Elastic wave numerical simulation and wave field separation method and device

Abstract

The embodiment of the invention relates to the technical field of seismic wave numerical simulation, and provides an elastic wave numerical simulation and wave field separation method and device.The method comprises the steps that firstly, the time-space domain longitudinal wave and transverse wave frequency dispersion relation of an elastic wave equation is derived based on a constructed mixed type space difference operator; further deriving a differential coefficient general solution based on a time-space domain longitudinal wave and transverse wave frequency dispersion relationship, then decoupling elastic wave equations to respectively obtain longitudinal wave and transverse wave elastic wave equations, and deriving a longitudinal wave and transverse wave differential discrete equation based on the constructed mixed space differential operator; and finally, a longitudinal wave and transverse wave differential discrete equation is solved through general solution iteration of a differential coefficient derived from a time-space domain longitudinal wave and transverse wave dispersion relation, so that elastic wave numerical simulation is realized, and wave field separation of longitudinal waves and transverse waves is automatically realized. According to the embodiment of the invention, the numerical dispersion of longitudinal waves and transverse waves can be effectively suppressed at the same time, so that the elastic wave numerical simulation precision is improved.

Description

Technical Field

[0001] The embodiments of this specification relate to the technical field of seismic data processing, and in particular to a method and device for elastic wave numerical simulation and wave field separation. Background Art

[0002] Numerical simulation of elastic waves is an important basic research topic in exploration seismology and plays an important role in multi-wave and multi-component oil and gas exploration. Numerical simulation of elastic waves can be used to study the propagation laws and characteristics of elastic waves in complex media, guide the optimization of multi-wave and multi-component seismic data processing and interpretation schemes, and is a key technical link in elastic wave reverse time migration and full waveform inversion.

[0003] At present, the conventional high-order staggered grid finite difference method is the most commonly used method for numerical simulation of acoustic and elastic waves. However, the conventional high-order staggered grid finite difference method only uses the coordinate axis grid points to construct the spatial difference operator. As the spatial difference operator increases, the distance between the newly added grid points and the difference center point becomes farther and farther, resulting in lower and lower simulation accuracy. In addition, the elastic wave differential discretization equation is iteratively solved in the time and space domain, but the differential coefficients of the conventional high-order staggered grid finite difference method are only calculated based on the spatial domain dispersion relationship. This results in the conventional high-order staggered grid finite difference method being able to make the spatial difference operator reach 2M-order differential accuracy, but the differential discretization wave equation still only has 2-order differential accuracy, so the numerical dispersion suppression effect is poor. In addition, the conventional high-order finite difference method usually solves the elastic wave equation directly, and the simulation results contain both longitudinal and transverse waves. It is necessary to use additional wave field decoupling operators to obtain the simulation results of pure longitudinal waves and pure transverse waves. The wave field decoupling operator will further increase the error source, resulting in poor simulation stability. In summary, the numerical simulation of elastic waves using the conventional high-order staggered grid finite difference method has the problems of poor numerical dispersion suppression, low simulation accuracy and poor stability. Summary of the invention

[0004] In view of the above-mentioned problems in the prior art, the purpose of the embodiments of this specification is to provide a method and device for elastic wave numerical simulation and wavefield separation, so as to solve the problems in the prior art of using conventional high-order staggered grid finite difference method for elastic wave numerical simulation, such as poor numerical dispersion suppression effect, low simulation accuracy and poor stability.

[0005] In order to solve the above technical problems, the specific technical solutions of the embodiments of this specification are as follows:

[0006] On the one hand, an embodiment of this specification provides a method for elastic wave numerical simulation and wave field separation, the method comprising:

[0007] Constructing a hybrid spatial difference operator using coordinate axis grid points and non-coordinate axis grid points, wherein the difference operator includes at least one group of non-coordinate axis grid points that are equidistant from a difference center point;

[0008] Using the hybrid spatial difference operator to perform differential discretization on the elastic wave equation to obtain the elastic wave differential discretization equation;

[0009] Based on the elastic wave differential discrete equation and discrete plane wave solution, the corresponding time-space domain longitudinal wave and transverse wave dispersion relations are derived;

[0010] A differential coefficient solution equation group is established based on the longitudinal wave and transverse wave dispersion relationship in the time and space domain, and a differential coefficient general solution based on the longitudinal wave and transverse wave dispersion relationship in the time and space domain is calculated;

[0011] A decoupled elastic wave differential dispersion equation is derived according to the hybrid spatial differential operator, and the decoupled elastic wave differential dispersion equation is iteratively solved using the differential coefficient general solution based on the dispersion relationship between longitudinal and transverse waves in the space-time domain to realize elastic wave numerical simulation and automatic separation of longitudinal and transverse waves.

[0012] Preferably, the construction of a hybrid spatial difference operator using coordinate axis grid points and non-coordinate axis grid points includes:

[0013] The coordinate axis grid points with equal distance from the difference center point are regarded as one group. According to the principle of increasing distance from the difference center point, M groups of coordinate axis grid points are selected in sequence to construct M spatial difference operators.

[0014] The non-coordinate axis grid points with equal distances from the difference center point are regarded as one group. According to the principle of increasing distances from the difference center point, N groups of non-coordinate axis grid points are selected in sequence to construct N spatial difference operators.

[0015] The M spatial difference operators constructed by the coordinate axis grid points and the N spatial difference operators constructed by the non-coordinate axis grid points are weighted averaged to obtain a hybrid spatial difference operator.

[0016] Preferably, the step of performing differential discretization on the elastic wave equation using the hybrid spatial differential operator to obtain the elastic wave differential discretization equation comprises:

[0017] Using the hybrid spatial differential operator to perform differential discretization on the spatial partial differential operator in the elastic wave equation, and obtaining a differential expression of the spatial partial differential operator;

[0018] The time partial differential operator in the elastic wave equation is differentially discretized using a preset second-order time difference operator to obtain a differential expression of the time partial differential operator;

[0019] Substituting the difference expressions of the spatial partial differential operator and the temporal partial differential operator into the elastic wave equation, the elastic wave differential discretization equation is obtained.

[0020] Preferably, the time-space domain longitudinal wave and shear wave dispersion relationship is derived from the following formula:

[0021]

[0022]

[0023] in,

[0024]

[0025]

[0026] λ=λ(x,z) and μ=μ(x,z) are the Lame constants, ρ=ρ(x,z) is the density, h and Δt are the spatial and temporal sampling intervals, respectively, and k x = kcosθ, k z =ksinθ, k is the wave number, ω is the angular frequency, a m , b1 is the differential coefficient.

[0027] Preferably, the general solution of the differential coefficients of longitudinal waves and shear waves in the time and space domain is calculated according to the following formula:

[0028]

[0029]

[0030] in, and are the general solutions of the differential coefficients of longitudinal waves, and are the general solutions of differential coefficients of shear waves, is the Courant condition number of the longitudinal wave, is the Courant condition number of the shear wave, v p and v s are the longitudinal and shear wave velocities, respectively, h and Δt are the spatial and temporal sampling intervals, respectively, and k is the wave number.

[0031] Preferably, the decoupled elastic wave differential dispersion equation is derived according to the hybrid spatial differential operator, and the decoupled elastic wave differential dispersion equation is iteratively solved using the differential coefficient general solution based on the dispersion relationship between longitudinal waves and shear waves in the time and space domain to realize elastic wave numerical simulation and automatically realize the separation of longitudinal waves and shear waves, including:

[0032] Based on the elastic wave equation, the elastic wave equation for decoupling longitudinal and transverse waves is derived;

[0033] Using the hybrid spatial difference operator, the elastic wave equations of the longitudinal wave and the transverse wave decoupling are differentially discretized to obtain differentially discretized equations of the longitudinal wave and the transverse wave;

[0034] The differential coefficient general solution based on the dispersion relationship between longitudinal and transverse waves in the time and space domain is used to iteratively solve the differential dispersion equations of the longitudinal and transverse waves respectively, to realize the numerical simulation of elastic waves, and to automatically realize the separation of longitudinal and transverse waves.

[0035] On the other hand, an embodiment of the present specification provides an elastic wave numerical simulation and wave field separation device, the device comprising:

[0036] A spatial difference operator construction module, used to construct a hybrid spatial difference operator using coordinate axis grid points and non-coordinate axis grid points, wherein the difference operator at least includes a group of non-coordinate axis grid points that are equidistant from a difference center point;

[0037] A differential discretization module, used for differentially discretizing the elastic wave equation using the hybrid spatial differential operator to obtain an elastic wave differential discretization equation;

[0038] A dispersion relation acquisition module, used to derive the corresponding time-space domain longitudinal wave and transverse wave dispersion relations according to the elastic wave differential dispersion equation and the discrete plane wave solution;

[0039] A differential coefficient calculation module is used to establish a differential coefficient solution equation group based on the longitudinal wave and shear wave dispersion relationship in the time and space domain, and calculate the differential coefficient general solution based on the longitudinal wave and shear wave dispersion relationship in the time and space domain;

[0040] The numerical simulation and wave field separation module is used to derive the decoupled elastic wave differential dispersion equation according to the hybrid spatial differential operator, and iteratively solve the decoupled elastic wave differential dispersion equation using the differential coefficient general solution based on the dispersion relationship between longitudinal and transverse waves in the time and space domain, so as to realize elastic wave numerical simulation and automatically realize the separation of longitudinal and transverse waves.

[0041] On the other hand, an embodiment of the present specification further provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein when the computer program is executed by the processor, the instructions of any one of the above methods are executed.

[0042] On the other hand, an embodiment of the present specification further provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor of a computer device, the computer program executes instructions of any one of the above-described methods.

[0043] On the other hand, the embodiments of this specification further provide a computer program product, which, when executed by a processor of a computer device, executes instructions of any one of the above methods.

[0044] One or more technical solutions provided by some embodiments of this specification have at least the following technical effects:

[0045] The embodiments of the present specification jointly use the coordinate axis grid points and the non-coordinate axis grid points to construct a hybrid spatial differential operator. Compared with the conventional high-order staggered grid finite difference method that only uses the coordinate axis to construct the spatial differential operator, it fully utilizes the non-coordinate axis grid points that are closer to the differential center point, and the obtained spatial differential operator is more compact. Based on the spatial-temporal domain longitudinal wave and transverse wave dispersion relationship, the corresponding differential coefficient general solution is calculated. Compared with the conventional high-order staggered grid finite difference method that only calculates the differential coefficient based on the spatial domain dispersion relationship, the numerical dispersion of longitudinal waves and transverse waves can be effectively suppressed, thereby improving the accuracy of numerical simulation. In addition, compared with the conventional high-order staggered grid finite difference method, which requires further decoupling of the simulation results to obtain the simulation results of pure longitudinal waves and pure transverse waves, the embodiments of the present specification use the differential coefficient general solution based on the spatial-temporal domain longitudinal wave and transverse wave dispersion relationship to iteratively solve the elastic wave differential discrete equation for decoupling longitudinal waves and transverse waves, automatically realize the wave field separation of longitudinal waves and wave fields, reduce the error source that requires additional decoupling, and improve the accuracy and stability of numerical simulation.

[0046] In order to make the above and other purposes, features and advantages of the embodiments of this specification more obvious and easy to understand, the following specifically cites preferred embodiments and describes them in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the embodiments of this specification or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this specification. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0048] Figure 1 A schematic diagram showing a flow chart of an elastic wave numerical simulation and wave field separation method in some embodiments of this specification;

[0049] Figure 2 A schematic diagram of a spatial difference operator of a conventional high-order staggered grid finite difference method in some embodiments of this specification is shown;

[0050] Figure 3(a)-Figure 3(d) A schematic diagram of a hybrid spatial difference operator constructed by jointly utilizing coordinate axis grid points and non-coordinate axis grid points proposed in some embodiments of this specification is shown;

[0051] Figure 4 A schematic diagram of the steps of constructing a hybrid spatial difference operator using coordinate axis grid points and non-coordinate axis grid points in some embodiments of this specification is shown;

[0052] Figure 5 A schematic diagram of the steps of performing differential discretization on the elastic wave equation according to a hybrid spatial differential operator to obtain the elastic wave differential discretization equation in some embodiments of this specification is shown;

[0053] Figure 6 A schematic diagram of the steps of iteratively solving the elastic wave differential dispersion equation for decoupling longitudinal and shear waves using a general solution of differential coefficients based on the dispersion relationship between longitudinal and shear waves in the time and space domain to achieve elastic wave numerical simulation in some embodiments of the present specification;

[0054] Figure 7 A schematic diagram of the structure of an elastic wave numerical simulation and wave field separation device in some embodiments of this specification is shown;

[0055] Figure 8(a)-Figure 8(d) The particle vibration velocity field υ at 2.4s generated by elastic wave simulation using a layered medium model in different methods in some embodiments of this specification is shown. z Snapshot of the wave field;

[0056] Figure 9(a)-Figure 9(b) The particle vibration velocity field υ at the time of 2.4s is obtained by automatically separating longitudinal waves and transverse waves in the elastic wave simulation process using the layered medium model in some embodiments of this specification. z P-wave and S-wave component diagrams of the wave field snapshot;

[0057] Fig.10 A P-wave velocity model diagram of a typical complex structural model of the Tarim Basin in some embodiments of this specification is shown;

[0058] Figure 11(a)-Figure 11(b) It shows the local shot gathering record diagram generated by elastic wave simulation using a typical complex structural model of the Tarim Basin in different methods in some embodiments of this specification;

[0059] Fig.12 A schematic diagram of the structure of a computer device provided in some embodiments of the present specification is shown.

[0060] Description of the accompanying symbols:

[0061] 701. Spatial difference operator construction module;

[0062] 702, differential separation module;

[0063] 703. Dispersion relationship acquisition module;

[0064] 704. differential coefficient calculation module;

[0065] 705. Numerical simulation and wave field separation module;

[0066] 1202. Computer equipment;

[0067] 1204, processor;

[0068] 1206. Memory;

[0069] 1208, driving mechanism;

[0070] 1210, input / output module;

[0071] 1212. Input device;

[0072] 1214. Output device;

[0073] 1216. Presentation equipment;

[0074] 1218. Graphical user interface;

[0075] 1220, network interface;

[0076] 1222, communication link;

[0077] 1224. Communication bus. DETAILED DESCRIPTION

[0078] The following will be combined with the drawings in the embodiments of this specification to clearly and completely describe the technical solutions in the embodiments of this specification. Obviously, the described embodiments are only part of the embodiments of this specification, not all of the embodiments. Based on the embodiments in this specification, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this specification.

[0079] In the prior art, the conventional high-order staggered grid finite difference method only uses the coordinate axis grid points to construct the spatial difference operator. As the spatial difference operator increases, the distance between the newly added grid points and the difference center point becomes farther and farther, resulting in lower and lower simulation accuracy. In addition, the differential coefficients of the conventional high-order staggered grid finite difference method are calculated only based on the spatial domain dispersion relationship. This results in that although the conventional high-order staggered grid finite difference method can make the spatial difference operator reach 2M-order differential accuracy, the differential discrete wave equation still only has 2-order differential accuracy, so the numerical dispersion suppression effect is poor. In addition, the conventional high-order finite difference method usually directly solves the elastic wave equation, and the simulation results contain both longitudinal waves and transverse waves. It is necessary to use additional wave field decoupling operators to obtain the simulation results of pure longitudinal waves and pure transverse waves, and the wave field decoupling operator will further increase the error source, resulting in poor simulation stability. In summary, the conventional high-order staggered grid finite difference method for elastic wave numerical simulation has the problems of poor numerical dispersion suppression effect, low simulation accuracy and poor stability.

[0080] In order to solve the above problems, an embodiment of the present specification provides a method for elastic wave numerical simulation and wave field separation. Figure 1 This is a flow chart of a method for numerical simulation of elastic waves and wave field separation provided by some embodiments of this specification. This specification provides method operation steps as described in the embodiments or flow charts, but more or fewer operation steps may be included based on conventional or non-creative labor. The order of steps listed in the embodiments is only one way of executing the order of many steps and does not represent the only execution order. When the actual system or device product is executed, it can be executed in the order of the method shown in the embodiments or the drawings or in parallel.

[0081] It should be noted that the terms "first", "second", etc. in this specification and claims and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of this specification described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, device, product or equipment that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or equipment.

[0082] Reference Figure 1 Some embodiments of this specification provide a method for elastic wave numerical simulation and wave field separation, the method comprising:

[0083] S101: constructing a hybrid spatial difference operator using coordinate axis grid points and non-coordinate axis grid points, wherein the difference operator includes at least one group of non-coordinate axis grid points that are equidistant from a difference center point;

[0084] S102: using the hybrid spatial difference operator to perform differential discretization on the elastic wave equation to obtain an elastic wave differential discretization equation;

[0085] S103: deriving the corresponding time-space domain longitudinal wave and transverse wave dispersion relations according to the elastic wave differential discrete equation and the discrete plane wave solution;

[0086] S104: establishing a differential coefficient solution equation group based on the longitudinal wave and shear wave dispersion relationship in the time and space domain, and calculating and obtaining a differential coefficient general solution based on the longitudinal wave and shear wave dispersion relationship in the time and space domain;

[0087] S105: Deriving a decoupled elastic wave differential dispersion equation according to the hybrid spatial differential operator, and iteratively solving the decoupled elastic wave differential dispersion equation using the differential coefficient general solution based on the dispersion relationship between longitudinal and transverse waves in the space-time domain to achieve elastic wave numerical simulation and automatic separation of longitudinal and transverse waves.

[0088] The embodiments of this specification jointly use the coordinate axis grid points and the non-coordinate axis grid points to construct a hybrid spatial differential operator. Compared with the conventional high-order staggered grid finite difference method that only uses the coordinate axis to construct the spatial differential operator, it fully utilizes the non-coordinate axis grid points that are closer to the differential center point, and the obtained spatial differential operator is more compact. The corresponding differential coefficient general solution is calculated based on the dispersion relationship of longitudinal waves and transverse waves in the time and space domain. Compared with the conventional high-order staggered grid finite difference method that only calculates the differential coefficient based on the dispersion relationship in the space domain, it can effectively suppress the numerical dispersion of longitudinal waves and transverse waves, thereby improving the accuracy of numerical simulation. In addition, compared with the conventional high-order staggered grid finite difference method, which requires further decoupling of the simulation results to obtain the simulation results of pure longitudinal waves and pure transverse waves, the embodiments of this specification use the differential coefficient general solution of longitudinal waves and transverse waves in the time and space domain to perform numerical simulations on the decoupled elastic wave discrete equations respectively, thereby achieving the wave field separation of longitudinal waves and wave fields, reducing the error sources that require additional decoupling, and improving the accuracy and stability of numerical simulations.

[0089] Elastic wave numerical simulation is an important basic research content in exploration seismology and plays an important role in multi-wave and multi-component oil and gas exploration. Elastic wave numerical simulation can be used to study the propagation law and characteristics of elastic waves in complex media, guide the optimization of multi-wave and multi-component seismic data processing and interpretation schemes, and is a key technical link in elastic wave reverse time migration and full waveform inversion. Conventional high-order staggered grid finite difference algorithm uses coordinate axis grid points to construct spatial difference operators. Figure 2 As shown, Figure 2This is a schematic diagram of the spatial difference operator of the conventional high-order staggered grid finite difference method. M can take any integer greater than 0. As the value of M increases, the distance between the newly added grid points and the difference center point becomes farther and farther, and the contribution to improving the simulation accuracy becomes smaller and smaller, resulting in the conventional high-order staggered grid finite difference method. The numerical simulation accuracy is usually relatively low and the numerical dispersion is serious. Figure 3(a)-Figure 3(d) This is a schematic diagram of a hybrid space difference operator constructed by jointly utilizing coordinate axis grid points and non-coordinate axis grid points proposed in some embodiments of this specification, which includes M groups of coordinate axis grid points and N groups of non-coordinate axis grid points, and M and N can be any integer greater than 0. Figure 3(a) is a schematic diagram of a hybrid space difference operator constructed when N=1, Figure 3(b) is a schematic diagram of a hybrid space difference operator constructed when N=2, Figure 3(c) is a schematic diagram of a hybrid space difference operator constructed when N=3, and Figure 3(d) is a schematic diagram of a hybrid space difference operator constructed when N=4. In some embodiments of this specification, numerical simulation of elastic waves is carried out using N=1 as an example. Referring to Figure 3(a), the non-coordinate axis grid points are parallel to the coordinate axis grid points, and the distance between the non-coordinate axis grid points and the differential center point is less than the distance between the Mth grid point in the coordinate axis grid points and the differential center point. For example, assuming that the distance between the first group of grid points in the coordinate axis is d, the distance between each grid point in the first group of grid points and the differential center point is The distance between each grid point in the second set of grid points and the difference center point is Similarly, as the value of M increases, the distance between the newly added grid points and the differential center point also increases. For the non-coordinate axis grid points, as shown in Figure 3(a), the distance between the first group of non-coordinate axis grid points and the differential center point is Obviously, it is smaller than the distance from the Mth group of grid points in the coordinate axis to the differential center point.

[0090] In some embodiments, reference Figure 4 As shown, a hybrid spatial difference operator is constructed using coordinate axis grid points and non-coordinate axis grid points, including:

[0091] S401: Consider the coordinate axis grid points with the same distance from the difference center point as one group, and select M groups of coordinate axis grid points in order according to the principle of increasing distance from the difference center point to construct M spatial difference operators;

[0092] S402: The non-coordinate axis grid points with the same distance from the difference center point are regarded as one group, and N groups of non-coordinate axis grid points are selected in sequence according to the principle of increasing distance from the difference center point to construct N spatial difference operators;

[0093] S403: Weighted average the M spatial difference operators constructed by the coordinate axis grid points and the N spatial difference operators constructed by the non-coordinate axis grid points to obtain a hybrid spatial difference operator. As shown in FIG3(a), it includes a group of non-coordinate axis grid points whose distance from the difference center point is A spatial difference operator is constructed using this group of non-coordinate axis grid points, which also includes M spatial difference operators constructed by M groups of coordinate axis grid points. A hybrid spatial difference operator can be obtained by weighted averaging one spatial difference operator of the coordinate axis grid points and the M spatial difference operators of the non-coordinate axis grid points. The hybrid difference operator in the embodiment of this specification makes full use of the non-coordinate axis grid points that are closer to the differential center point, and replaces the points in the coordinate axis that are farther away from the differential center point with non-coordinate axis grid points that are closer to the differential center point, so that the constructed hybrid spatial difference operator is more reasonable, thereby providing a reasonable basis for subsequent numerical simulations.

[0094] In some embodiments, reference Figure 5 As shown, the elastic wave equation is differentially discretized using the hybrid spatial differential operator to obtain the elastic wave differential discretization equation, including:

[0095] S501: using the hybrid spatial differential operator to perform differential discretization on the spatial partial differential operator in the elastic wave equation to obtain a differential expression of the spatial partial differential operator;

[0096] S502: using a preset second-order time difference operator to perform differential discretization on the time partial differential operator in the elastic wave equation to obtain a differential expression of the time partial differential operator;

[0097] S503: Substitute the difference expressions of the spatial partial differential operator and the temporal partial differential operator into the elastic wave equation to obtain the elastic wave difference discrete equation.

[0098] The velocity-stress elastic wave equation can be expressed as:

[0099]

[0100] where υ x , z , τ xx , τ xz and τ zz is the wave field variable, τ xx =τ xx (x,z,t),τ zz =τ zz (x,z,t) and τ xz =τ xz (x,z,t) is the stress field, υ x =υ x (x,z,t) and vz =υ z (x,z,t) is the particle vibration velocity field, λ, μ and ρ are elastic wave parameters, λ = λ(x,z) and μ = μ(x,z) are Lame constants, and ρ = ρ(x,z) is the density.

[0101] In some embodiments of this specification, according to the mixed spatial differential operator, the differential expression of the spatial partial differential operator is and It can be expressed as:

[0102]

[0103] where a1, a2, ..., a M , b1 is the differential coefficient, and h is the spatial sampling interval.

[0104] In some embodiments of this specification, a preset second-order time difference operator is used to approximate the partial differential operator of the wave field variable with respect to time in the elastic wave equation. The differential approximate expression of the time partial differential operator can be derived according to the Taylor series expansion: for:

[0105]

[0106] in h and Δt are the spatial and temporal sampling intervals, respectively. Similarly, we can derive and The differential expression of . Using Taylor series expansion to analyze the truncation error, it can be analyzed that the time difference operator has second-order differential accuracy. Substituting equations (2) and (3) into the first equation in the velocity-stress elastic wave equation, we can obtain:

[0107]

[0108] Formula (4) is the differential discretization equation of the first equation in the elastic wave equation using the hybrid spatial differential operator. The differential discretization equations of the other four equations in the elastic wave equation can be derived using the same method.

[0109] In some embodiments, after obtaining the differential discretization equation of elastic waves by a hybrid spatial differential operator, the dispersion relation of longitudinal and transverse waves in the space-time domain is derived according to the differential discretization equation of elastic waves and the discrete plane wave solution, and then the general solution of the differential coefficient is calculated using the dispersion relation of longitudinal and transverse waves in the space-time domain. The velocity-stress elastic wave equation has a plane wave solution in a homogeneous medium, and its discrete form is:

[0110]

[0111] in and is the amplitude of the plane wave, kx = kcosθ, k z =ksinθ, k is the wave number, θ is the angle between the plane wave propagation direction and the positive direction of the x-axis, ω is the angular frequency, and i is the imaginary unit, i.e. 2 =-1.

[0112] Substituting the discrete plane wave solution into the first discrete equation (4) yields:

[0113]

[0114] in:

[0115]

[0116] Similarly, substituting the discrete plane wave solution into the other four differential discrete equations, we can also obtain four equations about g, f x and f z The total of five equations are combined, and the elimination of and get:

[0117]

[0118] where g 2 is not always zero, we can get:

[0119]

[0120]

[0121] Equations (9) and (10) are the time-space domain longitudinal wave and transverse wave dispersion relations of the elastic wave differential dispersion equation, respectively.

[0122] In some embodiments, since the principle of calculating the general solution of differential coefficients by using the dispersion relation of longitudinal waves and transverse waves in the time and space domain is exactly the same, the general solution of differential coefficients is calculated by taking the dispersion relation of longitudinal waves in the time and space domain as an example. x and f z The trigonometric functions of are expanded by Taylor series to obtain:

[0123]

[0124] where r p =v p Δt / h is the Courant condition number of the longitudinal wave, β j , γ j and d j The expression is:

[0125]

[0126] The left and right sides of formula (11) The corresponding coefficients of are equal to:

[0127]

[0128] The left and right sides of formula (11) (or The corresponding coefficients of )(j=0,1,2,...,M-1) are equal to:

[0129]

[0130]

[0131] According to formula (14), d0 = ±1. When d0 changes from 1 to -1, the corresponding differential coefficients a1, a2, ..., a M It becomes its opposite number, which has no effect on the final result. Here, d0=1, and according to formula (15), we can calculate and deduce:

[0132]

[0133] Substituting formula (16) into formula (12), we get:

[0134]

[0135] Substituting d0=1 into equation (13) yields Then solving equation (17) yields:

[0136]

[0137] Formula (18) is a general solution of differential coefficients derived from the spatial-temporal longitudinal wave dispersion relationship in some embodiments of this specification. p Replace with r s The general solution of the differential coefficients derived from the shear wave dispersion relation in the time and space domain can be obtained, as shown in equation (19).

[0138]

[0139] The same method can be used to derive the general solution of the differential coefficients based on the dispersion relationship between longitudinal and shear waves in the time and space domain when N=2,3,4.

[0140] It can be seen from the general solution expression of the differential coefficient that the general solution of the differential coefficient based on the dispersion relationship between longitudinal and transverse waves in the time and space domain is not only related to the values ​​of M and N, but also to r. p (r s ), r p (r s ) and the propagation speed v of elastic waves in the medium p (vs ), the spatial sampling interval h is related to the time sampling interval Δt, that is, the general solution of the differential coefficient will change with the propagation speed v of the elastic wave in the medium. p (v s ), the spatial sampling interval h and the time sampling interval Δt change adaptively. Compared with the conventional high-order staggered grid finite difference method that only calculates the general solution of the differential coefficient based on the spatial domain dispersion relationship, the embodiment of this specification solves the general solution of the differential coefficient based on the time domain and spatial domain dispersion relationship, which is more in line with the requirements of iterative solution of elastic wave differential discrete equations in the time and space domains, thereby reducing numerical dispersion and improving the accuracy of numerical simulation.

[0141] In some embodiments, reference Figure 6 As shown, a decoupled elastic wave differential dispersion equation is derived according to the hybrid spatial differential operator, and the decoupled elastic wave differential dispersion equation is iteratively solved using the differential coefficient general solution based on the dispersion relationship between longitudinal waves and shear waves in the time and space domain to realize elastic wave numerical simulation and automatically realize the separation of longitudinal waves and shear waves, including:

[0142] S601: Based on the elastic wave equation, the elastic wave equation for decoupling longitudinal and transverse waves is derived;

[0143] S602: using the hybrid spatial difference operator to perform differential discretization on the elastic wave equations of the longitudinal wave and the shear wave decoupling, respectively, to obtain differential discretized equations of the longitudinal wave and the shear wave;

[0144] S603: using the differential coefficient general solution based on the dispersion relationship between longitudinal and transverse waves in the time and space domain to iteratively solve the differential discrete equations of the longitudinal and transverse waves respectively, to realize numerical simulation of elastic waves, and to automatically separate longitudinal and transverse waves.

[0145] The elastic wave equation with decoupling of longitudinal and shear waves can be expressed as:

[0146]

[0147]

[0148]

[0149] in and are the longitudinal and transverse components of the particle vibration velocity field, and are the longitudinal and transverse wave components of the stress field, υ i(i=x,z) is the particle vibration velocity field of the mixed elastic wave. After obtaining the elastic wave equations of the decoupled longitudinal and transverse waves, the hybrid spatial difference operator is used to perform differential discretization on the decoupled longitudinal and transverse wave equations respectively to obtain the differential discretization equations of the longitudinal and transverse waves. Then, the differential coefficients based on the spatial-temporal dispersion relation of the longitudinal wave are used to iteratively solve the differential discretization equation of the longitudinal wave corresponding to equation (21). The differential coefficients based on the spatial-temporal dispersion relation of the transverse wave are used to iteratively solve the differential discretization equation of the transverse wave corresponding to equation (22). The current moment υ is calculated using equation (20) x and z , repeat the above process until the iteration reaches the maximum time set for the numerical simulation.

[0150] Compared with the conventional high-order staggered grid finite difference method, which directly performs numerical simulation on elastic waves, and the simulation results contain both longitudinal waves and transverse waves, and an additional wavelength decoupling operator must be used to obtain the numerical simulation results of pure longitudinal waves and pure transverse waves, the embodiment of the present specification first obtains the general solution of the differential coefficients of longitudinal waves and transverse waves in the time and space domain based on the elastic wave equation, and then decouples the elastic wave equation to obtain the longitudinal wave and transverse wave elastic wave equations respectively, and differentially discretizes the longitudinal wave and transverse wave elastic wave equations through the constructed hybrid space differential operator to obtain the longitudinal wave The longitudinal and shear wave differential discrete equations are finally solved iteratively using the general solution of the longitudinal and shear wave differential coefficients, thereby realizing the numerical simulation of longitudinal and shear waves and automatically realizing the wave field separation of longitudinal and shear waves, so that the numerical simulation results of longitudinal waves are only based on the longitudinal wave differential coefficient solution, and the numerical simulation results of shear waves are only based on the shear wave differential coefficient solution. There is no need to resort to additional wave field decoupling operators to obtain the numerical simulation results of pure longitudinal waves and pure shear waves, which reduces the source of errors and improves the stability of numerical simulation.

[0151] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this specification are all information and data authorized by the user or fully authorized by all parties. The acquisition, storage, use, and processing of data in the technical solutions described in the embodiments of this specification are in compliance with relevant regulations.

[0152] Based on the above-mentioned elastic wave numerical simulation and wave field separation method, the embodiment of this specification also provides a corresponding elastic wave numerical simulation and wave field separation device. The device may include a system (including a distributed system), software (application), module, component, server, client, etc. using the method described in the embodiment of this specification and a device combined with necessary implementation hardware. Based on the same innovative concept, the device in one or more embodiments provided in the embodiment of this specification is as described in the following embodiments. Since the implementation scheme and method of the device to solve the problem are similar, the implementation of the specific device in the embodiment of this specification can refer to the implementation of the aforementioned method, and the repetitions will not be repeated. As used below, the term "unit" or "module" can be a combination of software and / or hardware that implements a predetermined function. Although the device described in the following embodiments is preferably implemented in software, the implementation of hardware, or a combination of software and hardware, is also possible and conceived.

[0153] Specifically, Figure 7 This is a schematic diagram of a module structure of an embodiment of an elastic wave numerical simulation and wave field separation device provided in the embodiment of this specification, referring to Figure 7 As shown, an elastic wave numerical simulation and wave field separation device provided in an embodiment of this specification includes:

[0154] A spatial difference operator construction module 701 is used to construct a hybrid spatial difference operator using coordinate axis grid points and non-coordinate axis grid points, wherein the difference operator at least includes a group of non-coordinate axis grid points that are equidistant from a difference center point;

[0155] A differential discretization module 702 is used to perform differential discretization on the elastic wave equation using the hybrid spatial differential operator to obtain an elastic wave differential discretization equation;

[0156] A dispersion relation acquisition module 703 is used to derive the corresponding time-space domain longitudinal wave and shear wave dispersion relations according to the elastic wave differential dispersion equation and the discrete plane wave solution;

[0157] The differential coefficient calculation module 704 is used to establish a differential coefficient solution equation group based on the longitudinal wave and shear wave dispersion relationship in the time and space domain, and calculate the differential coefficient general solution based on the longitudinal wave and shear wave dispersion relationship in the time and space domain;

[0158] The numerical simulation and wave field separation module 705 is used to derive a decoupled elastic wave differential dispersion equation according to the hybrid spatial differential operator, and iteratively solve the decoupled elastic wave differential dispersion equation using the differential coefficient general solution based on the dispersion relationship between longitudinal and transverse waves in the space-time domain, so as to realize elastic wave numerical simulation and automatically realize the separation of longitudinal and transverse waves.

[0159] The beneficial effects obtained by the device provided in the embodiments of this specification are consistent with the beneficial effects obtained by the above method and will not be repeated here.

[0160] Example 1

[0161] The effect of an elastic wave numerical simulation and wave field separation method according to the present specification is verified by an example below. Figure 8(a)-Figure 8(d) The conventional high-order staggered grid finite difference method (M = 10) and the elastic wave numerical simulation and wave field separation method proposed in this specification (M = 8; N = 1) are given. The particle vibration velocity field υ at 2.4s is generated by elastic wave simulation using a layered medium model. z The wave field snapshot, the horizontal and vertical coordinates represent the model size, that is, the model is 6 km in both longitudinal and lateral directions. Figure 8(a) shows the P-wave and S-wave dispersion curves of the conventional high-order staggered grid finite difference method (M=10), Figure 8(b) shows the P-wave and S-wave dispersion curves obtained by calculating the differential coefficients based on the P-wave dispersion relationship in the time-space domain, Figure 8(c) shows the P-wave and S-wave dispersion curves obtained by calculating the differential coefficients based on the S-wave dispersion relationship in the time-space domain, and Figure 8(d) shows the P-wave and S-wave dispersion curves obtained by calculating the differential coefficients based on the P-wave and S-wave dispersion relationship in the time-space domain respectively; it can be seen that: 1) The conventional high-order staggered grid finite difference method (M=10) uses the standard elastic wave equation for simulation, as shown in the arrow position in Figure 8(a), and both P-wave and S-wave have obvious time dispersion. 2) The present specification proposes a method for numerical simulation and wave field separation of elastic waves (M=8; N=1). When the standard elastic wave equation is used for simulation, and the general solution of the differential coefficient is calculated based only on the dispersion relationship of the longitudinal wave in the time and space domain, as shown in the arrow position in FIG8(b), the transverse wave has obvious spatial dispersion; when the differential coefficient is calculated based only on the dispersion relationship of the transverse wave in the time and space domain, as shown in the arrow position in FIG8(c), the longitudinal wave has a certain time dispersion; when the elastic wave equation with decoupling of longitudinal and transverse waves is used for simulation, and the differential coefficient is calculated based on the dispersion relationship of the longitudinal and transverse waves in the time and space domain, respectively, as shown in FIG8(d), there is no obvious numerical dispersion for both the longitudinal and transverse waves.

[0162] Figure 9(a)-Figure 9(b) The elastic wave numerical simulation and wave field separation method proposed in this specification (M = 8; N = 1) is given. In the elastic wave simulation process using the layered medium model, the particle vibration velocity field υ at the time of 2.4s is obtained by automatically separating the longitudinal and transverse waves. z The longitudinal and shear wave components of the wave field snapshot.

[0163] The elastic wave simulation example of the layered medium model shows that the hybrid staggered grid finite difference method proposed in this manual for solving the elastic wave equation with decoupling of longitudinal and transverse waves can ensure that both longitudinal and transverse waves can obtain high simulation accuracy and automatically achieve the separation of longitudinal and transverse waves.

[0164] Example 2

[0165] Fig.10 This is the P-wave velocity model of the typical complex structural model of the Tarim Basin. The S-wave velocity model is obtained by dividing the P-wave velocity model by 1.8. The horizontal and vertical coordinates in the figure represent the number of grid points in the longitudinal and transverse directions of the model, that is, the model has 1200 grid points in the transverse direction and 525 grid points in the longitudinal direction.

[0166] Figure 11(a)-Figure 11(b) The conventional high-order staggered grid finite difference method (M = 10) and the elastic wave numerical simulation and wave field separation method proposed in this specification (M = 8; N = 1) are given. The local shot gather records (υ z Component). It can be seen that: the conventional high-order staggered grid finite difference method (M = 10) uses the standard elastic wave equation to simulate, as shown in the arrow position in Figure 11 (a), and there is obvious time dispersion in the shot gather record; the elastic wave numerical simulation and wave field separation method (M = 8; N = 1) proposed in this specification uses the elastic wave equation simulation with decoupled longitudinal and transverse waves, and calculates the difference coefficient based on the spatial and temporal dispersion relationship of longitudinal waves or transverse waves, respectively, as shown in Figure 11 (b), and there is no obvious numerical dispersion in the shot gather record.

[0167] The example of elastic wave numerical simulation of a typical complex structural model in the Tarim Basin shows that the elastic wave numerical simulation and wave field separation method proposed in this specification to solve the elastic wave equation with decoupling of longitudinal and transverse waves can ensure that both longitudinal and transverse waves can obtain high simulation accuracy, and has good applicability to elastic wave simulation of complex structural models.

[0168] Reference Fig.12As shown, based on the elastic wave numerical simulation and wave field separation method described above, an embodiment of this specification also provides a computer device 1202, wherein the above method runs on the computer device 1202. The computer device 1202 may include one or more processors 1204, such as one or more central processing units (CPUs), each of which may implement one or more hardware threads. The computer device 1202 may also include any memory 1206, which is used to store any kind of information such as code, settings, data, etc. Non-limitingly, for example, the memory 1206 may include any one or more combinations of the following: any type of RAM, any type of ROM, flash memory device, hard disk, optical disk, etc. More generally, any memory may use any technology to store information. Further, any memory may provide volatile or non-volatile retention of information. Further, any memory may represent a fixed or removable component of the computer device 1202. In one case, when the processor 1204 executes an associated instruction stored in any memory or combination of memories, the computer device 1202 may perform any operation of the associated instruction. The computer device 1202 also includes one or more drive mechanisms 1208 for interacting with any storage, such as a hard disk drive mechanism, an optical disk drive mechanism, etc.

[0169] The computer device 1202 may also include an input / output module 1210 (I / O) for receiving various inputs (via input devices 1212) and for providing various outputs (via output devices 1214). A specific output mechanism may include a presentation device 1216 and an associated graphical user interface (GUI) 1218. In other embodiments, the input / output module 1210 (I / O), input device 1212, and output device 1214 may not be included, and the computer device 1202 may be used as a computer device in a network. The computer device 1202 may also include one or more network interfaces 1220 for exchanging data with other devices via one or more communication links 1222. One or more communication buses 1224 couple the components described above together.

[0170] The communication link 1222 may be implemented in any manner, for example, through a local area network, a wide area network (e.g., the Internet), a point-to-point connection, etc., or any combination thereof. The communication link 1222 may include any combination of hardwired links, wireless links, routers, gateway functions, name servers, etc. governed by any protocol or combination of protocols.

[0171] Corresponding to Figures 1 to 6 In addition to the method shown, an embodiment of the specification also provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above method are executed.

[0172] The embodiment of the present specification also provides a computer-readable instruction, wherein when the processor executes the instruction, the program therein causes the processor to execute the following Figures 1 to 6 The method shown.

[0173] The embodiments of the present specification also provide a computer program product, including at least one instruction or at least one program, wherein the at least one instruction or the at least one program is loaded and executed by a processor to implement the following Figures 1 to 6 The method shown.

[0174] It should be understood that in the various embodiments of this specification, the size of the serial numbers of the above-mentioned processes does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this specification.

[0175] It should also be understood that in the embodiments of this specification, the term "and / or" is only a description of the association relationship of the associated objects, indicating that three relationships can exist. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in this specification generally indicates that the associated objects before and after are in an "or" relationship.

[0176] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in this specification can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described in the above description according to function. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this specification.

[0177] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0178] In the several embodiments provided in this specification, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed can be an indirect coupling or communication connection through some interfaces, devices or units, or it can be an electrical, mechanical or other form of connection.

[0179] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the embodiments of this specification.

[0180] In addition, each functional unit in each embodiment of this specification may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0181] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this specification is essentially or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of this specification. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.

[0182] Specific embodiments are used in this specification to illustrate the principles and implementation methods of this specification. The description of the above embodiments is only used to help understand the methods and core ideas of this specification. At the same time, for those skilled in the art, according to the ideas of this specification, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on this specification.

Claims

1. A method for numerical simulation of elastic waves and wave field separation, characterized in that: The method comprises: Constructing a hybrid spatial difference operator using coordinate axis grid points and non-coordinate axis grid points, wherein the difference operator includes at least one group of non-coordinate axis grid points that are equidistant from a difference center point; Using the hybrid spatial difference operator to perform differential discretization on the elastic wave equation to obtain the elastic wave differential discretization equation; Based on the elastic wave differential discrete equation and discrete plane wave solution, the corresponding time-space domain longitudinal wave and transverse wave dispersion relations are derived; A differential coefficient solution equation group is established based on the longitudinal wave and transverse wave dispersion relationship in the time and space domain, and a differential coefficient general solution based on the longitudinal wave and transverse wave dispersion relationship in the time and space domain is calculated; A decoupled elastic wave differential dispersion equation is derived according to the hybrid spatial differential operator, and the decoupled elastic wave differential dispersion equation is iteratively solved using the differential coefficient general solution based on the dispersion relationship between longitudinal and transverse waves in the space-time domain to realize elastic wave numerical simulation and automatic separation of longitudinal and transverse waves.

2. The method according to claim 1, characterized in that The method of constructing a hybrid spatial difference operator using coordinate axis grid points and non-coordinate axis grid points includes: The coordinate axis grid points with equal distance from the difference center point are regarded as a group. According to the principle of increasing distance from the difference center point, M groups of coordinate axis grid points are selected in sequence to construct M spatial difference operators. The non-coordinate axis grid points with equal distance from the difference center point are regarded as a group. According to the principle of increasing distance from the difference center point, N groups of non-coordinate axis grid points are selected in sequence to construct N spatial difference operators. The M spatial difference operators constructed by the coordinate axis grid points and the N spatial difference operators constructed by the non-coordinate axis grid points are weighted averaged to obtain a hybrid spatial difference operator.

3. The method according to claim 1, characterized in that The step of performing differential discretization on the elastic wave equation using the hybrid spatial differential operator to obtain the elastic wave differential discretization equation includes: Using the hybrid spatial differential operator to perform differential discretization on the spatial partial differential operator in the elastic wave equation, and obtaining a differential expression of the spatial partial differential operator; The time partial differential operator in the elastic wave equation is differentially discretized using a preset second-order time difference operator to obtain a differential expression of the time partial differential operator; Substituting the difference expressions of the spatial partial differential operator and the temporal partial differential operator into the elastic wave equation, the elastic wave differential discretization equation is obtained.

4. The method according to claim 1, characterized in that: The time-space domain longitudinal wave and shear wave dispersion relationship is derived from the following formula: in, λ=λ(x,z) and μ=μ(x,z) are the Lame constants, ρ=ρ(x,z) is the density, h and Δt are the spatial and temporal sampling intervals, respectively, and k x = kcosθ, k z =ksinθ, k is the wave number, ω is the angular frequency, a m , b1 is the differential coefficient.

5. The method according to claim 1, characterized in that The general solution of the differential coefficient based on the dispersion relationship between longitudinal and shear waves in the time and space domain is calculated according to the following formula: in, and are the general solutions of the differential coefficients of longitudinal waves, and are the general solutions of differential coefficients of shear waves, is the Courant condition number of the longitudinal wave, is the Courant condition number of the shear wave, v p and v s are the longitudinal and shear wave velocities, respectively, h and Δt are the spatial and temporal sampling intervals, respectively, and k is the wave number.

6. The method according to claim 1, characterized in that The decoupled elastic wave differential dispersion equation is derived according to the hybrid spatial differential operator, and the decoupled elastic wave differential dispersion equation is iteratively solved by using the differential coefficient general solution based on the dispersion relationship between longitudinal waves and shear waves in the time and space domain to realize elastic wave numerical simulation and automatically realize the separation of longitudinal waves and shear waves, including: Based on the elastic wave equation, the elastic wave equation for decoupling longitudinal and transverse waves is derived; Using the hybrid spatial difference operator, the elastic wave equations of the longitudinal wave and the transverse wave decoupling are differentially discretized to obtain differentially discretized equations of the longitudinal wave and the transverse wave; The differential coefficient general solution based on the dispersion relationship between longitudinal and transverse waves in the time and space domain is used to iteratively solve the differential dispersion equations of the longitudinal and transverse waves respectively, to realize the numerical simulation of elastic waves, and to automatically realize the separation of longitudinal and transverse waves.

7. An elastic wave numerical simulation and wave field separation device, characterized in that: The device comprises: A spatial difference operator construction module, used to construct a hybrid spatial difference operator using coordinate axis grid points and non-coordinate axis grid points, wherein the difference operator at least includes a group of non-coordinate axis grid points that are equidistant from a difference center point; A differential discretization module, used for differentially discretizing the elastic wave equation using the hybrid spatial differential operator to obtain an elastic wave differential discretization equation; A dispersion relation acquisition module, used to derive the corresponding time-space domain longitudinal wave and transverse wave dispersion relations according to the elastic wave differential dispersion equation and the discrete plane wave solution; A differential coefficient calculation module is used to establish a differential coefficient solution equation group based on the longitudinal wave and shear wave dispersion relationship in the time and space domain, and calculate the differential coefficient general solution based on the longitudinal wave and shear wave dispersion relationship in the time and space domain; The numerical simulation and wave field separation module is used to derive the decoupled elastic wave differential dispersion equation according to the hybrid spatial differential operator, and iteratively solve the decoupled elastic wave differential dispersion equation using the differential coefficient general solution based on the dispersion relationship between longitudinal and transverse waves in the time and space domain, so as to realize elastic wave numerical simulation and automatically realize the separation of longitudinal and transverse waves.

8. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the method according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

10. A computer program product, characterized in that The computer program product comprises a computer program, and when the computer program is executed by a processor of a computer device, the method according to any one of claims 1 to 6 is implemented.

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