M=4 and N=2; Figure 4 shows the improved temporal high-order implicit staggered grid finite difference method with M=4, N=3, and rs=0.225. Figure 2 and Figure 3 As shown, the dispersion curve calculated by the traditional implicit difference method deviates significantly from the reference value, indicating its low accuracy. In contrast, the dispersion curve calculated by the improved high-order implicit difference scheme is closer to the reference line, indicating its higher accuracy, and the accuracy increases continuously with the increase of parameter N.

[0113] To compare the computational accuracy of the traditional implicit staggered grid difference method and the improved staggered grid difference method, this application further employs a uniform elastic model to test the different methods in its embodiments. The model parameters are v. p =3000m / s,v s =1800m / s, ρ=2000kg / m 3 The model dimensions are 4000m × 4000m, with a grid spacing of 10m × 10m. The time step is 1.5ms, and the difference operator length is M = 4. The seismic source uses a Ricker wavelet with a dominant frequency of 30Hz. See [link to seismic source]. Figure 4 Figure (a) shows a comparison of wavefield snapshots calculated in a uniform elastic model using the improved temporal high-order implicit staggered grid difference method and the traditional implicit difference method, as provided in the embodiments of this application. Figure (b) shows the traditional implicit staggered grid difference scheme, and N=2. Figure 4 As shown, simulations obtained based on traditional implicit difference methods exhibit strong numerical dispersion, such as... Figure 4 As indicated by the arrows in Figure (a). In contrast, the improved temporal high-order implicit staggered grid difference method can significantly improve simulation accuracy and obtain high-precision simulation results, such as... Figure 4 As shown by the arrow in Figure (b).

[0114] To further verify the advantages of the above algorithm in improving simulation accuracy, Figure 5 The test was conducted using the non-standard Marmousi velocity model shown as an example. Figure 5 The model shown has dimensions of 5000m × 3530m. A Ricker wavelet with a dominant frequency of 24Hz is used to generate the P-wave source. For the traditional implicit staggered grid finite difference method, considering the stability of wave field propagation, a time step of 1ms is used. For the improved time-order implicit staggered grid finite difference method, due to its higher accuracy and stability, a time step of 1.2ms is used. See [link to relevant documentation] Figure 6 Figure (a) shows a comparison of wavefield snapshots calculated by the improved temporal high-order implicit staggered grid difference method and the traditional implicit difference method in a non-standard Marmousi velocity model, as provided in the embodiments of this application. Figure (b) shows the traditional implicit staggered grid difference scheme, and N=2. Figure 6 As shown, the traditional implicit difference method exhibits strong numerical dispersion in wavefield snapshots calculated using small time steps, as indicated by the arrows in the enlarged local figure. In contrast, the improved implicit difference method demonstrates higher accuracy and less numerical dispersion in simulations using larger time steps, thus verifying the accuracy advantage of the improved scheme in seismic wavefield numerical simulation.

[0115] Corresponding to the above embodiments, this application also provides a high-precision seismic elastic wave field forward modeling device.

[0116] See Figure 7 This is a structural block diagram of the high-precision seismic elastic wave field forward modeling device provided in the embodiments of this application. Figure 7 As shown, it mainly includes the following modules.

[0117] The two-class spatiotemporal dispersion relation construction module 701 is used to jointly apply the improved time-order implicit staggered grid difference method to discretize the wave equation in the elastic medium, and obtain two-class spatiotemporal dispersion relations for P-wave and S-wave based on plane wave simplification.

[0118] The higher-order difference coefficient acquisition module 702 is used to solve the spatiotemporal dispersion relation by combining the least squares method and the Taylor series expansion method to obtain the higher-order difference coefficients corresponding to the P-wave and S-wave.

[0119] The high-precision fully elastic wavefield acquisition module 703 is used to calculate the P-wave wavefield component based on wavefield separation technology, using the higher-order difference coefficients corresponding to the P-wave and the higher-order difference coefficients corresponding to the S-wave to calculate the S-wave wavefield component. The high-precision fully elastic wavefield can be obtained by superimposing the components.

[0120] It should be noted that the specific content involved in the embodiments of this application can be found in the description of the above method embodiments, and will not be repeated here for the sake of brevity.

[0121] Corresponding to the above embodiments, this application also provides an electronic device.

[0122] See Figure 8 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Figure 8 As shown, the electronic device 800 may include a processor 801, a memory 802, and a communication unit 803. These components communicate via one or more buses. Those skilled in the art will understand that the electronic device structure shown in the figure does not constitute a limitation on the embodiments of this application. It may be a bus topology or a star topology, and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0123] The communication unit 803 is used to establish a communication channel, thereby enabling the electronic device to communicate with other devices.

[0124] The processor 801 serves as the control center of the electronic device, connecting various parts of the device via various interfaces and lines. It executes software programs and / or modules stored in the memory 802, and calls data stored in the memory to perform various functions and / or process data. The processor can be composed of integrated circuits (ICs), such as a single packaged IC or multiple packaged ICs with the same or different functions connected together. For example, the processor 801 may consist only of a central processing unit (CPU). In this embodiment, the CPU may have a single processing core or include multiple processing cores.

[0125] Memory 802 is used to store the execution instructions of processor 801. Memory 802 can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk or optical disk.

[0126] When the execution instructions in memory 802 are executed by processor 801, the electronic device 800 is able to perform some or all of the steps in the above method embodiments.

[0127] Corresponding to the above embodiments, this application also provides a computer-readable storage medium, wherein the computer-readable storage medium may store a program, wherein when the program runs, it can control the device where the computer-readable storage medium is located to execute some or all of the steps in the above method embodiments. Specifically, the computer-readable storage medium may be a magnetic disk, an optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0128] Corresponding to the above embodiments, this application also provides a computer program product containing executable instructions that, when executed on a computer, cause the computer to perform some or all of the steps in the above method embodiments.

[0129] In this application embodiment, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent the existence of A alone, the simultaneous existence of A and B, or the existence of B alone. A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one of the following" and similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b, and c can represent: a, b, c, ab, ac, bc, or abc, where a, b, and c can be single or multiple.

[0130] Those skilled in the art will recognize that the units and algorithm steps described in the embodiments disclosed herein can be implemented using electronic hardware, computer software, or a combination of electronic hardware and software. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0131] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0132] In the several embodiments provided in this application, any function, if implemented as a software functional unit and sold or used as an independent product, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0133] The above description is merely a specific embodiment of this application. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the protection scope of this application. The protection scope of this application should be determined by the protection scope of the claims.

Claims

1. A high-precision forward modeling method for seismic elastic wave fields, characterized in that, include: An improved time-order implicit staggered grid difference method is used to discretize the wave equation in elastic media, and two types of spatiotemporal dispersion relations for P-waves and S-waves are obtained by simplification based on plane waves. By combining the least squares method and the Taylor series expansion method, two types of spatiotemporal dispersion relations of P-waves and S-waves are solved to obtain the higher-order difference coefficients corresponding to P-waves and S-waves. Based on wave field separation technology, the P-wave wave field component is calculated using the higher-order difference coefficients corresponding to the P-wave, and the S-wave wave field component is calculated using the higher-order difference coefficients corresponding to the S-wave. The components are then superimposed to obtain a high-precision fully elastic wave field.

2. The method according to claim 1, characterized in that, The wave equation in the elastic medium is as follows: Among them, v x and v z For the velocity component, τ xx τ zz and τ xz Let ρ be the stress component and ρ be the density. and Let v be Lamé constant. p and v s Let be the longitudinal wave velocity and the transverse wave velocity, respectively; t be the time term; x be the horizontal coordinate in space; and z be the vertical coordinate in space.

3. The method according to claim 2, characterized in that, An improved time-order implicit staggered grid finite difference method is used to discretize the wave equation in the elastic medium, and the discretized form of the wave equation in the elastic medium is obtained as follows: In the above formula, Δt is the time sampling interval; In the table, the subscripts i and j are the grid indices in the spatial x and z directions, and the superscript o is the time grid index; f1, f3, g1, g3, p1, q1, w1, w3 are implicit scheme finite difference solutions; f2, f4, g2, g4, p2, q2, w2, w4 are explicit scheme finite difference solutions, and their specific forms are as follows: Where h is the spatial grid step size; d m d m,n To improve the higher-order difference coefficients involved in the discrete scheme; M is half the length of the spatial difference operator, N is half the length of the temporal difference operator, m is the grid index of the spatial difference operator M, n is the grid index of the temporal difference operator N; b is the difference coefficient in the implicit scheme; and has Where X is an arbitrary wave field component; Let be the wave field value at any time, where the subscripts i and j are the grid indices in the spatial x and z directions, and the superscript o is the time grid index; Find the sign of the second-order partial derivative along the x-direction.

4. The method according to claim 3, characterized in that, The two types of spatiotemporal dispersion relationships concerning P-waves and S-waves are as follows: in, ω is the angular frequency; Δt is the time sampling interval; r p =v p Δt / h is the Courand number of the P-wave, v p r is the longitudinal wave velocity, h is the spatial grid step size; s =v s Δt / h is the S-wave Courland number, v s d represents the transverse wave velocity. m d m,n To improve the higher-order difference coefficients involved in the discrete scheme; M is half the length of the spatial difference operator, N is half the length of the temporal difference operator, m is the index of the spatial difference operator M, and n is the index of the temporal difference operator N; k x is the wavenumber in the x-direction; b is the difference coefficient in the implicit scheme; k z Let be the wave number in the z-direction.

5. The method according to claim 1, characterized in that, The formulas for calculating the higher-order difference coefficients corresponding to P-waves and S-waves are as follows: By solving equations (34)-(37), the corresponding P-wave differential coefficients in the improved time-high-order implicit staggered grid differential method can be obtained; by solving equations (34)-(38), the corresponding S-wave differential coefficients in the improved time-high-order implicit staggered grid differential method can be obtained; where ε, δ, f ε,δ f δ,ε w ε+δ , γ, w γ , All are intermediate variables.

6. The method according to claim 1, characterized in that, The P-wave field components are: in, For the velocity components associated with the P-wave, The stress component associated with the P-wave, ρ is the density, and v is the stress component associated with the P-wave. p Let v be the longitudinal wave velocity. x and v z Let t be the velocity component, t be the time term, x be the horizontal coordinate in space, and z be the vertical coordinate in space.

7. The method according to claim 1, characterized in that, The S-wave field components are: in, For the velocity components associated with the S-wave, The stress component is associated with the S-wave, ρ is the density, and v is the stress component associated with the S-wave. s v is the transverse wave velocity. x and v z Let t be the velocity component, t be the time term, x be the horizontal coordinate in space, and z be the vertical coordinate in space.

8. A high-precision seismic elastic wave field forward modeling device, characterized in that, include: Two types of spatiotemporal dispersion relation construction modules are used to jointly apply the improved temporal high-order implicit staggered grid difference method to discretize the wave equation in the elastic medium, and obtain two types of spatiotemporal dispersion relations for P-wave and S-wave based on plane wave simplification. The higher-order difference coefficient acquisition module is used to solve the spatiotemporal dispersion relation by combining the least squares method and the Taylor series expansion method to obtain the higher-order difference coefficients corresponding to the P-wave and S-wave. The high-precision fully elastic wavefield acquisition module is used to calculate the P-wave wavefield component based on wavefield separation technology, using the higher-order difference coefficients corresponding to the P-wave and the higher-order difference coefficients corresponding to the S-wave to calculate the S-wave wavefield component. The high-precision fully elastic wavefield can be obtained by superimposing the components.

9. An electronic device, characterized in that, include: processor; Memory; And a computer program, wherein the computer program is stored in the memory, the computer program including instructions that, when executed by the processor, cause the electronic device to perform the method of any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored program, wherein, when the program is executed, it controls the device on which the computer-readable storage medium is located to perform the method according to any one of claims 1 to 7.

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