Elastic wave reverse time migration method and device, electronic equipment and medium

Abstract

This application discloses a method, apparatus, electronic device, and medium for elastic wave reverse-time migration. The method may include: obtaining a wavefield extension formula based on the first-order velocity-stress elastic wave equation of a two-phase medium; obtaining a wavefield separation formula; sequentially performing wavefield extension and wavefield separation on a target shot to obtain forward and reverse propagation wavefield extensions, storing the pure P-wave wavefield value at each moment; extracting imaging values ​​from the pure P-wave wavefield values ​​using cross-correlation imaging conditions; repeating the above steps for all shots to obtain an elastic wave reverse-time migration superimposed profile. This invention performs elastic wavefield separation in forward and reverse migration extension operators under a two-phase medium model to obtain the pure P-wave component in the two-phase medium, and uses the pure P-wave component for migration imaging. Compared to traditional two-phase medium elastic wave reverse-time migration methods that use velocity components containing mixed wavefields for imaging, the imaging accuracy is significantly improved.

Description

Technical Field

[0001] This invention relates to the field of geophysical exploration technology, and more specifically, to an elastic wave reverse time migration method, apparatus, electronic device, and medium. Background Technology

[0002] With the development of seismic exploration, acoustic wave reverse time migration and elastic wave reverse time migration based on single-phase medium models are difficult to accurately describe underground media and meet complex engineering requirements, especially when dealing with underground porous media containing fluids. In reality, oil and gas reservoirs are two-phase media with both solid and fluid states.

[0003] Traditional methods simplify reservoirs as single-phase elastic media, thus ignoring the coupling effect between the solid and fluid phases, resulting in a biased description of seismic wave propagation. It is more meaningful to establish a two-phase medium model that better reflects the actual strata. However, traditional two-phase medium elastic wave reverse time migration only images the vertical velocity component containing mixed wave fields. Since P-waves and S-waves coexist and the wave field in two-phase media is relatively complex, the resulting imaging profiles are not only noisy and of low quality, but also contain false structures caused by the coexistence of P-waves and S-waves.

[0004] Therefore, it is necessary to develop an elastic wave reverse-time migration method, device, electronic equipment, and medium based on two-phase medium wavefield separation. This method utilizes a two-phase medium model that better reflects actual geological conditions to more accurately describe the subsurface medium. Traditional reverse-time migration methods based on single-phase medium models have some deviations in describing the actual medium. Furthermore, elastic wavefield separation is performed in the forward and reverse migration extension operators under the two-phase medium model to obtain the pure P-wave component in the two-phase medium. Migration imaging is then performed using the pure P-wave component. Compared to the traditional two-phase medium elastic wave reverse-time migration method that uses velocity components containing mixed wavefields for imaging, the imaging accuracy is significantly improved.

[0005] The information disclosed in the background section of this invention is intended only to enhance the understanding of the general background of this invention, and should not be construed as an admission or in any way implying that such information constitutes prior art known to those skilled in the art. Summary of the Invention

[0006] This invention proposes an elastic wave reverse time migration method, device, electronic device, and medium. The elastic wave field is separated in the forward and reverse migration extension operators under a two-phase medium model to obtain the pure longitudinal wave component in the two-phase medium. The pure longitudinal wave component is used for migration imaging. Compared with the traditional two-phase medium elastic wave reverse time migration method that uses velocity components containing mixed wave fields for imaging, the imaging accuracy is significantly improved.

[0007] In a first aspect, embodiments of this disclosure provide a method for elastic wave reverse-time migration, including:

[0008] Based on the first-order velocity-stress elastic wave equation of a two-phase medium, the wave field extension formula is obtained.

[0009] Obtain the wave field separation formula;

[0010] For the target gun, wavefield extension and wavefield separation are performed sequentially to obtain forward propagation wavefield extension and reverse propagation wavefield extension, and the pure longitudinal wavefield value at each moment is stored.

[0011] Imaging values ​​are extracted from pure P-wave field values ​​using cross-correlation imaging conditions;

[0012] Repeat the above steps for all shots to obtain the elastic wave reverse time migration superposition profile.

[0013] Preferably, obtaining the wavefield extension formula includes:

[0014] The wave field extension formula is obtained by using the first-order velocity-stress elastic wave equation of the two-phase medium and the PML absorbing boundary conditions, and by employing the second-order time and tenth-order spatial high-order staggered grid finite difference method.

[0015] Preferably, the wavefield extension formula is:

[0016]

[0017] Among them, v x Let x be the velocity component, k be the current time loop number, Δt be the time interval, Δx and Δz be the grid size in the x and z directions, and d be the distance from the x-axis to the z-axis. x d z Let ρ be the decay function in the x and z directions. 11 ρ is the equivalent density of the solid phase. 22 ρ is the equivalent density of the flow phase. 12 is the density coupling coefficient between the solid and the fluid phase. For finite difference coefficients, τ xx τ is the normal stress in the x-direction. xz Where is the shear stress, S is the effective pressure of the flow phase, and b is the dissipation coefficient.

[0018] Preferably, obtaining the wavefield separation formula includes:

[0019] By using Helmholtz vortex theory for divergence and curl fields, the longitudinal and transverse wave fields are decoupled and separated to achieve wave field separation in a two-phase medium, and the wave field separation formula is obtained.

[0020] Preferably, the wavefield separation formula is:

[0021]

[0022] in, Φ and ψ are the longitudinal wave velocity potentials in the solid and fluid phases, respectively; Ψ and ψ are the transverse wave velocity potentials in the solid and fluid phases, respectively; θ is the solid phase divergence field; Θ is the fluid phase divergence field; ω is the solid phase curl field; and Ω is the fluid phase curl field.

[0023] Preferably, the imaging values ​​are extracted using formula (3):

[0024]

[0025] Where Image(x, z) is the image value at the point (x, z) in space. For the extension of the forward wave field, It is an extension of the reverse propagation wave field.

[0026] Preferably, obtaining the elastic wave reverse-time migration superposition profile includes:

[0027] The imaging values ​​of all shots are superimposed according to the observation system to obtain the elastic wave reverse time migration superimposed profile.

[0028] As one specific implementation of this disclosure,

[0029] Secondly, embodiments of this disclosure also provide an elastic wave reverse-time offset device, comprising:

[0030] The wave field extension formula acquisition module obtains the wave field extension formula based on the first-order velocity-stress elastic wave equation of a two-phase medium.

[0031] The wavefield separation formula acquisition module retrieves the wavefield separation formula.

[0032] The wavefield extension and separation module sequentially performs wavefield extension and wavefield separation on the target shot to obtain forward propagation wavefield extension and reverse propagation wavefield extension, and stores the pure longitudinal wavefield value at each moment.

[0033] The imaging module extracts imaging values ​​from pure P-wave field values ​​using cross-correlation imaging conditions.

[0034] The stacking module repeats the above steps for all shots to obtain the elastic wave reverse time migration stacking profile.

[0035] Preferably, obtaining the wavefield extension formula includes:

[0036] The wave field extension formula is obtained by using the first-order velocity-stress elastic wave equation of the two-phase medium and the PML absorbing boundary conditions, and by employing the second-order time and tenth-order spatial high-order staggered grid finite difference method.

[0037] Preferably, the wavefield extension formula is:

[0038]

[0039] Among them, vx Let x be the velocity component, k be the current time loop number, Δt be the time interval, Δx and Δz be the grid size in the x and z directions, and d be the distance from the x-axis to the z-axis. x d z Let ρ be the decay function in the x and z directions. 11 ρ is the equivalent density of the solid phase. 22 ρ is the equivalent density of the flow phase. 12 is the density coupling coefficient between the solid and the fluid phase. For finite difference coefficients, τ xx τ is the normal stress in the x-direction. xz Where is the shear stress, S is the effective pressure of the flow phase, and b is the dissipation coefficient.

[0040] Preferably, obtaining the wavefield separation formula includes:

[0041] By using Helmholtz vortex theory for divergence and curl fields, the longitudinal and transverse wave fields are decoupled and separated to achieve wave field separation in a two-phase medium, and the wave field separation formula is obtained.

[0042] Preferably, the wavefield separation formula is:

[0043]

[0044] in, Φ and ψ are the longitudinal wave velocity potentials in the solid and fluid phases, respectively; Ψ and ψ are the transverse wave velocity potentials in the solid and fluid phases, respectively; θ is the solid phase divergence field; Θ is the fluid phase divergence field; ω is the solid phase curl field; and Ω is the fluid phase curl field.

[0045] Preferably, the imaging values ​​are extracted using formula (3):

[0046]

[0047] Where Image(x, z) is the image value at the point (x, z) in space. For the extension of the forward wave field, It is an extension of the reverse propagation wave field.

[0048] Preferably, obtaining the elastic wave reverse-time migration superposition profile includes:

[0049] The imaging values ​​of all shots are superimposed according to the observation system to obtain the elastic wave reverse time migration superimposed profile.

[0050] Thirdly, embodiments of this disclosure also provide an electronic device, the electronic device comprising:

[0051] Memory, which stores executable instructions;

[0052] A processor that executes the executable instructions in the memory to implement the elastic wave reverse time migration method.

[0053] Fourthly, embodiments of this disclosure also provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the elastic wave reverse time offset method.

[0054] Its beneficial effects are as follows: it solves the problem that reverse-time migration of single-phase medium models cannot accurately describe the actual underground medium; it also solves the problem that existing reverse-time migration methods for two-phase media use velocity components containing mixed wave fields without wavefield separation for imaging, resulting in high noise in the imaging profile and the presence of spurious structures. The pure P-wave imaging profile of the two-phase medium model obtained by this invention has significantly improved accuracy compared to traditional methods, with significantly reduced noise and no spurious structures.

[0055] The methods and apparatus of the present invention have other features and advantages that will be apparent from or will be set forth in detail in the accompanying drawings and following detailed description, which together serve to explain the particular principles of the invention. Attached Figure Description

[0056] The above and other objects, features and advantages of the present invention will become more apparent from the more detailed description of exemplary embodiments of the invention in conjunction with the accompanying drawings, wherein the same reference numerals generally represent the same parts.

[0057] Figure 1 A flowchart illustrating the steps of an elastic wave reverse time migration method according to an embodiment of the present invention is shown.

[0058] Figure 2 A schematic diagram of a two-dimensional biphase medium interlaced grid according to an embodiment of the present invention is shown.

[0059] Figure 3 A schematic diagram of the PML absorption boundary according to an embodiment of the present invention is shown.

[0060] Figure 4a and Figure 4b The diagram shows a wave field snapshot at 0.25s after forward modeling of the solid longitudinal wave component and the solid transverse wave component following wave field separation in a two-phase medium according to an embodiment of the present invention.

[0061] Figure 5a and Figure 5bThe diagram shows a wave field snapshot at 0.25s after forward modeling of the longitudinal wave component and the transverse wave component of the flow phase following wave field separation in a two-phase medium according to an embodiment of the present invention.

[0062] Figure 6 A schematic diagram of a two-phase medium four-layer floor mat model according to an embodiment of the present invention is shown.

[0063] Figure 7a and Figure 7b Schematic diagrams of a pure longitudinal wave imaging profile after wavefield separation and a mixed wavefield imaging profile of the vertical velocity components of a two-phase medium without wavefield separation are shown respectively, according to an embodiment of the present invention.

[0064] Figure 8 A block diagram of an elastic wave reverse time offset device according to an embodiment of the present invention is shown.

[0065] Explanation of reference numerals in the attached figures:

[0066] 201. Wavefield continuation formula acquisition module; 202. Wavefield separation formula acquisition module; 203. Continuation separation module; 204. Imaging module; 205. Superposition module. Detailed Implementation

[0067] Preferred embodiments of the invention will now be described in more detail. While preferred embodiments of the invention are described below, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein.

[0068] This invention provides a method for reverse time migration of elastic waves, comprising:

[0069] Based on the first-order velocity-stress elastic wave equation of a two-phase medium, the wave field extension formula is obtained.

[0070] Obtain the wave field separation formula;

[0071] For the target gun, wavefield extension and wavefield separation are performed sequentially to obtain forward propagation wavefield extension and reverse propagation wavefield extension, and the pure longitudinal wavefield value at each moment is stored.

[0072] Imaging values ​​are extracted from pure P-wave field values ​​using cross-correlation imaging conditions;

[0073] Repeat the above steps for all shots to obtain the elastic wave reverse time migration superposition profile.

[0074] In one example, the wavefield continuation formula is obtained by:

[0075] By using the first-order velocity-stress elastic wave equation of two-phase medium and the PML absorbing boundary condition, and employing the high-order staggered grid finite difference method of second-order time and tenth-order space, the wave field extension formula is obtained.

[0076] In one example, the wave field extension formula is:

[0077]

[0078] Among them, v x Let x be the velocity component, k be the current time loop number, Δt be the time interval, Δx and Δz be the grid size in the x and z directions, and d be the distance from the x-axis to the z-axis. x d z Let ρ be the decay function in the x and z directions. 11 ρ is the equivalent density of the solid phase. 22 ρ is the equivalent density of the flow phase. 12 is the density coupling coefficient between the solid and the fluid phase. For finite difference coefficients, τ xx τ is the normal stress in the x-direction. xz Where is the shear stress, S is the effective pressure of the fluid phase, and b is the dissipation coefficient, which is calculated from permeability, porosity, and fluid viscosity.

[0079] In one example, the formula for obtaining wavefield separation includes:

[0080] By using Helmholtz vortex theory of divergence and curl fields, the longitudinal and transverse wave fields are decoupled and separated to achieve wave field separation in a two-phase medium, and the wave field separation formula is obtained.

[0081] In one example, the wave field separation formula is:

[0082]

[0083] in, Φ and ψ are the longitudinal wave velocity potentials in the solid and fluid phases, respectively; Ψ and ψ are the transverse wave velocity potentials in the solid and fluid phases, respectively; θ is the solid phase divergence field; Θ is the fluid phase divergence field; ω is the solid phase curl field; and Ω is the fluid phase curl field.

[0084] In one example, the imaging values ​​are extracted using formula (3):

[0085]

[0086] Where Image(x, z) is the image value at the point (x, z) in space. For the extension of the forward wave field, It is an extension of the reverse propagation wave field.

[0087] In one example, obtaining the elastic wave reverse time migration stacked profile includes:

[0088] The imaging values ​​of all shots are superimposed according to the observation system to obtain the elastic wave reverse time migration superimposed profile.

[0089] Specifically, input the parameters related to the seismic record and the two-phase medium model; based on Biot theory, derive the first-order velocity-stress elastic wave equation for the two-phase medium as follows:

[0090]

[0091] By combining the first-order velocity-stress elastic wave equation of the two-phase medium with the PML absorbing boundary conditions, the higher-order staggered mesh finite difference of the two-phase medium is derived as the wave field extension operator. Equation (1) is based on v x The difference scheme for example is the wavefield extension formula, and similarly, v can be derived. z V x V z τ xx τ zz τ xz 、S.

[0092] During the wave field extension process, the Helmholtz vortex theory of divergence field and curl field is used to decouple and separate the longitudinal and transverse wave fields, thereby realizing the wave field separation of the two-phase medium.

[0093] The longitudinal wave velocity potentials in the solid phase and the fluid phase are defined as follows: Let ψ and Ψ be the transverse wave velocity potentials in the solid phase and the flow direction, respectively. Then the velocities v and V in the solid and flow phases satisfy the following relationship:

[0094]

[0095] The divergence field and curl field of the particle vibration velocity vector in the solid phase and the fluid phase are defined as follows:

[0096]

[0097] Substituting formula (6) into formula (5) yields formula (2), which is the wave field separation formula.

[0098] The above-mentioned wavefield extension and wavefield separation formulas are used to perform forward propagation wavefield extension with the seismic source as input and reverse propagation wavefield extension with the seismic record response as input, while storing the pure P-wave wavefield value at each time moment.

[0099] The imaging values ​​of the pure longitudinal wave component are extracted using the cross-correlation imaging condition by formula (3); the above steps are repeated for all shots, and then the imaging values ​​of all shots are superimposed according to the observation system to output the final elastic wave reverse time migration superposition profile based on the separation of the two-phase medium wave field.

[0100] The present invention also provides an elastic wave reverse time offset device, comprising:

[0101] The wave field extension formula acquisition module obtains the wave field extension formula based on the first-order velocity-stress elastic wave equation of a two-phase medium.

[0102] The wavefield separation formula acquisition module retrieves the wavefield separation formula.

[0103] The wavefield extension and separation module sequentially performs wavefield extension and wavefield separation on the target shot to obtain forward propagation wavefield extension and reverse propagation wavefield extension, and stores the pure longitudinal wavefield value at each moment.

[0104] The imaging module extracts imaging values ​​from pure P-wave field values ​​using cross-correlation imaging conditions.

[0105] The stacking module repeats the above steps for all shots to obtain the elastic wave reverse time migration stacking profile.

[0106] In one example, the wavefield continuation formula is obtained by:

[0107] By using the first-order velocity-stress elastic wave equation of two-phase medium and the PML absorbing boundary condition, and employing the high-order staggered grid finite difference method of second-order time and tenth-order space, the wave field extension formula is obtained.

[0108] In one example, the wave field extension formula is:

[0109]

[0110] Among them, v x Let x be the velocity component, k be the current time loop number, Δt be the time interval, Δx and Δz be the grid size in the x and z directions, and d be the distance from the x-axis to the z-axis. x d z Let ρ be the decay function in the x and z directions. 11 ρ is the equivalent density of the solid phase. 22 ρ is the equivalent density of the flow phase. 12 is the density coupling coefficient between the solid and the fluid phase. For finite difference coefficients, τ xx τ is the normal stress in the x-direction. xz Where is the shear stress, S is the effective pressure of the flow phase, and b is the dissipation coefficient.

[0111] In one example, the formula for obtaining wavefield separation includes:

[0112] By using Helmholtz vortex theory of divergence and curl fields, the longitudinal and transverse wave fields are decoupled and separated to achieve wave field separation in a two-phase medium, and the wave field separation formula is obtained.

[0113] In one example, the wave field separation formula is:

[0114]

[0115] in, Φ and ψ are the longitudinal wave velocity potentials in the solid and fluid phases, respectively; Ψ and ψ are the transverse wave velocity potentials in the solid and fluid phases, respectively; θ is the solid phase divergence field; Θ is the fluid phase divergence field; ω is the solid phase curl field; and Ω is the fluid phase curl field.

[0116] In one example, the imaging values ​​are extracted using formula (3):

[0117]

[0118] Where Image(x, z) is the image value at the point (x, z) in space. For the extension of the forward wave field, It is an extension of the reverse propagation wave field.

[0119] In one example, obtaining the elastic wave reverse time migration stacked profile includes:

[0120] The imaging values ​​of all shots are superimposed according to the observation system to obtain the elastic wave reverse time migration superimposed profile.

[0121] Specifically, input the parameters related to the seismic record and the two-phase medium model; based on Biot theory, derive the first-order velocity-stress elastic wave equation for the two-phase medium as follows:

[0122]

[0123] By combining the first-order velocity-stress elastic wave equation of the two-phase medium with the PML absorbing boundary conditions, the higher-order staggered mesh finite difference of the two-phase medium is derived as the wave field extension operator. Equation (1) is based on v x The difference scheme for example is the wavefield extension formula, and similarly, v can be derived. z V x V z τ xx τ zz τ xz 、S.

[0124] During the wave field extension process, the Helmholtz vortex theory of divergence field and curl field is used to decouple and separate the longitudinal and transverse wave fields, thereby realizing the wave field separation of the two-phase medium.

[0125] The longitudinal wave velocity potentials in the solid phase and the fluid phase are defined as follows: Let ψ and Ψ be the transverse wave velocity potentials in the solid phase and the flow phase, respectively. Then the velocities v and V in the solid and flow phases satisfy the following relationship.

[0126]

[0127] The divergence field and curl field of the particle vibration velocity vector in the solid phase and the fluid phase are defined as follows:

[0128]

[0129] Substituting formula (6) into formula (5) yields formula (2), which is the wave field separation formula.

[0130] The above-mentioned wavefield extension and wavefield separation formulas are used to perform forward propagation wavefield extension with the seismic source as input and reverse propagation wavefield extension with the seismic record response as input, while storing the pure P-wave wavefield value at each time moment.

[0131] The imaging values ​​of the pure longitudinal wave component are extracted using the cross-correlation imaging condition by formula (3); the above steps are repeated for all shots, and then the imaging values ​​of all shots are superimposed according to the observation system to output the final elastic wave reverse time migration superposition profile based on the separation of the two-phase medium wave field.

[0132] The present invention also provides an electronic device, comprising: a memory storing executable instructions; and a processor executing the executable instructions in the memory to implement the above-described elastic wave reverse time offset method.

[0133] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described elastic wave reverse time offset method.

[0134] To facilitate understanding of the solutions and effects of the embodiments of the present invention, four specific application examples are given below. Those skilled in the art should understand that these examples are merely for the purpose of understanding the present invention, and any specific details therein are not intended to limit the present invention in any way.

[0135] Example 1

[0136] Figure 1 A flowchart illustrating the steps of an elastic wave reverse time migration method according to an embodiment of the present invention is shown.

[0137] like Figure 1 As shown, the elastic wave reverse time migration method includes: Step 101, obtaining the wavefield extension formula based on the first-order velocity-stress elastic wave equation of a two-phase medium; Step 102, obtaining the wavefield separation formula; Step 103, performing wavefield extension and wavefield separation sequentially on the target shot to obtain the forward propagation wavefield extension and the reverse propagation wavefield extension, and storing the pure P-wave wavefield value at each moment; Step 104, extracting the imaging value from the pure P-wave wavefield value through cross-correlation imaging conditions; Step 105, repeating the above steps for all shots to obtain the elastic wave reverse time migration superimposed profile.

[0138] Figure 2A schematic diagram of a two-dimensional two-phase medium staggered grid according to an embodiment of the present invention is shown, wherein the applied velocity and stress are respectively placed on different grid nodes by using staggered grid finite difference.

[0139] Figure 3 A schematic diagram of a PML absorption boundary according to an embodiment of the present invention is shown, in which PML absorption boundary conditions are used to absorb and attenuate the boundary and corner regions.

[0140] Figure 4a and Figure 4b The diagram shows a wave field snapshot at 0.25s after forward modeling of the solid longitudinal wave component and the solid transverse wave component following wave field separation in a two-phase medium according to an embodiment of the present invention.

[0141] Figure 5a and Figure 5b The diagram shows a wave field snapshot at 0.25s after forward modeling of the longitudinal wave component and the transverse wave component of the flow phase following wave field separation in a two-phase medium according to an embodiment of the present invention.

[0142] Figure 6 A schematic diagram of a two-phase medium four-layer ground surface model according to an embodiment of the present invention is shown, using the two-phase medium four-layer graben model shown in the figure as input, and the seismic record obtained by forward modeling using this model as input.

[0143] Figure 7a and Figure 7b Schematic diagrams of a pure longitudinal wave imaging profile after wavefield separation and a mixed wavefield imaging profile of the vertical velocity components of a two-phase medium without wavefield separation are shown respectively according to an embodiment of the present invention. The offset imaging profile obtained by this method has significantly reduced noise, higher imaging accuracy, and does not contain false structures.

[0144] The reverse time migration method based on the separation of the two-phase medium elastic wave field was successfully used to perform migration imaging on a four-layer concave model. The noise was significantly reduced on the migration superposition profile without Laplace filtering, and the imaging accuracy was higher. At the same time, the false structure phenomenon that occurs on the conventional migration profile due to the complexity of the two-phase medium elastic wave field was suppressed. The effect was significantly improved compared with the conventional two-phase medium elastic wave reverse time migration imaging effect.

[0145] Example 2

[0146] Figure 8 A block diagram of an elastic wave reverse time offset device according to an embodiment of the present invention is shown.

[0147] like Figure 8 As shown, the elastic wave counter-time offset device includes:

[0148] The wave field extension formula acquisition module 201 obtains the wave field extension formula based on the first-order velocity-stress elastic wave equation of a two-phase medium.

[0149] Wavefield separation formula acquisition module 202 acquires the wavefield separation formula;

[0150] The extension and separation module 203 performs wavefield extension and wavefield separation sequentially for the target shot to obtain forward propagation wavefield extension and reverse propagation wavefield extension, and stores the pure longitudinal wavefield value at each moment.

[0151] Imaging module 204 extracts imaging values ​​from pure longitudinal wave field values ​​through cross-correlation imaging conditions;

[0152] The stacking module 205 repeats the above steps for all shots to obtain the elastic wave reverse time migration stacking profile.

[0153] As an optional approach, the wavefield extension formula can be obtained as follows:

[0154] By using the first-order velocity-stress elastic wave equation of two-phase medium and the PML absorbing boundary condition, and employing the high-order staggered grid finite difference method of second-order time and tenth-order space, the wave field extension formula is obtained.

[0155] As an alternative, the wavefield extension formula is:

[0156]

[0157] Among them, v x Let x be the velocity component, k be the current time loop number, Δt be the time interval, Δx and Δz be the grid size in the x and z directions, and d be the distance from the x-axis to the z-axis. x d z Let ρ be the decay function in the x and z directions. 11 ρ is the equivalent density of the solid phase. 22 ρ is the equivalent density of the flow phase. 12 is the density coupling coefficient between the solid and the fluid phase. For finite difference coefficients, τ xx τ is the normal stress in the x-direction. xz Where is the shear stress, S is the effective pressure of the flow phase, and b is the dissipation coefficient.

[0158] As an optional approach, the wavefield separation formula can be obtained as follows:

[0159] By using Helmholtz vortex theory of divergence and curl fields, the longitudinal and transverse wave fields are decoupled and separated to achieve wave field separation in a two-phase medium, and the wave field separation formula is obtained.

[0160] As an alternative, the wavefield separation formula is:

[0161]

[0162] in, Φ and ψ are the longitudinal wave velocity potentials in the solid and fluid phases, respectively; Ψ and ψ are the transverse wave velocity potentials in the solid and fluid phases, respectively; θ is the solid phase divergence field; Θ is the fluid phase divergence field; ω is the solid phase curl field; and Ω is the fluid phase curl field.

[0163] As an optional approach, the imaging values ​​can be extracted using formula (3):

[0164]

[0165] Where Image(x, z) is the image value at the point (x, z) in space. For the extension of the forward wave field, It is an extension of the reverse propagation wave field.

[0166] As an optional approach, obtaining the elastic wave reverse-time migration superposition profile includes:

[0167] The imaging values ​​of all shots are superimposed according to the observation system to obtain the elastic wave reverse time migration superimposed profile.

[0168] Example 3

[0169] This disclosure provides an electronic device comprising: a memory storing executable instructions; and a processor executing the executable instructions in the memory to implement the aforementioned elastic wave reverse time offset method.

[0170] An electronic device according to an embodiment of the present disclosure includes a memory and a processor.

[0171] This memory is used to store non-transitory computer-readable instructions. Specifically, the memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include random access memory (RAM) and / or cache memory. The non-volatile memory may, for example, include read-only memory (ROM), hard disk, flash memory, etc.

[0172] The processor may be a central processing unit (CPU) or other form of processing unit with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. In one embodiment of this disclosure, the processor is used to execute computer-readable instructions stored in the memory.

[0173] Those skilled in the art will understand that, in order to solve the technical problem of how to achieve a good user experience, this embodiment may also include well-known structures such as communication buses and interfaces, and these well-known structures should also be included within the protection scope of this disclosure.

[0174] For a detailed description of this embodiment, please refer to the corresponding descriptions in the foregoing embodiments, which will not be repeated here.

[0175] Example 4

[0176] This disclosure provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the elastic wave reverse time migration method.

[0177] A computer-readable storage medium according to embodiments of the present disclosure stores non-transitory computer-readable instructions. When these non-transitory computer-readable instructions are executed by a processor, all or part of the steps of the methods described in the foregoing embodiments of the present disclosure are performed.

[0178] The aforementioned computer-readable storage media include, but are not limited to: optical storage media (e.g., CD-ROM and DVD), magneto-optical storage media (e.g., MO), magnetic storage media (e.g., magnetic tape or portable hard drive), media with built-in rewritable non-volatile memory (e.g., memory card), and media with built-in ROM (e.g., ROM cartridge).

[0179] Those skilled in the art should understand that the above description of the embodiments of the present invention is only intended to illustrate the beneficial effects of the embodiments of the present invention, and is not intended to limit the embodiments of the present invention to any of the examples given.

[0180] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A method for reverse-time migration of elastic waves, characterized in that, include: Based on the first-order velocity-stress elastic wave equation of a two-phase medium, the wave field extension formula is obtained. Obtain the wave field separation formula; For the target gun, wavefield extension and wavefield separation are performed sequentially to obtain forward propagation wavefield extension and reverse propagation wavefield extension, and the pure longitudinal wavefield value at each moment is stored. Imaging values ​​are extracted from pure P-wave field values ​​using cross-correlation imaging conditions; Repeat the above steps for all shots to obtain the elastic wave reverse time migration superposition profile; Among them, the formulas for obtaining the wave field extension include: The wave field extension formula is obtained by using the first-order velocity-stress elastic wave equation of the two-phase medium and the PML absorbing boundary conditions, and by employing the second-order time and tenth-order spatial high-order staggered grid finite difference method. The wave field extension formula is as follows: （1） in, Let x be the velocity component, and k be the current time loop number. For time intervals, , The grid size is in the x and z directions. , Let be the decay function in the x and z directions. The equivalent density of the solid phase, The equivalent density of the flow phase, is the density coupling coefficient between the solid and the fluid phase. For finite difference coefficients, Let be the normal stress in the x-direction. Where is the shear stress, S is the effective pressure of the flow phase, and b is the dissipation coefficient; The imaging values ​​are extracted using formula (3): （3） in, In space Image value at point For the extension of the forward wave field, For the extension of the reverse propagation wave field; The process of obtaining the elastic wave reverse time migration superposition profile includes: The imaging values ​​of all shots are superimposed according to the observation system to obtain the elastic wave reverse time migration superimposed profile.

2. The elastic wave reverse-time migration method according to claim 1, wherein, The formulas for obtaining wavefield separation include: By using Helmholtz vortex theory for divergence and curl fields, the longitudinal and transverse wave fields are decoupled and separated to achieve wave field separation in a two-phase medium, and the wave field separation formula is obtained.

3. An elastic wave reverse-time offset device, characterized in that, include: The wave field extension formula acquisition module obtains the wave field extension formula based on the first-order velocity-stress elastic wave equation of a two-phase medium. The wavefield separation formula acquisition module retrieves the wavefield separation formula. The wavefield extension and separation module sequentially performs wavefield extension and wavefield separation on the target shot to obtain forward propagation wavefield extension and reverse propagation wavefield extension, and stores the pure longitudinal wavefield value at each moment. The imaging module extracts imaging values ​​from pure P-wave field values ​​using cross-correlation imaging conditions. The stacking module repeats the above steps for all shots to obtain the elastic wave reverse time migration stacking profile. Among them, the formulas for obtaining the wave field extension include: The wave field extension formula is obtained by using the first-order velocity-stress elastic wave equation of the two-phase medium and the PML absorbing boundary conditions, and by employing the second-order time and tenth-order spatial high-order staggered grid finite difference method. The wave field extension formula is as follows: （1） in, Let x be the velocity component, and k be the current time loop number. For time intervals, , The grid size is in the x and z directions. , Let be the decay function in the x and z directions. The equivalent density of the solid phase, The equivalent density of the flow phase, is the density coupling coefficient between the solid and the fluid phase. For finite difference coefficients, Let be the normal stress in the x-direction. Where is the shear stress, S is the effective pressure of the flow phase, and b is the dissipation coefficient; The imaging values ​​are extracted using formula (3): （3） in, In space Image value at point For the extension of the forward wave field, For the extension of the reverse propagation wave field; The process of obtaining the elastic wave reverse time migration superposition profile includes: The imaging values ​​of all shots are superimposed according to the observation system to obtain the elastic wave reverse time migration superimposed profile.

4. An electronic device, characterized in that, The electronic device includes: Memory, which stores executable instructions; A processor that executes the executable instructions in the memory to implement the elastic wave reverse time migration method of claim 1 or 2.

5. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the elastic wave reverse time migration method as described in claim 1 or 2.

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