Method and device for improving simulation precision of free surface wave field

Abstract

The invention relates to the field of seismic exploration data processing methods, and particularly discloses a method and a device for improving the simulation precision of a free surface wave field, and the method comprises the steps: carrying out the spatial staggered discretization of a field component of a free surface, and obtaining a discrete field component; performing space-time discretization on the elastic wave equation of the wave field component to obtain a discrete elastic wave equation; adjusting a finite difference format of a staggered grid formed by spatial staggering to obtain a variable finite difference approximation; and performing simulation processing on the discrete field component based on the discrete elastic wave equation and the variable finite difference approximation expression. According to the method disclosed by the invention, the problem that no field component exists on a free surface serving as an upper interface of a model in an existing finite difference format is solved by carrying out space interlacing discretization on the field component of the free surface, carrying out space-time discretization on an elastic wave equation and adjusting the finite difference format of an interlaced grid formed by space interlacing; the processing precision and the result instability of the field component of the free surface are improved.

Description

Technical Field

[0001] The invention relates to the field of seismic exploration data processing methods, and in particular to a method and device for improving the simulation accuracy of free surface wave fields. Background Art

[0002] As the focus of oil and gas resource exploration gradually shifts to underground complex structural areas, the requirements for underground structural imaging quality are becoming increasingly higher. Boundary conditions include free surface boundary conditions, absorbing boundary conditions, and interface boundary conditions, which will affect the numerical simulation of seismic wave fields. Among them, the free surface boundary is the boundary condition that has the greatest impact on the wave field. The free surface is the interface between the medium and the air. During the processing process, problems such as insufficient processing accuracy or unstable calculation results are prone to occur, which affects the propagation results of the seismic wave field. Therefore, it is necessary to select a suitable method when processing. Although the horizontal free surface is relatively simple, there are also many problems in processing. At present, there are mainly the following methods for processing horizontal free surfaces: (1) Single-sided difference or low-order expansion method. The disadvantage of this method is that when the Poisson ratio of the medium is relatively large, the same-position grid difference format is unstable. The implicit difference grid method solves this problem well. (2) Vacuum method or zero velocity method: The numerical accuracy of the boundary condition of the vacuum method is first order, which is only suitable for the cleanliness difference format, otherwise it is unstable. (3) Characteristic variable method: The same-position grid method is the most commonly used method for solving the first-order velocity-stress equation for numerical simulation of seismic waves. However, the calculation of Rayleigh surface waves has a relatively low accuracy.

[0003] Seismic exploration is an important means of prospecting for mineral resources such as oil and gas. It infers underground structures, lithology and fluid content by processing and analyzing reflected wave information. The strata in the entire range from the surface to the bottom of the low-velocity zone include two important interfaces: the surface free surface, the strong reflection surface at the bottom of the low-velocity zone, and a low-velocity stratum, collectively referred to as the near-surface medium. The near-surface medium is not thick, but it has the properties of "free surface, low velocity, and high absorption", which distorts the received signal and seriously restricts the accuracy of seismic exploration. The free surface is the interface between the solid earth and the air. It is a special interface with zero stress. The free surface strongly affects the propagation process of seismic waves in the earth medium and the physical properties of the wave field. In the process of numerical simulation of seismic wave fields using the finite difference method, the difference grid area exceeds the free surface range, which brings difficulty to the processing. In addition, the free surface processing process is prone to problems such as insufficient processing accuracy or unstable calculation results, which affects the simulated seismic wave field propagation results.

[0004] With the further improvement of exploration in recent years, how to obtain more accurate underground velocity and seismic imaging quality has become a top priority for experts and scholars. For a long time, oil exploration has mainly used seismic reflection waves to search for oil and gas, and surface wave signals are treated as interference waves and removed by various means such as denoising and excision in the early stage of seismic data processing. In fact, about 2 / 3 of the energy excited by the source is recorded in the form of surface waves. This surface wave shows obvious characteristics of low speed, low frequency, strong amplitude and dispersion. If the surface wave is regarded as an effective signal and its characteristic of carrying a large amount of near-surface information is fully utilized, it will be more conducive to the study of underground medium characteristics.

[0005] Based on this technical background, the present invention studies a method and a device for improving the simulation accuracy of free surface wave fields. Summary of the invention

[0006] In view of the shortcomings of the prior art, the present invention provides a method and device for improving the accuracy of free surface wave field simulation. The method solves the problem that the free surface is used as the upper interface of the model and there is no field component on it in the existing finite difference format by spatially interlacing the field components of the free surface, time-space discretizing the elastic wave equation, and adjusting the finite difference format of the interlaced grid formed by the spatial interlacing, thereby improving the processing accuracy of the free surface field components and the instability of the results.

[0007] In order to achieve the above object, a first aspect of the present invention provides a method for improving the accuracy of free surface wave field simulation, comprising:

[0008] The field components of the free surface are spatially staggered to obtain discrete field components;

[0009] Performing time-space discretization on the elastic wave equation of the wave field component to obtain a discrete elastic wave equation;

[0010] Adjusting the finite difference format of the staggered grid formed by the spatial staggering to obtain a variable finite difference approximation;

[0011] The discrete field components are simulated based on the discrete elastic wave equation and the variable finite difference approximation.

[0012] A second aspect of the present invention provides a device for improving the simulation accuracy of a free surface wave field, comprising:

[0013] The spatial staggered discretization module discretizes the field components of the free surface by spatial staggered discretization to obtain discrete field components;

[0014] A space-time discretization module performs space-time discretization on the elastic wave equation of the wave field component to obtain a discrete elastic wave equation;

[0015] A variable difference approximation module adjusts the finite difference format of the staggered grid formed by the spatial staggering to obtain a variable finite difference approximation formula;

[0016] A simulation processing module performs simulation processing on the discrete field component based on the discrete elastic wave equation and the variable finite difference approximation.

[0017] A third aspect of the present invention provides an electronic device, the electronic device comprising:

[0018] A memory storing executable instructions;

[0019] A processor is used to execute the executable instructions in the memory to implement the method for improving the accuracy of free surface wave field simulation according to the first aspect.

[0020] A fourth aspect of the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the method for improving the accuracy of free surface wave field simulation as described in the first aspect.

[0021] The beneficial effects of the present invention include:

[0022] (1) The method for improving the accuracy of free surface wave field simulation proposed in the present invention solves the problem that the free surface is used as the upper interface of the model and there is no field component on it in the existing finite difference format by spatially interleaving the field components of the free surface, spatially and temporally discretizing the elastic wave equation, and adjusting the finite difference format of the interleaved grid formed by the spatial interleaving, thereby improving the processing accuracy of the field components of the free surface and the instability of the results.

[0023] (2) The method proposed in the present invention for improving the accuracy of free surface wave field simulation adjusts the finite difference format through the variable finite difference method, and replaces the derivatives of the field components on the free surface with the difference quotients of the corresponding physical quantities at the grid points below the free surface, thereby solving the problem that the free surface is the upper interface of the model and has no field components on it. The method is applied to the theoretical model to obtain better forward simulation results.

[0024] Other features and advantages of the present invention will be described in detail in the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The above and other objects, features and advantages of the present invention will become more apparent through a more detailed description of exemplary embodiments of the present invention with reference to the accompanying drawings.

[0026] Figure 1 The present invention is a flow chart of a method for improving the simulation accuracy of free surface wave fields.

[0027] Figure 2The present invention is a flowchart of a specific implementation of the method for improving the accuracy of free surface wave field simulation.

[0028] Figure 3 This is a schematic diagram of grid distribution of a staggered grid finite difference format in a specific implementation of the method for improving the free surface wave field simulation accuracy proposed by the present invention.

[0029] Figure 4 The present invention provides snapshots of x and z component wave fields of a two-dimensional isotropic medium model at different times in a specific implementation of the method for improving the simulation accuracy of free surface wave fields proposed by the present invention.

[0030] Figure 5 A horizontal layered medium model is provided in a specific implementation of the method for improving the simulation accuracy of free surface wave fields proposed by the present invention.

[0031] Figure 6 Snapshots of x and z component wave fields of a horizontal layered medium model at different times in a specific implementation of the method for improving the simulation accuracy of free surface wave fields proposed by the present invention. DETAILED DESCRIPTION

[0032] The preferred embodiments of the present invention will be described in more detail below. Although the preferred embodiments of the present invention are described below, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein.

[0033] The present invention provides a method for improving the simulation accuracy of free surface wave fields, such as Figure 1 As shown, including:

[0034] The field components of the free surface are spatially staggered to obtain discrete field components;

[0035] Discrete elastic wave equations are obtained by time-space discretization of elastic wave equations of wave field components;

[0036] The finite difference format of the staggered grid formed by the spatial staggering is adjusted to obtain a variable finite difference approximation;

[0037] The discrete field components are simulated based on the discrete elastic wave equation and the variable finite difference approximation.

[0038] In the present invention, by performing spatial staggered discretization on the field components of the free surface, performing space-time discretization on the elastic wave equation, and adjusting the finite difference format of the staggered grid formed by the spatial staggering, the problem of the free surface being used as the upper interface of the model and having no field components on it in the existing finite difference format is solved, and the processing accuracy of the field components of the free surface and the instability of the results are improved.

[0039] According to the present invention, the field components include velocity and stress;

[0040] The spatial staggered discretization of the wave field physical quantities of the free surface includes:

[0041] The velocity and stress are defined on two different grid systems with a difference of half a grid spacing.

[0042] The velocity is defined on the full grid points, and the stress is defined on the half grid points.

[0043] According to the present invention, the elastic wave equation is a two-dimensional isotropic medium elastic wave equation, and its formula is:

[0044]

[0045] Among them, x is the horizontal direction, z is the vertical direction, ρ is the density of the elastic medium, λ and μ are the Lame coefficients, v is the velocity, and τ is the stress;

[0046] When z = 0, The elastic wave equation is:

[0047]

[0048] According to the present invention, the formula of the discrete elastic wave equation is:

[0049]

[0050] in, v x 、v z , σ xx , σ zz , τ xz The discrete value of , k is the discrete grid point position in time, i and j are the discrete grid point positions in the x and z directions of space respectively.

[0051] Preferably, adjusting the finite difference format of the staggered grid formed by the spatial staggering to obtain a variable finite difference approximation includes:

[0052] Based on the staggered grid finite difference scheme, the derivatives of the discrete field components are replaced by the difference quotients of the corresponding physical quantities at the grid points below the free surface, and a variable finite difference approximation is obtained.

[0053] According to the present invention, the variable finite difference approximation is:

[0054] 1°:

[0055] 2°:

[0056] 3°:

[0057] 4°:

[0058] Where f is velocity or stress, j is 0 is the vertical position of the current calculation grid point, and Δh is the vertical interval of the grid points.

[0059] Preferably, the free surface range is 0≤Z≤Δh;

[0060] The process of simulating the discrete field components is as follows:

[0061] Find σ zz (0) = 0, that is

[0062] Using the elastic wave equation when z = 0 and the formula of the discrete elastic wave equation, we can get σ xx (0), its discrete form expression is:

[0063]

[0064] Using the formula of the discrete elastic wave equation when z = 0 and the 2° formula of the variable finite difference approximation, we can obtain

[0065] Using the formula of the discrete elastic wave equation and the 3° formula of the variable finite difference approximation, we can calculate σ xx (Δh) and σ zz (Δh);

[0066] Using the formula of the discrete elastic wave equation when z = 0 and the 1° formula of the variable finite difference approximation, we can obtain v x (0);

[0067] Using the formula of the discrete elastic wave equation when z = 0 and the 2° formula of the variable finite difference approximation, we can obtain

[0068] Using the formula of the discrete elastic wave equation when z = 0 and the 4° formula of the variable finite difference approximation, we can calculate v x (Δh).

[0069] In the present invention, the finite difference format is adjusted by the variable finite difference method, and the derivatives of the field components on the free surface are replaced by the difference quotients of the corresponding physical quantities on the grid points below the free surface, which solves the problem that the free surface is used as the upper interface of the model and there are no field components on it. The method is applied to the theoretical model to obtain better forward simulation effects.

[0070] The present invention will be described in more detail below by way of examples.

[0071] Embodiment 1:

[0072] like Figure 2As shown, this embodiment provides a method for improving the simulation accuracy of free surface wave fields, which specifically includes the following steps:

[0073] 1) Time domain elastic wave finite difference forward modeling:

[0074] Based on the elastic medium theory, the first-order velocity-stress equations for elastic waves in 2D isotropic media can be obtained from the Navier equations and the generalized Hooke's law:

[0075]

[0076] In the formula, v a (a=x,z) corresponds to the velocity component in the a direction, x represents the horizontal direction, z represents the vertical direction, ρ is the density of the elastic medium, σ aa , τ ab (a, b = x, z) represents stress in different directions, λ and μ are called Lame coefficients;

[0077] The underground medium is continuous, and its physical quantities such as velocity, stress, density, etc. are continuous in space and time, and the solution of the wave equation is also continuous; however, it is difficult for computers to simulate the continuous seismic wave propagation process, so it is necessary to discretize the physical quantities to simulate the seismic wave field propagation; the most commonly used is the alternating grid finite difference technique, which defines the velocity and stress on two different grid systems with a difference of half a grid spacing, such as Figure 3 As shown, each field component is then discretely solved;

[0078] Figure 3 The middle circle represents stress σ xx , σ zz The circle with a cross inside represents τ xz The position, square represents v x The location, triangle represents v z The staggered grid finite difference method uses two sets of grids, where the velocity is defined on the full grid points and the stress is defined on the half grid points, thus achieving the spatial discretization of the physical quantity;

[0079] Set up separately is the speed v x 、v z and stress σ xx , σ zz , τ xz The discrete value of k represents the discrete grid point position in time, i and j represent the discrete grid point positions in the x and z directions of space, and the two-dimensional isotropic medium elastic wave equation is discretized to obtain the following formula:

[0080]

[0081] The recursive formula of discrete stress and velocity is obtained from the above formula, which can simulate the wave field propagation seismic record;

[0082] 2) Forward modeling of free surface wave field using finite difference method:

[0083] The free surface divides the earth into two half-spaces, vacuum and elastic half-space. Although the properties of the medium on both sides of the free surface are discontinuous, the movement of the medium is continuous; there is no wave propagation in the vacuum, that is, the stress is zero at the interface, and the displacement can be arbitrary; at the depth z = 0 on the two-dimensional plane surface, it satisfies:

[0084]

[0085] Substituting equation (3) into equation (1), we can obtain the first-order velocity-stress equations for elastic waves in a 2D isotropic medium at z = 0:

[0086]

[0087] It can be seen from formula (2) that when the staggered grid finite difference method is used for numerical simulation of seismic wave fields, the derivative of the field component in the partial differential equation is replaced by the interpolation quotient of the corresponding physical quantity at the grid point, but this is no longer applicable to the field component near the free surface. When i, j ≤ (n-1), the subscript of the difference format is out of bounds and calculation cannot be performed. Therefore, it is necessary to adjust the finite difference format and replace the derivative of the field component on the free surface with the difference quotient of the corresponding physical quantity at the grid point below the free surface. This solves the problem that the free surface is the upper interface of the model and there is no field component on it. The variable finite difference method approximation under the staggered grid is as follows:

[0088]

[0089] Where f is the field component, j 0 is the vertical position of the current calculation grid point, Δh is the vertical interval of the grid points;

[0090] 3) The free surface (0≤Z≤Δh) wave field simulation process is as follows:

[0091] (1)σ zz (0) = 0, that is

[0092] (2)σ xx (0) can be calculated by formula (4). Combined with formula (2), its discrete form can be written as follows:

[0093]

[0094] (3) It can be calculated by the discrete form of equation (4), where It can be approximately calculated by (5-2°);

[0095] (4)σ xx (Δh) and σ zz (Δh) can be calculated from the discrete form of equation (1), where It can be approximately calculated by (5-3°);

[0096] (5)v x (0) can be calculated from the discrete form of equation (4), where It can be approximately calculated by (5-1°);

[0097] (6) It can be calculated by the discrete form of equation (4), where It can be approximately calculated by (5-2°);

[0098] (7)v x (Δh) can be calculated from the discrete form of equation (4), where It can be approximately calculated by (5-4°);

[0099] This can complete the wave field simulation at the free surface.

[0100] In seismic exploration, surface wave signals occupy the main part of the shallow seismic wave field energy. Rayleigh surface waves are formed by the mutual interference of P waves and SV waves, and contain a large amount of shallow shear wave information. Based on this, this embodiment designs a two-dimensional isotropic medium model with a grid size of 300×300 and a vertical and horizontal grid spacing of 1m; the horizontal coordinate range is 0 to 300m; the surface is blasted, and the source wavelet is a 20Hz zero-phase Ricker wavelet; Figure 4 These are snapshots of the wavelengths of the x and z components at different times after the explosive source was blasted. It can be seen that since there is no medium above the free surface, when the wave encounters this interface, it can only bend back to the original medium and will not pass through it, that is, there is only a reflected wave but no transmitted wave; when the lower longitudinal wave is incident on the free surface, it will not only cause displacement along the normal direction of the surface, but also cause displacement along the tangential direction, so the reflected wave contains both P waves and SV waves;

[0101] Figure 5 For the designed horizontal layered medium, Figure 6 The snapshots of the x and z component wave fields at different times after the blasting of the surface explosive source show that this method can simulate P waves and SV waves very well, which is more conducive to the study of seismic wave field propagation.

[0102] Embodiment 2:

[0103] This embodiment provides a method for improving the simulation accuracy of free surface wave fields. Figure 1 As shown, including:

[0104] The field components of the free surface are spatially staggered to obtain discrete field components;

[0105] Discrete elastic wave equations are obtained by time-space discretization of elastic wave equations of wave field components;

[0106] The finite difference format of the staggered grid formed by the spatial staggering is adjusted to obtain a variable finite difference approximation;

[0107] The discrete field components are simulated based on the discrete elastic wave equation and the variable finite difference approximation;

[0108] Field components include velocity and stress;

[0109] The spatial staggered discretization of the wave field physical quantities of the free surface includes:

[0110] The velocity and stress are defined on two different grid systems with a difference of half a grid spacing.

[0111] Among them, the velocity is defined on the full grid points, and the stress is defined on the half grid points;

[0112] The elastic wave equation is a two-dimensional isotropic medium elastic wave equation, and its formula is:

[0113]

[0114] Among them, x is the horizontal direction, z is the vertical direction, ρ is the density of the elastic medium, λ and μ are the Lame coefficients, v is the velocity, and τ is the stress;

[0115] When z = 0, The elastic wave equation is:

[0116]

[0117] The formula for the discrete elastic wave equation is:

[0118]

[0119] in, v x 、v z , σ xx , σ zz , τ xz The discrete value of , k is the discrete grid point position in time, i and j are the discrete grid point positions in the x and z directions of space respectively;

[0120] Adjusting the finite difference format of the staggered grid formed by spatial staggering, the variable finite difference approximation formula includes:

[0121] Based on the staggered grid finite difference scheme, the derivatives of the discrete field components are replaced by the difference quotients of the corresponding physical quantities at the grid points below the free surface, and a variable finite difference approximation is obtained;

[0122] The variable finite difference approximation is:

[0123] 1°:

[0124] 2°:

[0125] 3°:

[0126] 4°:

[0127] Where f is velocity or stress, j is 0 is the vertical position of the current calculation grid point, Δh is the vertical interval of the grid points;

[0128] The free surface range is 0≤Z≤Δh;

[0129] The process of simulating the discrete field components is as follows:

[0130] Find σ zz (0) = 0, that is

[0131] Using the elastic wave equation when z = 0 and the formula of the discrete elastic wave equation, we can get σ xx (0), its discrete form expression is:

[0132]

[0133] Using the formula of the discrete elastic wave equation when z = 0 and the 2° formula of the variable finite difference approximation, we can obtain

[0134] Using the formula of the discrete elastic wave equation and the 3° formula of the variable finite difference approximation, we can calculate σ xx (Δh) and σ zz (Δh);

[0135] Using the formula of the discrete elastic wave equation when z = 0 and the 1° formula of the variable finite difference approximation, we can obtain v x (0);

[0136] Using the formula of the discrete elastic wave equation when z = 0 and the 2° formula of the variable finite difference approximation, we can obtain

[0137] Using the formula of the discrete elastic wave equation when z = 0 and the 4° formula of the variable finite difference approximation, we can calculate v x (Δh).

[0138] Embodiment three:

[0139] This embodiment provides a device for improving the simulation accuracy of a free surface wave field, including:

[0140] The spatial staggered discretization module discretizes the field components of the free surface by spatial staggered discretization to obtain discrete field components;

[0141] The space-time discretization module discretizes the elastic wave equation of the wave field component in space and time to obtain the discrete elastic wave equation;

[0142] The variable difference approximation module adjusts the finite difference format of the staggered grid formed by the spatial staggering to obtain a variable finite difference approximation;

[0143] A simulation processing module simulates the discrete field components based on the discrete elastic wave equation and the variable finite difference approximation;

[0144] Field components include velocity and stress;

[0145] The spatial staggered discretization of the wave field physical quantities of the free surface includes:

[0146] The velocity and stress are defined on two different grid systems with a difference of half a grid spacing.

[0147] Among them, the velocity is defined on the full grid points, and the stress is defined on the half grid points;

[0148] The elastic wave equation is a two-dimensional isotropic medium elastic wave equation, and its formula is:

[0149]

[0150] Among them, x is the horizontal direction, z is the vertical direction, ρ is the density of the elastic medium, λ and μ are the Lame coefficients, v is the velocity, and τ is the stress;

[0151] When z = 0, The elastic wave equation is:

[0152]

[0153] The formula for the discrete elastic wave equation is:

[0154]

[0155] in, v x 、v z , σ xx , σ zz , τ xzThe discrete value of , k is the discrete grid point position in time, i and j are the discrete grid point positions in the x and z directions of space respectively;

[0156] Adjusting the finite difference format of the staggered grid formed by spatial staggering, the variable finite difference approximation formula includes:

[0157] Based on the staggered grid finite difference scheme, the derivatives of the discrete field components are replaced by the difference quotients of the corresponding physical quantities at the grid points below the free surface, and a variable finite difference approximation is obtained;

[0158] The variable finite difference approximation is:

[0159] 1°:

[0160] 2°:

[0161] 3°:

[0162] 4°:

[0163] Where f is velocity or stress, j is 0 is the vertical position of the current calculation grid point, Δh is the vertical interval of the grid points;

[0164] The free surface range is 0≤Z≤Δh;

[0165] The process of simulating the discrete field components is as follows:

[0166] Find σ zz (0) = 0, that is

[0167] Using the elastic wave equation when z = 0 and the formula of the discrete elastic wave equation, we can get σ xx (0), its discrete form expression is:

[0168]

[0169] Using the formula of the discrete elastic wave equation when z = 0 and the 2° formula of the variable finite difference approximation, we can obtain

[0170] Using the formula of the discrete elastic wave equation and the 3° formula of the variable finite difference approximation, we can calculate σ xx (Δh) and σ zz (Δh);

[0171] Using the formula of the discrete elastic wave equation when z = 0 and the 1° formula of the variable finite difference approximation, we can obtain v x (0);

[0172] Using the formula of the discrete elastic wave equation when z = 0 and the 2° formula of the variable finite difference approximation, we can obtain

[0173] Using the formula of the discrete elastic wave equation when z = 0 and the 4° formula of the variable finite difference approximation, we can calculate v x (Δh).

[0174] Embodiment 4:

[0175] An embodiment of the present invention provides an electronic device including a memory and a processor.

[0176] A memory storing executable instructions;

[0177] The processor runs the executable instructions in the memory to implement the method for improving the accuracy of free surface wave field simulation.

[0178] The memory is used to store non-temporary computer-readable instructions. Specifically, the memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include random access memory (RAM) and / or cache memory (cache), etc. The non-volatile memory may, for example, include read-only memory (ROM), hard disk, flash memory, etc.

[0179] The processor may be a central processing unit (CPU) or other forms of processing units with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. In one embodiment of the present invention, the processor is used to run the computer-readable instructions stored in the memory.

[0180] Those skilled in the art should be able to understand that in order to solve the technical problem of how to obtain a good user experience, the present embodiment may also include well-known structures such as a communication bus and an interface, and these well-known structures should also be included in the protection scope of the present invention.

[0181] For detailed description of this embodiment, reference may be made to the corresponding descriptions in the aforementioned embodiments, which will not be repeated here.

[0182] Embodiment five:

[0183] An embodiment of the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, a method for improving the simulation accuracy of a free surface wave field is implemented.

[0184] The computer-readable storage medium according to the embodiment of the present invention stores non-transitory computer-readable instructions, and when the non-transitory computer-readable instructions are executed by a processor, all or part of the steps of the above-mentioned methods of the embodiments of the present invention are executed.

[0185] The above-mentioned computer-readable storage media include, but are not limited to: optical storage media (e.g., CD-ROM and DVD), magneto-optical storage media (e.g., MO), magnetic storage media (e.g., magnetic tape or mobile hard disk), media with built-in rewritable non-volatile memory (e.g., memory card) and media with built-in ROM (e.g., ROM box).

[0186] The method for improving the accuracy of free surface wave field simulation proposed in an embodiment of the present invention solves the problem of the free surface being the upper interface of the model with no field components on it in the existing finite difference format by performing spatial staggered discretization of the field components of the free surface, performing spatiotemporal discretization of the elastic wave equation, and adjusting the finite difference format of the staggered grid formed by the spatial staggering, thereby improving the processing accuracy of the field components of the free surface and the instability of the results.

[0187] The embodiments of the present invention have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A method to improve the accuracy of free surface wave field simulation, It is characterized in that include: The field components of the free surface are spatially staggered to obtain discrete field components; Performing time-space discretization on the elastic wave equation of the wave field component to obtain a discrete elastic wave equation; Adjusting the finite difference format of the staggered grid formed by the spatial staggering to obtain a variable finite difference approximation; The discrete field components are simulated based on the discrete elastic wave equation and the variable finite difference approximation.

2. The method according to claim 1, It is characterized in that The field components include velocity and stress; The spatially staggered discretization of the wave field physical quantity of the free surface includes: The velocity and stress are defined on two different grid systems with a difference of half a grid spacing; The velocity is defined on the full grid points, and the stress is defined on the half grid points.

3. The method according to claim 2, It is characterized in that The elastic wave equation is a two-dimensional isotropic medium elastic wave equation, and its formula is: Among them, x is the horizontal direction, z is the vertical direction, ρ is the density of the elastic medium, λ and μ are the Lame coefficients, v is the velocity, and τ is the stress; When z = 0, The elastic wave equation is:

4. The method according to claim 3, It is characterized in that The formula of the discrete elastic wave equation is: in, v x 、v z , σ xx , σ zz , τ xz The discrete value of , k is the discrete grid point position in time, i and j are the discrete grid point positions in the x and z directions of space respectively.

5. The method according to claim 4, It is characterized in that The finite difference format of the staggered grid formed by the spatial staggering is adjusted to obtain a variable finite difference approximation formula including: Based on the staggered grid finite difference format, the derivatives of the discrete field components are replaced by the difference quotients of the corresponding physical quantities at the grid points below the free surface, and a variable finite difference approximation is obtained.

6. The method according to claim 5, It is characterized in that The variable finite difference approximation is: Where f is velocity or stress, j is 0 is the vertical position of the current calculation grid point, and Δh is the vertical interval of the grid points.

7. The method according to claim 6, It is characterized in that The free surface range is 0≤Z≤Δh; The process of simulating the discrete field components is as follows: Find σ zz (0) = 0, that is Using the elastic wave equation when z = 0 and the formula of the discrete elastic wave equation, we can get σ xx (0), its discrete form expression is: Using the formula of the discrete elastic wave equation when z = 0 and the 2° formula of the variable finite difference approximation, we can obtain The formula of discrete elastic wave equation and the 3° formula of variable finite difference approximation are used to calculate σ xx (Δh) and σ zz (Δh); Using the formula of the discrete elastic wave equation when z = 0 and the 1° formula of the variable finite difference approximation, we can obtain v x (0); Using the formula of the discrete elastic wave equation when z = 0 and the 2° formula of the variable finite difference approximation, we can obtain Using the formula of the discrete elastic wave equation when z = 0 and the 4° formula of the variable finite difference approximation, we can calculate v x (Δh).

8. A device for improving the simulation accuracy of free surface wave fields, It is characterized in that include: The spatial staggered discretization module discretizes the field components of the free surface by spatial staggered discretization to obtain discrete field components; A space-time discretization module performs space-time discretization on the elastic wave equation of the wave field component to obtain a discrete elastic wave equation; A variable difference approximation module adjusts the finite difference format of the staggered grid formed by the spatial staggering to obtain a variable finite difference approximation; A simulation processing module performs simulation processing on the discrete field component based on the discrete elastic wave equation and the variable finite difference approximation.

9. An electronic device, It is characterized in that The electronic device comprises: A memory storing executable instructions; A processor, wherein the processor runs the executable instructions in the memory to implement the method for improving the accuracy of free surface wave field simulation according to any one of claims 1-7.

10. A computer-readable storage medium, It is characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for improving the simulation accuracy of a free surface wave field according to any one of claims 1 to 7 is implemented.

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