High-order finite difference method and apparatus for elastic Born first-order scattering wave equation

Abstract

This invention discloses a high-order finite-difference method and apparatus for the elastic Born first-order scattering wave equation. The method includes: constructing the elastic Born multi-order scattering wave equation; constructing the elastic Born first-order scattering wave equation based on the elastic Born multi-order scattering wave equation; constructing an interleaved-grid finite-difference scheme for the elastic Born first-order scattering wave equation based on the elastic Born first-order scattering wave equation and a pre-determined staggered-grid spatial difference scheme and a second-order temporal difference scheme; and constructing an interleaved-grid finite-difference scheme for the PML boundary elastic Born first-order scattering wave equation based on the interleaved-grid finite-difference scheme for the elastic Born first-order scattering wave equation and pre-determined PML absorbing boundary conditions. This technical solution simulates elastic first-order scattered waves generated by underground non-uniform scatterers, avoiding wavefield aliasing of elastic scattered waves, facilitating better analysis of the wavefield characteristics of different types of scatterers, and providing high-precision forward modeling records for subsequent inversion imaging.

Description

Technical Field

[0001] This invention relates to the field of geophysical exploration technology for oil and gas resources, and in particular to a high-order finite difference method and apparatus for the elastic Born first-order scattering wave equation. Background Technology

[0002] With the continuous development of oil and gas exploration technology, the focus of oil and gas exploration has begun to shift from simple reservoirs to complex heterogeneous reservoirs. Complex heterogeneous oil and gas reservoirs no longer satisfy the layered medium assumption, which means that traditional far-field plane wave theory is no longer applicable to solving the prediction problem of such oil and gas reservoirs. The forward and inverse methods based on the wave equation break through the layered medium assumption and are suitable for describing the wave propagation problem in non-homogeneous media.

[0003] Seismic waves are diverse and contain a wealth of information. Among them, using reflected waves for seismic exploration is a relatively mature technology.

[0004] However, when there are special underground structures such as pinch-outs and caves, the reflected signals received by the geophone are weak, resulting in a low signal-to-noise ratio, which is not conducive to characterizing such structures. Seismic scattered waves are waves generated after the incident wave interacts with underground inhomogeneous bodies following the excitation of the seismic source. They contain a large amount of information related to the inhomogeneous scattering bodies. When there are multiple underground scattering bodies, due to the Huygens-Fresnel principle, multiple secondary wave sources will be generated among the scattering bodies. After the secondary wave sources interact with scattering bodies other than themselves, they will generate multi-level scattered waves. The superposition of scattered waves at each level may cause subsequent imaging noise or artifacts. Summary of the Invention

[0005] This invention provides a high-order finite difference method and apparatus for the elastic Born first-order scattering wave equation, which simulates elastic first-order scattering waves generated by underground non-uniform scatterers. It avoids wave field aliasing of elastic scattering waves, facilitates better analysis of the wave field characteristics of different types of scatterers, and provides high-precision forward modeling records for subsequent inversion imaging.

[0006] According to one aspect of the present invention, a higher-order finite-difference method for the elastic Born first-order scattering wave equation is provided, the method comprising:

[0007] Construct the elastic Born multi-stage scattering wave equation;

[0008] Based on the elastic Born multi-stage scattering wave equation, construct the elastic Born first-stage scattering wave equation.

[0009] Based on the elastic Born first-order scattering wave equation and the predetermined staggered grid spatial difference scheme and time second-order difference scheme, a staggered grid finite difference scheme for the elastic Born first-order scattering wave equation is constructed.

[0010] Based on the staggered grid finite difference scheme of the elastic Born first-order scattering wave equation and the predetermined PML absorbing boundary conditions, a staggered grid finite difference scheme of the PML boundary elastic Born first-order scattering wave equation is constructed to analyze the wave field characteristics of different types of scatterers.

[0011] According to another aspect of the invention, a higher-order finite-difference apparatus for the elastic Born first-order scattering wave equation is provided, the apparatus comprising:

[0012] The Elastic Born Multi-Scattering Wave Equation Construction Module is used to construct the elastic Born multi-scattering wave equation.

[0013] The elastic Born first-order scattering wave equation construction module is used to construct the elastic Born first-order scattering wave equation based on the elastic Born multi-order scattering wave equation.

[0014] The module for constructing the staggered grid finite difference scheme of the elastic Born first-order scattering wave equation is used to construct the staggered grid finite difference scheme of the elastic Born first-order scattering wave equation based on the elastic Born first-order scattering wave equation and the predetermined staggered grid spatial difference scheme and time second-order difference scheme.

[0015] The PML boundary elastic Born first-order scattering wave equation staggered grid finite difference scheme construction module is used to construct the PML boundary elastic Born first-order scattering wave equation staggered grid finite difference scheme based on the elastic Born first-order scattering wave equation staggered grid finite difference scheme and the pre-determined PML absorbing boundary conditions, so as to analyze the wave field characteristics of different types of scatterers.

[0016] The technical solution of this invention involves constructing an elastic Born multi-level scattering wave equation; constructing an elastic Born first-level scattering wave equation based on the elastic Born multi-level scattering wave equation; constructing an elastic Born first-level scattering wave equation with a pre-determined staggered grid spatial difference scheme and a second-order temporal difference scheme based on the elastic Born first-level scattering wave equation; and constructing a PML boundary elastic Born first-level scattering wave equation with a pre-determined PML absorbing boundary condition based on the staggered grid finite difference scheme of the elastic Born first-level scattering wave equation. This technical solution simulates elastic first-level scattered waves generated by underground non-uniform scatterers, avoiding wavefield aliasing of elastic scattered waves, facilitating better analysis of the wavefield characteristics of different types of scatterers, and providing high-precision forward modeling records for subsequent inversion imaging.

[0017] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of the present invention, nor is it intended to limit the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart of the high-order finite difference method for the elastic Born first-order scattering wave equation provided in Embodiment 1 of the present invention;

[0020] Figure 2 This is a flowchart of the construction of a higher-order difference scheme for the elastic Born first-order scattering wave equation provided in Embodiment 1 of this application;

[0021] Figure 3 The longitudinal wave scattering point velocity model and the transverse wave scattering point velocity model provided in Embodiment 1 of this application;

[0022] Figure 4 Snapshots of the elastic reference wavefield in the horizontal and vertical directions at three different times provided in Embodiment 1 of this application;

[0023] Figure 5 Snapshots of the elastic Born first-order scattered wave field in the horizontal and vertical directions at three different times provided in Embodiment 1 of this application;

[0024] Figure 6 A comparison chart of horizontal seismic records at different offsets for channels 60, 100, and 140, provided in Embodiment 1 of this application;

[0025] Figure 7 A comparison of vertical seismic records at different offsets for channels 60, 100, and 140 provided in Embodiment 1 of this application;

[0026] Figure 8 This is a schematic diagram of the structure of the high-order finite difference device for the elastic Born first-order scattering wave equation provided in Embodiment 2 of the present invention;

[0027] Figure 9 This is a schematic diagram of the structure of an electronic device that implements the higher-order finite difference method of the elastic Born first-order scattering wave equation according to an embodiment of the present invention. Detailed Implementation

[0028] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0029] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0030] Example 1

[0031] Figure 1 This is a flowchart of a higher-order finite-difference method for the elastic Born first-order scattering wave equation according to Embodiment 1 of the present invention. This embodiment is applicable to the construction of a higher-order finite-difference scheme for the elastic Born first-order scattering wave equation. This method can be executed by a higher-order finite-difference device for the elastic Born first-order scattering wave equation, which can be implemented in hardware and / or software and can be configured in an electronic device. Figure 1 As shown, the method includes:

[0032] S110. Construct the elastic Born multi-stage scattering wave equation.

[0033] In this scheme, based on the model medium decomposition theory, the model parameters are decomposed into background model parameters and disturbance model parameters, as expressed below:

[0034] ;

[0035] in, For model parameters, For background model parameters, These are the parameters of the perturbation model.

[0036] In this embodiment, based on the seismic wave scattering theory, the total wave field is decomposed into a background wave field and a scattered wave field. Correspondingly, the total stress is divided into background stress and scattered stress:

[0037] ;

[0038] Furthermore, we present the two-dimensional constant-density first-order displacement-stress elastic wave equation that satisfies both the total wave field and the background wave field:

[0039] ;

[0040] in, This represents the total velocity displacement of the elastic wave field. This represents the total stress component in the elastic medium. For the focal term, Indicates spatial location, Here, density is constant. For time, For partial differential operators, This is the transpose symbol.

[0041] ;

[0042] in, For background displacement, This represents the background stress component in the elastic medium.

[0043] Specifically, the elastic Born multi-stage scattering wave equation is constructed by subtracting the two equations mentioned above.

[0044] .

[0045] S120. Based on the elastic Born multi-stage scattering wave equation, construct the elastic Born first-stage scattering wave equation.

[0046] Furthermore, the scattered wave field can be further subdivided into:

[0047] ;

[0048] in, This represents the elastic Born multi-stage scattered wave field. This represents the elastic Born first-order scattered wave field. It represents the sum of elastic Born second-order and higher scattered wave fields.

[0049] In this scheme, the elastic Born first-order scattering wave equation can be constructed based on the elastic Born multi-level scattering wave equation and the scattering wave field.

[0050] Specifically, the elastic Born first-order scattering wave equation is constructed using the following formula;

[0051] ;

[0052] in, This represents the elastic Born first-order scattered wave field. For the elastic Born first-order stress components in an elastic medium, the terms on the right side of the equation are... It can be viewed as the source term of the first-order scattering wave equation of elastic Born.

[0053] in, .

[0054] S130. Based on the elastic Born first-order scattering wave equation and the predetermined staggered grid spatial difference scheme and time second-order difference scheme, construct the staggered grid finite difference scheme of the elastic Born first-order scattering wave equation.

[0055] In this scheme, the elastic Born first-order scattering wave equation can be studied by forward modeling under staggered grid finite difference. The principal stress, shear stress and displacement components in different directions are spatially staggered. The principal stress is located at the whole grid point, and the other variables are located at the half grid point.

[0056] Specifically, the difference scheme for the first derivative in spatial directions can be expressed as (with... (Taking direction as an example)

[0057] ;

[0058] in, For parameter variables, For finite difference coefficients, The grid spacing is [split length].

[0059] The second derivative difference scheme in the time direction is as follows (taking the horizontal displacement direction as an example):

[0060] ;

[0061] in, The grid spacing is [split length].

[0062] Furthermore, based on the elastic Born first-order scattering wave equation and the predetermined staggered grid spatial difference scheme and time second-order difference scheme, a staggered grid finite difference scheme for the elastic Born first-order scattering wave equation can be constructed.

[0063] Specifically, the staggered grid finite difference scheme of the elastic Born first-order scattering wave equation is constructed using the following formula;

[0064] ;

[0065] Substituting the stress term into the displacement term in the above equation, we get:

[0066] ;

[0067] Among them, superscript Indicates time, subscript Representation space direction and Points in the direction, Let be the Lamé parameters, which are expressions for the P-wave velocity and S-wave velocity, specifically: .

[0068] S140. Based on the staggered grid finite difference scheme of the elastic Born first-order scattering wave equation and the predetermined PML absorption boundary conditions, construct the staggered grid finite difference scheme of the PML boundary elastic Born first-order scattering wave equation for analysis of the wave field characteristics of different types of scatterers.

[0069] In this embodiment, a perfectly matched layer (PML) is used to absorb boundary conditions to eliminate the influence of artificial boundaries, and finally a high-order finite difference scheme for the elastic Born first-order scattering wave equation with PML boundary is constructed.

[0070] Specifically, the elastic Born first-order scattering wave equation is transformed into the frequency domain;

[0071] ;

[0072] in, Angular frequency, It represents the horizontal and vertical components in the frequency domain.

[0073] Furthermore, an attenuation factor is introduced;

[0074] ;

[0075] in, To represent the decay function, The imaginary unit, ω is the angular frequency.

[0076] The relationship between the first derivatives in complex coordinates and conventional coordinates is as follows:

[0077] ;

[0078] Substituting the above equation into the wave field terms (i.e., the first two terms) of the elastic Born first-order scattering wave equation in the frequency domain, we get:

[0079] ;

[0080] Furthermore, the wave field is split:

[0081] ;

[0082] in, For horizontal displacement wave field Directional components, For horizontal displacement wave field Directional components, For vertical displacement wave field Directional components, For vertical displacement wave field Directional component.

[0083] The wave field term can then be expressed as:

[0084] ;

[0085] Further processing yielded the following results;

[0086] ;

[0087] Perform an inverse Fourier transform on the above equations to the time domain:

[0088] ;

[0089] Furthermore, a staggered-grid finite-difference scheme for the PML boundary elastic Born first-order scattering wave equation is constructed, and the expressions for the second and first time derivatives are substituted into the above equation:

[0090] ;

[0091] Substituting the stress term and the spatial first derivative into the above equation, the horizontal displacement component is expressed in subscript as follows:

[0092] ;

[0093] Among them, superscript Indicates time, subscript Representation space direction and Points in a direction.

[0094] The vertical displacement components are represented by subscripts as follows:

[0095] .

[0096] The technical solution of this invention involves constructing an elastic Born multi-level scattering wave equation; constructing an elastic Born first-level scattering wave equation based on the elastic Born multi-level scattering wave equation; constructing an elastic Born first-level scattering wave equation using an interleaved grid finite difference scheme based on the elastic Born first-level scattering wave equation and a pre-determined interleaved grid spatial difference scheme and a second-order time difference scheme; and constructing a PML boundary elastic Born first-level scattering wave equation using an interleaved grid finite difference scheme based on the interleaved grid finite difference scheme of the elastic Born first-level scattering wave equation and pre-determined PML absorbing boundary conditions. By implementing this technical solution, when simulating special scatterers (holes, pinch-outs, etc.), the simulation results only include the first-level longitudinal wave and converted longitudinal wave scattered wave fields, as well as the first-level transverse wave and converted transverse wave scattered wave fields, avoiding the aliasing phenomenon of scattered wave fields at each level. Starting from the two-dimensional constant-density first-order displacement-stress elastic wave equation, and combining the model medium decomposition theory and seismic wave scattering theory, the elastic Born multi-level scattering wave equation is derived. Then, the elastic scattered wave field is finely divided, and combined with the Born first-order approximation, the elastic Born first-order scattering wave equation is constructed. The above equation is discretized in time and space using staggered grids. Finally, artificial boundary reflections from PML boundary absorption are added to complete the construction of a high-order finite-difference scheme for the PML boundary elastic Born first-order scattering wave equation. This scheme can simulate elastic first-order scattered waves generated by subsurface non-uniform scatterers, avoiding wavefield aliasing and facilitating better analysis of the wavefield characteristics of different types of scatterers, providing a high-precision forward modeling record for subsequent inversion imaging.

[0097] In this scheme, the forward modeling of the wave field using a two-point scattering medium model is used to illustrate and verify the seismic forward modeling effect and accuracy of the higher-order difference scheme of the elastic Born first-order scattering wave equation.

[0098] Specifically, the first step is to provide a flowchart for constructing a higher-order difference scheme for the elastic Born first-order scattering wave equation. Figure 2 The flowchart for constructing a higher-order difference scheme for the elastic Born first-order scattering wave equation provided in Embodiment 1 of this application is as follows: Figure 2 As shown in the flowchart, a higher-order difference scheme for the PML boundary elastic Born first-order scattering wave equation is constructed.

[0099] Step 2: Generate a medium model with two scattering points and a 200*200 grid of longitudinal and transverse waves. Figure 3 The longitudinal wave scattering point velocity model and the transverse wave scattering point velocity model provided in Embodiment 1 of this application are as follows: Figure 2 As shown, the background longitudinal wave velocity Background transverse wave velocity Longitudinal wave velocity of the two scatterers transverse wave velocities of the two scatterers The two scattering points are located at grid points with coordinates (100, 60) and (120, 140) respectively, with a spatial grid spacing of 10m.

[0100] Step 3: Using the two-dimensional constant-density first-order displacement-stress elastic wave equation, respectively, the uniform background model and... Figure 3 The two point scattering models shown are subjected to forward modeling respectively. The difference between the two wave fields obtained from the forward modeling is used to obtain the elastic reference wave field. Figure 4 These are snapshots of the elastic reference wavefield in the horizontal and vertical directions at three different times, provided in Embodiment 1 of this application. Figure 4 (a), (b), and (c) are snapshots of the horizontal wave field at times t=0.7s, t=1.0s, and t=1.4s, respectively. Figure 4 (d), (e), and (f) are snapshots of the wave field of the vertical component at times t=0.7s, t=1.0s, and t=1.4s, respectively. Figure 4 As shown, the wave field obtained by direct subtraction using this method contains multiple levels of scattered wave fields, which has the problem of aliasing of scattered wave fields, and may cause subsequent imaging noise or artifacts.

[0101] Step 4: Realize the forward wave field of the high-order difference scheme of the elastic Born first-order scattering wave equation. Figure 5 These are snapshots of the elastic Born first-order scattered wave fields in the horizontal and vertical directions at three different times, provided in Embodiment 1 of this application. Figure 5 (a), (b), and (c) are snapshots of the horizontal wave field at times t=0.7s, t=1.0s, and t=1.4s, respectively. Figure 5 (d), (e), and (f) are snapshots of the wavefield of the vertical component at times t=0.7s, t=1.0s, and t=1.4s, respectively. (Comparison) Figure 4 The second-order scattered wave field indicated by the white dashed box in the horizontal and vertical components at time t=1.4s does not exist in the forward modeling wave field simulated using the higher-order difference scheme of the elastic Born first-order scattering wave equation. This verifies that the wave field simulated by the elastic Born first-order scattering wave equation only contains the first-order elastic scattered wave field, avoiding the problem of aliasing of scattered wave fields, and providing a good forward modeling basis for subsequent inversion imaging.

[0102] Step 5: Extract traces 60, 100, and 140 of the reference seismic record and compare them with the seismic record simulated by the elastic Born first-order scattering wave equation. Figure 6 This is a comparison chart of horizontal seismic records at different offsets (channels 60, 100, and 140) provided in Embodiment 1 of this application. Figure 6 (a), (b), and (c) are comparison diagrams of the 60th, 100th, and 140th seismic records in the horizontal direction, respectively. Figure 7A comparison chart of vertical seismic records from traces 60, 100, and 140 at different offsets, provided in Embodiment 1 of this application. Figure 7 (a), (b), and (c) are comparison diagrams of the 60th, 100th, and 140th seismic records in the vertical direction, respectively. The solid black line represents the reference record, and the dashed black line represents the elastic Born first-order scattered wave record. As can be seen from the figure, the phase of the elastic Born first-order scattered wave seismic record is completely consistent with the reference record, the amplitude error is within the allowable range of the Born weak scattering approximation, and the overall waveform match is relatively good, which proves the correctness of the numerical simulation of this scheme.

[0103] Example 2

[0104] Figure 8 This is a schematic diagram of the structure of the high-order finite difference device for the elastic Born first-order scattering wave equation provided in Embodiment 2 of the present invention. Figure 8 As shown, the device includes:

[0105] The Elastic Born Multi-Stage Scattering Wave Equation Construction Module 810 is used to construct the elastic Born multi-stage scattering wave equation.

[0106] The elastic Born first-order scattering wave equation construction module 820 is used to construct the elastic Born first-order scattering wave equation based on the elastic Born multi-order scattering wave equation.

[0107] The module 830 for constructing the staggered grid finite difference scheme of the elastic Born first-order scattering wave equation is used to construct the staggered grid finite difference scheme of the elastic Born first-order scattering wave equation based on the elastic Born first-order scattering wave equation and the predetermined staggered grid spatial difference scheme and time second-order difference scheme.

[0108] The PML boundary elastic Born first-order scattering wave equation staggered grid finite difference scheme construction module 840 is used to construct the PML boundary elastic Born first-order scattering wave equation staggered grid finite difference scheme according to the elastic Born first-order scattering wave equation staggered grid finite difference scheme and the predetermined PML absorbing boundary conditions, so as to analyze the wave field characteristics of different types of scatterers.

[0109] Optional, the Elastic Born Multi-Stage Scattering Wave Equation Construction Module 810, specifically used for:

[0110] The elastic Born multi-stage scattering wave equation is constructed using the following formula;

[0111] ;

[0112] in, Indicates density, This represents the elastic Born multi-level scattering wave field. Indicates time, To represent a partial differential operator, This represents the scattered stress component in an elastic medium. Indicates model parameters, This represents the parameters of the perturbation model. Indicates the transpose symbol. Indicates spatial location, This indicates the background displacement.

[0113] Optional, the Elastic Born First-Order Scattering Wave Equation Construction Module 820, specifically used for:

[0114] The elastic Born first-order scattering wave equation is constructed using the following formula;

[0115] ;

[0116] in, This represents the elastic Born first-order scattered wave field. This represents the first-order elastic Born stress component in an elastic medium.

[0117] Optional, the staggered grid finite difference scheme construction module 830 for the elastic Born first-order scattering wave equation is specifically used for:

[0118] The staggered grid spatial difference scheme is constructed using the following formula;

[0119] ;

[0120] in, Indicates parameter variables, Represents the finite difference coefficients. Indicates grid spacing;

[0121] The second-order time difference scheme in the x-direction is constructed using the following formula;

[0122] ;

[0123] in, Indicates the grid spacing.

[0124] Optionally, the staggered grid finite difference scheme construction module 830 for the elastic Born first-order scattering wave equation is also used for:

[0125] The following formula is used to construct the staggered grid finite difference scheme for the elastic Born first-order scattering wave equation;

[0126] ;

[0127] Substituting the stress term into the displacement term in the above equation yields:

[0128] ;

[0129] Among them, superscript Indicates time, subscript Representation space direction and Points in the direction, Let be the Lamé parameters, which are expressions for the P-wave velocity and S-wave velocity, specifically: , .

[0130] Optional, the PML boundary elastic Born first-order scattering wave equation staggered mesh finite difference scheme construction module 840 is specifically used for:

[0131] The staggered grid finite difference scheme for the PML boundary elastic Born first-order scattering wave equation is constructed using the following formula;

[0132] ;

[0133] The horizontal displacement component is represented by subscripts;

[0134] ;

[0135] The vertical displacement component is represented by subscripts;

[0136] ;

[0137] Among them, superscript Indicates time, subscript Representation space direction and Points in a direction.

[0138] The high-order finite difference device for the elastic Born first-order scattering wave equation provided in the embodiments of the present invention can execute the high-order finite difference method for the elastic Born first-order scattering wave equation provided in any embodiment of the present invention, and has the corresponding functional modules and beneficial effects of the execution method.

[0139] Example 3

[0140] Figure 9A schematic diagram of an electronic device 10, which can be used to implement embodiments of the present invention, is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices (e.g., helmets, glasses, watches, etc.), and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the invention described and / or claimed herein.

[0141] like Figure 9 As shown, the electronic device 10 includes at least one processor 11 and a memory, such as a read-only memory (ROM) 12 or a random access memory (RAM) 13, communicatively connected to the at least one processor 11. The memory stores computer programs executable by the at least one processor. The processor 11 can perform various appropriate actions and processes based on the computer program stored in the ROM 12 or loaded from storage unit 18 into the RAM 13. The RAM 13 can also store various programs and data required for the operation of the electronic device 10. The processor 11, ROM 12, and RAM 13 are interconnected via a bus 14. An input / output (I / O) interface 15 is also connected to the bus 14.

[0142] Multiple components in electronic device 10 are connected to I / O interface 15, including: input unit 16, such as keyboard, mouse, etc.; output unit 17, such as various types of displays, speakers, etc.; storage unit 18, such as disk, optical disk, etc.; and communication unit 19, such as network card, modem, wireless transceiver, etc. Communication unit 19 allows electronic device 10 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0143] Processor 11 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of processor 11 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. Processor 11 performs the various methods and processes described above, such as the higher-order finite-difference method for the elastic Born first-order scattering wave equation.

[0144] In some embodiments, the higher-order finite-difference method for the elastic Born first-order scattering wave equation can be implemented as a computer program tangibly contained in a computer-readable storage medium, such as storage unit 18. In some embodiments, part or all of the computer program can be loaded and / or installed on electronic device 10 via ROM 12 and / or communication unit 19. When the computer program is loaded into RAM 13 and executed by processor 11, one or more steps of the higher-order finite-difference method for the elastic Born first-order scattering wave equation described above can be performed. Alternatively, in other embodiments, processor 11 can be configured to execute the higher-order finite-difference method for the elastic Born first-order scattering wave equation by any other suitable means (e.g., by means of firmware).

[0145] Various embodiments of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SoCs), payload-programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0146] Computer programs used to implement the methods of the present invention may be written in any combination of one or more programming languages. These computer programs may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the processor, the computer programs cause the functions / operations specified in the flowcharts and / or block diagrams to be performed. The computer programs may be executed entirely on a machine, partially on a machine, or as a standalone software package, partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0147] In the context of this invention, a computer-readable storage medium can be a tangible medium that may contain or store a computer program for use by or in conjunction with an instruction execution system, apparatus, or device. A computer-readable storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination thereof. Alternatively, a computer-readable storage medium may be a machine-readable signal medium. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0148] To provide interaction with a user, the systems and techniques described herein can be implemented on an electronic device having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the electronic device. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0149] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as data servers), or middleware components (e.g., application servers), or frontend components (e.g., user computers with graphical user interfaces or web browsers through which users can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., communication networks). Examples of communication networks include local area networks (LANs), wide area networks (WANs), blockchain networks, and the Internet.

[0150] A computing system can include clients and servers. Clients and servers are generally located far apart and typically interact through communication networks. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other. The server can be a cloud server, also known as a cloud computing server or cloud host, which is a hosting product within the cloud computing service system to address the shortcomings of traditional physical hosts and VPS services, such as high management difficulty and weak business scalability.

[0151] It should be understood that the various forms of processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this invention can be achieved, and this is not limited herein.

[0152] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A high-order finite difference method for the elastic Born first-order scattering wave equation, characterized in that, include: Construct the elastic Born multi-stage scattering wave equation; Based on the elastic Born multi-stage scattering wave equation, construct the elastic Born first-stage scattering wave equation. Based on the elastic Born first-order scattering wave equation and the predetermined staggered grid spatial difference scheme and time second-order difference scheme, a staggered grid finite difference scheme for the elastic Born first-order scattering wave equation is constructed. Based on the staggered grid finite difference scheme of the elastic Born first-order scattering wave equation and the predetermined PML absorbing boundary conditions, a staggered grid finite difference scheme of the PML boundary elastic Born first-order scattering wave equation is constructed to analyze the wave field characteristics of different types of scatterers. Specifically, based on the staggered-grid finite-difference scheme of the elastic Born first-order scattering wave equation and the predetermined PML absorbing boundary conditions, a staggered-grid finite-difference scheme of the PML boundary elastic Born first-order scattering wave equation is constructed, including: The staggered grid finite difference scheme for the PML boundary elastic Born first-order scattering wave equation is constructed using the following formula; ； The horizontal displacement component is represented by subscripts; ； The vertical displacement component is represented by subscripts; ； Among them, superscript Indicates time, subscript Representation space direction and Points in a direction.

2. The method according to claim 1, characterized in that, Constructing the elastic Born multi-level scattering wave equation, including: The elastic Born multi-stage scattering wave equation is constructed using the following formula; ； in, Indicates density, This represents the elastic Born multi-level scattering wave field. Indicates time, To represent a partial differential operator, This represents the scattered stress component in an elastic medium. Indicates model parameters, This represents the parameters of the perturbation model. Indicates the transpose symbol. Indicates spatial location, This indicates the background displacement.

3. The method according to claim 1, characterized in that, Based on the elastic Born multi-stage scattering wave equation, the elastic Born first-stage scattering wave equation is constructed, including: The elastic Born first-order scattering wave equation is constructed using the following formula; ； in, This represents the elastic Born first-order scattered wave field. This represents the first-order Born stress component in an elastic medium. Indicates density, Indicates time, To represent a partial differential operator, For background model parameters, This represents the parameters of the perturbation model. This indicates the background displacement.

4. The method according to claim 1, characterized in that, The process of determining the staggered grid spatial difference scheme and the second-order temporal difference scheme includes: The staggered grid spatial difference scheme is constructed using the following formula; ； in, Indicates parameter variables, Represents the finite difference coefficients. Indicates grid spacing; The second-order time difference scheme in the x-direction is constructed using the following formula; ； in, Indicates time, Indicates direction.

5. The method according to claim 4, characterized in that, Based on the elastic Born first-order scattering wave equation and the pre-determined staggered grid spatial difference scheme and time second-order difference scheme, a staggered grid finite difference scheme for the elastic Born first-order scattering wave equation is constructed, including: The following formula is used to construct the staggered grid finite difference scheme for the elastic Born first-order scattering wave equation; ； Substituting the stress term into the displacement term in the above equation yields: ； Among them, superscript Indicates time, subscript Representation space direction and Points in the direction, Let be the Lamé parameters, which are expressions for the P-wave velocity and S-wave velocity, specifically: , , Indicates time.

6. A high-order finite difference device for the elastic Born first-order scattering wave equation, characterized in that, include: The Elastic Born Multi-Scattering Wave Equation Construction Module is used to construct the elastic Born multi-scattering wave equation. The elastic Born first-order scattering wave equation construction module is used to construct the elastic Born first-order scattering wave equation based on the elastic Born multi-order scattering wave equation. The module for constructing the staggered grid finite difference scheme of the elastic Born first-order scattering wave equation is used to construct the staggered grid finite difference scheme of the elastic Born first-order scattering wave equation based on the elastic Born first-order scattering wave equation and the predetermined staggered grid spatial difference scheme and time second-order difference scheme. The PML boundary elastic Born first-order scattering wave equation staggered grid finite difference scheme construction module is used to construct the PML boundary elastic Born first-order scattering wave equation staggered grid finite difference scheme according to the elastic Born first-order scattering wave equation staggered grid finite difference scheme and the pre-determined PML absorbing boundary conditions, so as to analyze the wave field characteristics of different types of scatterers. The PML boundary elastic Born first-order scattering wave equation staggered mesh finite difference scheme construction module is specifically used for: The staggered grid finite difference scheme for the PML boundary elastic Born first-order scattering wave equation is constructed using the following formula; ； The horizontal displacement component is represented by subscripts; ； The vertical displacement component is represented by subscripts; ； Among them, superscript Indicates time, subscript Representation space direction and Points in a direction.

7. The apparatus according to claim 6, characterized in that, The Elastic Born Multilevel Scattering Wave Equation Construction Module is specifically used for: The elastic Born multi-stage scattering wave equation is constructed using the following formula; ； in, Indicates density, This represents the elastic Born multi-level scattering wave field. Indicates time, To represent a partial differential operator, This represents the scattered stress component in an elastic medium. Indicates model parameters, This represents the parameters of the perturbation model. Indicates the transpose symbol. Indicates spatial location, This indicates the background displacement.

8. The apparatus according to claim 6, characterized in that, The module for constructing the elastic Born first-order scattering wave equation is specifically used for: The elastic Born first-order scattering wave equation is constructed using the following formula; ； in, This represents the elastic Born first-order scattered wave field. This represents the first-order Born stress component in an elastic medium. Indicates density, Indicates time, To represent a partial differential operator, For background model parameters, This represents the parameters of the perturbation model. This indicates the background displacement.

9. The apparatus according to claim 6, characterized in that, The module for constructing the staggered-grid finite-difference scheme of the elastic Born first-order scattering wave equation is specifically used for: The staggered grid spatial difference scheme is constructed using the following formula; ； in, Indicates parameter variables, Represents the finite difference coefficients. Indicates grid spacing; The second-order time difference scheme in the x-direction is constructed using the following formula; ； in, Indicates time, Indicates direction.

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