Wave field separation method and device considering medium microstructure interaction and medium

Abstract

The invention discloses a wave field separation method and device considering medium microstructure interaction and a medium, and relates to the field of seismic exploration, and the method comprises the steps: building a generalized wave equation through combining a high-order moment balance relation and medium characteristic scale parameters under a modified even stress theory; the medium characteristic scale parameters are used for representing medium microstructure characteristics; based on the seismic wave field simulation task, constructing a corresponding medium parameter model set and a task observation system, and further performing numerical simulation to obtain a vector seismic wave field considering the interaction of medium microstructures; based on the polarization characteristics of the seismic longitudinal waves and the seismic transverse waves, a divergence operator and a curl operator are used for conducting decoupling separation on the vector seismic wave field, so that a corresponding longitudinal wave field and a corresponding transverse wave field are obtained. According to the method, on the basis of decoupling separation of the generalized wave equation, efficient and accurate separation of the vector seismic wave field considering the interaction of fine microstructures in the medium is realized.

Description

Technical Field

[0001] The present application relates to the field of seismic exploration, and in particular to a wave field separation method, device and medium taking into account medium microstructure interaction. Background Art

[0002] The core content of seismic exploration is to construct a medium model that conforms to reality and a model that can accurately describe the propagation of seismic waves in the medium. The actual earth medium often contains characteristics such as non-complete elasticity and multiphase state. Whether it is a natural medium or an artificial medium, the existence of various complex microstructures is inevitable. The various fine microstructures inside the medium cause the physical property changes of the medium to be extremely complex, which in turn makes the medium have strong spatial variability and inhomogeneity. The inhomogeneity caused by the complex microstructure inside the medium has an important impact on the macroscopic seismic wave field. For example, for seafloor seismic waves, the physical properties and spatial distribution of seafloor sediments have a profound impact on the propagation characteristics of seafloor seismic waves. At the same time, in recent years, with the continuous deepening of human exploration of the earth, coupled with the rapid development of computer storage and computing efficiency, the development of fine seismic technology has received more and more attention. Scholars are paying more and more attention to the influence of the complex structure of the medium and the pores, cracks and fillings inside it on the propagation of seismic waves, and then seek a wave propagation model that is more in line with physical reality, laying a theoretical foundation for achieving higher-precision imaging and inversion.

[0003] In the framework of classical continuum mechanics theory, the stress description of material points only uses the first-order derivative of displacement, that is, strain, and does not involve higher-order derivatives of displacement. It is precisely because of the limitation of this kinematic field that the classical continuum mechanics theory cannot always fully describe the heterogeneity of the medium. Moreover, when singularities in the stress and / or strain field appear near micro-defects (micro-pores / micro-cracks / micro-holes) in the medium, it is impossible to regularize or smooth the singularities in the stress and / or strain field. In addition, for the localized deformation area in the wave field, in the framework of classical continuum mechanics theory, there will also be a loss of mathematical expression and ill-posed grid dependence in numerical simulation. Summary of the invention

[0004] The purpose of this application is to provide a wave field separation method, device and medium that considers the interaction of medium microstructure, and on the basis of decoupling and separation of generalized wave equations, realizes the efficient and accurate separation of vector seismic wave fields that consider the interaction of fine microstructures in the medium.

[0005] To achieve the above objectives, this application provides the following solutions:

[0006] In a first aspect, the present application provides a wave field separation method considering medium microstructure interaction, comprising:

[0007] Under the modified couple stress theory, a generalized wave equation is constructed by combining the high-order moment balance relationship and the characteristic scale parameter of the medium; the characteristic scale parameter of the medium is used to characterize the microstructure characteristics of the medium;

[0008] Based on the seismic wave field simulation task, a corresponding medium parameter model set and a task observation system are constructed; the medium parameter model set includes a longitudinal wave velocity model, a transverse wave velocity model, a density model and a medium characteristic scale parameter model; the task observation system includes the source location, source type, source main frequency and detection point location;

[0009] According to the medium parameter model set and the mission observation system, the generalized wave equation is numerically simulated to obtain a vector seismic wave field that takes into account the interaction of medium microstructures;

[0010] Based on the polarization characteristics of seismic longitudinal waves and seismic shear waves, the vector seismic wave field is decoupled and separated using a divergence operator and a curl operator to obtain corresponding longitudinal wave fields and shear wave fields.

[0011] In a second aspect, the present application provides a computer device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a wave field separation method that considers medium microstructure interaction.

[0012] In a third aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a wave field separation method that takes into account medium microstructure interaction.

[0013] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0014] The present application provides a wave field separation method, device and medium considering the interaction of medium microstructure. Based on the modified couple stress theory, by introducing the high-order spatial derivative of displacement (i.e., high-order moment balance relationship) and the medium characteristic scale parameter reflecting the characteristics of medium microstructure, the ability to describe the influence of heterogeneity caused by the interaction of microstructure in the medium on the propagation of seismic waves is further enhanced, and a new research idea is provided for the interpretation of medium physical property information of complex structures. The generalized wave equation under the modified couple stress theory is finally obtained by equation derivation. Then, according to the medium parameter model set and the task observation system, the generalized wave equation is numerically simulated to obtain the vector seismic wave field considering the interaction of medium microstructure, and then the divergence operator and the curl operator are used to decouple and separate the vector seismic wave field, and more accurate longitudinal wave field and transverse wave field are obtained efficiently, which is not only helpful for analyzing the propagation mechanism of various types of waves in multi-component wave fields, but also can use the separated longitudinal and transverse waves for imaging, avoiding the crosstalk noise caused by the coupling of longitudinal and transverse waves, thereby improving the imaging accuracy and physical interpretability. In summary, the present application realizes the simulation and separation of seismic wave fields taking into account the microstructure interaction within the medium under the modified couple stress theory. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0016] Figure 1 A schematic flow chart of a wave field separation method considering medium microstructure interaction provided in one embodiment of the present application;

[0017] Figure 2 A schematic diagram of a shear wave phase velocity dispersion curve under the modified couple stress theory provided in one embodiment of the present application;

[0018] Figure 3 A schematic diagram for comparing wave field snapshots obtained at t=0.4s from numerical simulation of the generalized wave equation under the modified couple stress theory provided in one embodiment of the present application;

[0019] Figure 4 A schematic diagram of comparison of seismic records obtained by numerical simulation of the generalized wave equation under the modified couple stress theory provided in one embodiment of the present application;

[0020] Figure 5 A schematic diagram showing a comparison of wave field snapshots obtained by simulating a uniform medium model using a generalized wave equation based on a divergence-curl separation strategy provided in an embodiment of the present application;

[0021] Figure 6 A schematic diagram of comparison of seismic records obtained by simulating a uniform model using a generalized wave equation based on a divergence-curl separation strategy provided in an embodiment of the present application;

[0022] Figure 7 A schematic diagram of the structure of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0023] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0024] The constitutive relations of the generalized continuum mechanics theory include high-order gradient terms, which facilitates the successful overcoming of the shortcomings of the classical continuum mechanics theory. As an important branch of the generalized continuum mechanics theory, the modified couple stress theory considers that the material constituting the medium has volume properties rather than particles from the theoretical starting point. In this way, the micro-element constituting the medium can simultaneously bear the effects of stress and couples, and then by introducing high-order spatial derivatives of displacement, the torsional bending deformation of the micro-element of the medium is described, and the characteristic scale parameters describing the micro-structural characteristics of the medium are added to reflect the connotation of the medium. Therefore, by introducing high-order spatial derivatives of displacement and characteristic scale parameters reflecting the micro-structural characteristics of the medium, the modified couple stress theory further enhances the ability to describe the influence of heterogeneity caused by the interaction of microstructures in the medium on the propagation of seismic waves, and provides a new research idea for the interpretation of the physical property information of complex structures.

[0025] Numerical simulation and wavefield separation technology are the basis for analyzing the propagation mechanism and waveform characteristics of seismic waves, and also have a profound impact on the quality of subsequent seismic imaging and inversion. In particular, for the propagation characteristics analysis and migration imaging of multi-component seismic wave fields, wavefield decoupling and separation are the key technologies. Accurate and efficient extraction of P-wave and S-wave components in the wavefield not only helps to analyze the propagation mechanism of various types of waves in the multi-component wavefield, but also can use the separated P-wave and S-wave to perform imaging separately, avoiding the crosstalk noise caused by the coupling of P-wave and S-wave, thereby improving the imaging accuracy and physical interpretability. Therefore, in order to better analyze the influence of microstructural characteristics described by the modified couple stress theory on the propagation of P-wave and S-wave, and analyze the law of the influence of P-wave and S-wave wavefields on the microstructural characteristics of the medium, it is necessary to establish a method for numerical simulation and wavefield separation of seismic waves under the modified couple stress theory, so as to lay the foundation for the subsequent development of seismic exploration technology that considers the fine microstructural characteristics of the medium.

[0026] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0027] In an exemplary embodiment, Figure 1 As shown, a wave field separation method considering the interaction of medium microstructure is provided. The method is executed by a computer device, and can be specifically executed by a computer device such as a terminal or a server alone, or by a terminal and a server together. In the embodiment of the present application, the method is applied to a server as an example for explanation, including the following steps 101 to 104.

[0028] Step 101, under the modified couple stress theory, a generalized wave equation is constructed by combining a high-order moment balance relationship and a medium characteristic scale parameter; the medium characteristic scale parameter is used to characterize the medium microstructure characteristics.

[0029] As an important branch of the generalized continuum mechanics theory, the modified couple stress theory considers that the material constituting the medium has volume properties from the theoretical starting point, which enables the micro-element constituting the medium to bear the effects of stress and couple at the same time. Then, by introducing the high-order spatial derivative of displacement, the torsional bending deformation of the micro-element of the medium is described, and the characteristic scale parameters describing the micro-structure characteristics of the medium are added to reflect the connotation of the medium. Specifically, step 101 includes:

[0030] (1) Under the modified couple stress theory, according to the high-order moment equilibrium relationship, the equilibrium equation satisfied by the stress tensor and the couple stress tensor is determined as follows:

[0031]

[0032] Among them, τ is the stress tensor; e is the preset displacement symbol; m is the couple stress tensor, M is the body couple, F is the body force, u is the displacement vector, ρ is the density, and t is the time; the subscripts i, j, k, n, s represent different directional components, and each directional component has three values, such as i, j, k, n, s = {1, 2, 3}. It should be noted that 1 / 2 / 3 here is only an example and can be adjusted as needed in actual applications. In addition, these three values ​​generally correspond to the x-axis, y-axis, and z-axis directions in the coordinate system.

[0033] When a variable has multiple direction vectors and there is no comma between the direction components, the multiple direction vectors represent the space; the subscripts (,i) and (,ij) represent the partial derivatives of the space, that is, when a variable has multiple direction components and there is a comma between the direction components, the direction component after the comma represents the derivative of the variable in the direction corresponding to the direction component. Specifically, τ ji,j is the stress tensor τ jiThe first derivative in the j direction, e ikt The symbol for substitution with the subscript ikt; m st,sk is the couple stress tensor m st The second-order spatial derivative of m st,sk represents the couple stress tensor m st We perform the derivative in the s direction and the derivative in the k direction respectively, but s, t, and k all have three possible values, so m st,sk It does not refer to a specific value, but includes all possible sets of different values ​​of s, t, and k. ist Represents the substitution symbol with the subscript ist. t,s is the derivative of the component of the body couple in the t direction in the s direction, which can also be expressed as the first-order derivative of the one-dimensional body couple. i is the component of the body force in direction i, u i is the i component of the displacement vector. For example, for M t,s , assign t = 1, s = 3, since t = 1 corresponds to the x-axis direction and s = 3 corresponds to the z-axis direction, then M t,s That is, the derivative of the body couple component in the x-axis direction in the z-axis direction is a first-order derivative.

[0034] (2) Under the modified couple stress theory, the relationship between the curvature tensor and the strain tensor and the displacement is constructed, that is, the geometric equation is constructed as follows:

[0035]

[0036] Among them, ε is the strain tensor, χ is the curvature tensor, and ω is the rotation vector; more specifically, ε ij (i, j = x, y, z) represents the strain component, χ ij is the curvature component, u i,j is the displacement vector u i The first-order spatial derivative in the j direction, u j,i is the displacement vector u j The first-order spatial derivative in the i direction, ω i,j is the rotation vector ω i The first-order spatial derivative in the j direction, ω j,i is the rotation vector ω j The first-order spatial derivative in the i direction, e jkl The substitution symbol with the subscript jkl; u l,ki is the displacement vector u l The second-order spatial derivatives in the k direction and i direction respectively. ijl Represents the permutation symbol with the subscript ikl. l,kj is the displacement vector u lThe second-order spatial derivatives in the k direction and the j direction respectively. l represents the directional component and has three possible values, such as l = {1, 2, 3}.

[0037] (3) The constitutive relation of modified couple stress not only includes the constraint relation of traditional stress, but also the constraint relation of couple stress. Considering isotropic medium, according to the work conjugation relation and generalized Hooke's law, the constitutive equation under the modified couple stress theory can be derived, that is, based on the work conjugation relation and generalized Hooke's law, the constitutive equation under the modified couple stress theory can be determined; the constitutive equation under the modified couple stress theory is:

[0038] τ ij =λδ ij ε kk +2με ij , m ij =2μl e 2 χ ij =2ηχ ij .

[0039] Among them, m ij Couple stress component, λ, μ are Lame constants, δ ij is the Kronecker symbol, l e is the characteristic scale parameter of the medium, μ is the shear modulus, and η is the parameter that characterizes the rotation characteristics of the medium microelement. According to the constitutive relationship, it can be seen that the parameter η that characterizes the rotation characteristics of the medium microelement is not only related to the characteristic scale parameter l e It is also related to the shear modulus μ. At the same time, the medium characteristic scale parameter l e It is regarded as a comprehensive effect parameter describing the microstructure characteristics of the medium, which is expressed by the comprehensive coefficient α and the micropore characteristic scale parameter l m The connection of e =αl m .

[0040] (3) Substitute the geometric equation and the constitutive equation under the modified couple stress theory into the equilibrium equation satisfied by the stress tensor and the couple stress tensor to obtain the generalized wave equation, as shown below:

[0041]

[0042] Among them, u j,ij To take the second-order derivative of the vector wave field component, that is, to take the displacement vector u j Derivatives are taken in the i direction and in the j direction respectively; u i,jj is the displacement vector u i Perform the derivative in the j direction and the derivative in the j direction respectively, e ijk represents the permutation symbol with the subscript ijk; ekmn The permutation symbol representing the kmn subscript, u n,mllj is the fourth-order derivative of the vector wave field component in the mllj direction, that is, the displacement vector u n Perform the derivative in the m direction, the derivative in the l direction, the derivative in the l direction, and the derivative in the j direction; e lmn The substitution symbol representing the subscript lmn. n,mklj is the fourth-order derivative of the vector wavelength component in the mklj direction, that is, the displacement vector u n Perform the derivative in the m direction, the k direction, the l direction, and the j direction.

[0043] In order to verify that the above generalized wave equation can be applied to the simulation and separation of wave fields, this application verifies the feasibility and accuracy of the method of this application from the theoretical analysis level and the numerical simulation test level.

[0044] Based on the need for this verification, at the theoretical analysis level, this application considers the wave field separation method of medium microstructure interaction, and also includes:

[0045] Step 201, determine the vector expression corresponding to the generalized wave equation, as shown below:

[0046]

[0047] in,

[0048] Step 202, based on the Helmholtz decomposition theorem, determine the calculation function of the irrotational scalar potential and the calculation function of the divergence-free vector potential obtained after the wave field decomposition. Specifically, in order to analyze the propagation characteristics of longitudinal waves and transverse waves under the modified couple stress theory, the wave field can be decomposed into the irrotational scalar potential associated with the longitudinal wave and the divergence-free vector potential associated with the transverse wave according to the Helmholtz decomposition, that is:

[0049]

[0050] in, is the Hamiltonian operator, is the longitudinal wave component of the wave field, and ψ is the transverse wave component of the wave field.

[0051] Step 203, the calculation function of the irrotational scalar potential and the calculation function of the divergence-free vector potential are respectively substituted into the vector expressions corresponding to the generalized wave equation to determine the corresponding longitudinal wave control equation and transverse wave control equation, as shown below:

[0052]

[0053] Step 204, rewriting the longitudinal wave control equation and the shear wave control equation based on the plane strain of the two-dimensional xoz surface.

[0054] Specifically, consider the plane strain problem of the two-dimensional xoz surface, that is, u y = 0, the divergence-free vector potential associated with the shear wave can be expressed as ψ = ψ y (x,z)e y , then the longitudinal wave control equation and the transverse wave control equation can be rewritten as follows:

[0055]

[0056] Step 205, define the two-dimensional xoz in-plane body wave solution, and substitute it into the rewritten longitudinal wave control equation and the shear wave control equation to determine the corresponding longitudinal wave phase velocity equation and shear wave phase velocity equation. The specific process is as follows:

[0057] First, define the two-dimensional xoz in-plane body wave solution as follows:

[0058] ψ y =Bexp(o(Kx-wt)).

[0059] Among them, o is an imaginary number (please note that the letter i is commonly used to represent an imaginary number, but in order to distinguish it from the letter i representing the subscript in the above text, the letter o is used here to represent it), x is space, A and B are the longitudinal wave amplitude and transverse wave amplitude respectively, w is the angular frequency, and K is the wave number.

[0060] Then, the above two-dimensional xoz in-plane body wave solution is substituted into the rewritten longitudinal wave control equation and the transverse wave control equation to obtain the longitudinal wave phase velocity equation and the transverse wave phase velocity equation as shown below:

[0061]

[0062] Among them, c p is the longitudinal wave phase velocity, c s is the shear wave phase velocity.

[0063] According to the longitudinal wave phase velocity equation and the transverse wave phase velocity equation, it can be seen that the longitudinal wave phase velocity expression under the modified couple stress theory is consistent with the phase velocity expression of the traditional wave equation. However, its transverse wave phase velocity expression is not only related to λ, μ and density, but also to the characteristic scale parameters and frequency of the medium. That is to say, under the modified couple stress theory, the heterogeneity caused by the interaction of the medium microstructure is considered, which causes the propagation of transverse waves to be dispersed.

[0064] Step 206, obtaining variable data sets corresponding to different media; each of the variable data sets includes medium characteristic scale parameters.

[0065] Step 207, respectively substitute the variable data sets corresponding to the different media into the longitudinal wave phase velocity equation and the transverse wave phase velocity equation to obtain the corresponding longitudinal wave phase velocity theoretical dispersion curve and transverse wave phase velocity theoretical dispersion curve; the longitudinal wave phase velocity theoretical dispersion curve is used to characterize the influence of the characteristic scale parameters and frequency of the medium on the longitudinal wave; the transverse wave phase velocity theoretical dispersion curve is used to characterize the influence of the characteristic scale parameters and frequency of the medium on the transverse wave.

[0066] In one example, the elastic modulus is 6 GPa, the Poisson's ratio is 0.25, and the density is 1800 kg / m 3 Take the medium as an example, and set the medium micropore gap characteristic scale parameter l m is 0 μm, 500 μm, 1000 μm, 1500 μm, 2000 μm, thereby obtaining multiple variable data sets. According to the longitudinal wave phase velocity equation and the shear wave phase velocity equation obtained in step 205, the corresponding theoretical dispersion curves can be given, thereby more effectively reflecting the influence of the heterogeneity caused by the interaction of the medium microstructure on the shear wave propagation. Figure 2 As shown in the figure, it is a schematic diagram of the shear wave phase velocity dispersion curve under the modified couple stress theory (since the expression of the longitudinal wave phase velocity is consistent with the traditional wave equation, it is not shown). Figure 2 The theoretical dispersion curve can effectively reflect the influence of the characteristic scale parameters and frequency of the medium on the propagation of shear waves, and the shear wave phase velocity increases with the increase of the characteristic scale parameters and frequency of the medium.

[0067] According to the above steps, the present application substitutes the relevant parameters of different media (density, medium characteristic scale parameters, etc.) into the phase velocity expressions of longitudinal waves and transverse waves to obtain the corresponding phase velocity curves, which can effectively reflect the influence of the heterogeneity caused by the interaction of fine microstructures in the medium on the longitudinal and transverse wave fields. Furthermore, based on this, the proposed wave field separation scheme can be used to effectively separate the vector seismic wave field calculated under the modified couple stress theory, which can lay a research foundation for the subsequent imaging and inversion considering the fine microstructure in the medium.

[0068] Step 102, based on the seismic wave field simulation task, construct a corresponding medium parameter model set and a task observation system; the medium parameter model set includes a longitudinal wave velocity model, a transverse wave velocity model, a density model and a medium characteristic scale parameter model; the task observation system includes the source location, source type, source main frequency and detection point location.

[0069] In an application example, taking the uniform model as an example, the longitudinal wave velocity is set to 2000m / s, the shear wave velocity is set to 1154.7m / s, and the density is set to 1800kg / m 3The characteristic scale parameter of the medium micropores is 900 μm. The source uses Ricker wavelet with a main frequency of 40 Hz, which is excited in the central area of ​​the model and set as a concentrated force source in the z direction. The detector is located on the surface.

[0070] Step 103: numerically simulate the generalized wave equation according to the medium parameter model set and the mission observation system to obtain a vector seismic wave field that takes into account the interaction of medium microstructures.

[0071] Specifically, according to the medium parameter model set and the mission observation system, when the generalized wave equation is numerically simulated, the calculation method used is: finite difference method or finite element method. Taking the uniform model mentioned in step 102 as an example, according to the model parameters under the set uniform medium and the observation system information, the staggered grid finite difference scheme is used for numerical simulation, so as to obtain the vector seismic wave field considering the influence of medium microstructure interaction under the modified couple stress theory. In order to effectively suppress the influence of numerical dispersion and boundary reflection on wave field calculation, the optimized staggered grid finite difference operator and convolution fully matched layer artificial boundary conditions are also used in the numerical simulation.

[0072] like Figure 3 As shown, it is a schematic diagram for comparing the wave field snapshots obtained at t = 0.4s from the numerical simulation of the generalized wave equation under the modified couple stress theory. Figure 3 (a) and Figure 3 (b) in the figure are the x-components of the wave field snapshot when the characteristic scale parameter of the medium micropore gap is 0 μm (i.e., the traditional wave equation), and the x-components of the wave field snapshot when the characteristic scale parameter of the medium micropore gap is 900 μm. Figure 3 (c) in Figure 3 The difference between (a) and (b) in . Figure 3 (d) and Figure 3 (e) in the figure are the z components of the wave field snapshot when the characteristic scale parameter of the medium micropore gap is 0 μm (i.e., the traditional wave equation), and the z components of the wave field snapshot when the characteristic scale parameter of the medium micropore gap is 900 μm. Figure 3 (f) in Figure 3 The difference between (d) and (e).

[0073] At the same time, observe the seismic records obtained by the detectors on the surface, such as Figure 4 shown. Figure 4 (a) and (b) are the x-component of the seismic record when the characteristic scale parameter of the medium micropores is 0 μm (i.e., the traditional wave equation), and the x-component of the seismic record when the characteristic scale parameter of the medium micropores is 900 μm, respectively. Figure 4 (c) in Figure 4 The difference between (a) and (b) in . Figure 4(d) and (e) are the z components of the seismic records when the characteristic scale parameter of the medium micropores is 0 μm (i.e., the traditional wave equation) and the z components of the seismic records when the characteristic scale parameter of the medium micropores is 900 μm, respectively. Figure 4 (f) Figure 4 The difference between (d) and (e).

[0074] from Figure 3 and Figure 4 The numerical simulation results clearly show the influence of the heterogeneity caused by the interaction of microstructures in the medium on the propagation of seismic waves. It can also be found that under the modified couple stress theory, the heterogeneity caused by the interaction of microstructures in the medium has an effect on the propagation of shear waves, but has no effect on the propagation of longitudinal waves, which is consistent with the analysis results of the phase velocity expressions of longitudinal and shear waves and the theoretical dispersion curves.

[0075] Step 104, based on the polarization characteristics of the seismic longitudinal wave and the seismic shear wave, the vector seismic wave field is decoupled and separated by using a divergence operator and a curl operator respectively to obtain the corresponding longitudinal wave field and shear wave field.

[0076] According to the polarization characteristics of longitudinal waves and transverse waves, in isotropic media, longitudinal waves can be expressed as irrotational scalar potentials, and transverse waves can be expressed as divergence-free vector potentials. Thus, the separated longitudinal and transverse waves can be obtained by calculating the divergence and curl:

[0077]

[0078] Where, is the vibration velocity vector of the medium microelement, v = (v x ,v y ,v z ).

[0079] On the two-dimensional xoz plane, the above divergence operator and curl operator can be written as:

[0080]

[0081] Among them, P and S are the divergence operator and the curl operator respectively, and the divergence operator is used to characterize the separated longitudinal wave field, and the curl operator is used to characterize the separated shear wave field; u x is the x component of the vector wave field, u z is the z component of the vector wave field.

[0082] In general, the divergence operator is applied to the vector seismic wave field under the modified couple stress theory obtained above to obtain a scalar longitudinal wave field that takes into account the interaction of the medium microstructure; the curl operator is applied to the vector seismic wave field under the modified couple stress theory obtained above to obtain a vector shear wave field that takes into account the interaction of the medium microstructure, which is a scalar wave field in the two-dimensional case.

[0083] The essence of step 104 is to project the coupled wave field in the polarization directions of the longitudinal wave and the transverse wave respectively. The implementation is simple, and the longitudinal wave field and the transverse wave field can be obtained by only calculating the divergence and the rotation of the vector wave field respectively.

[0084] like Figure 5 As shown, it is a schematic diagram of the comparison of wave field snapshots obtained by simulating the uniform medium model using the generalized wave equation based on the divergence-curl separation strategy. Figure 5 (a)-(d) in the figure are the x component of the coupled wave field, the z component of the coupled wave field, the separated longitudinal wave component, and the separated transverse wave component. Further, the seismic records obtained by the geophone placed on the surface are extracted, such as Figure 6 As shown in the figure, it is a schematic diagram of the comparison of seismic records simulated on a uniform model using the generalized wave equation based on the divergence-curl separation strategy. Figure 6 (a)-(d) in the figure are the x component of the coupled wave field, the z component of the coupled wave field, the separated longitudinal wave, and the separated transverse wave component. Figure 5 and Figure 6 It can be seen from the results that the above wave field separation method can be used to effectively separate the longitudinal and transverse waves of the coupled wave field obtained by numerical simulation of the generalized wave equation, which lays a research foundation for the subsequent imaging and inversion considering the fine microstructure in the medium.

[0085] In summary, the present application derives the governing equation expressions of longitudinal and transverse waves under the modified couple stress theory based on the given vector expression of the generalized wave equation under the modified couple stress theory and in combination with the Helmholtz decomposition theorem; at the same time, the body wave solution is substituted into the derived governing equations of longitudinal and transverse waves to derive the phase velocity expressions of longitudinal and transverse waves under the modified couple stress theory, and the parameter information of different media is substituted into the phase velocity expression to obtain the corresponding phase velocity dispersion curve. According to the phase velocity curve, it can be used to analyze the influence of the heterogeneity caused by the microstructure interaction of the medium on the propagation of longitudinal and transverse waves under different media; further, according to the actual According to the physical parameter information and task requirements of the work area, the longitudinal wave velocity model, shear wave velocity model, density model, medium characteristic scale parameter model are set, and the corresponding observation system is set, including the source location, source type, source main frequency, and detection point location; according to the set parameters, the seismic wave field under the modified couple stress theory is numerically calculated to obtain the vector seismic wave field that considers the influence of medium microstructure interaction; finally, according to the polarization characteristics of longitudinal waves and shear waves, the divergence operator and the curl operator are used to obtain the scalar longitudinal wave field and the vector shear wave field (in the two-dimensional case, it is a scalar wave field) of the vector seismic wave field under the modified couple stress theory.

[0086] This application aims to enhance the description of the influence of the heterogeneity caused by the fine microstructure of the medium on the longitudinal and transverse wave fields, and to construct the relationship between the longitudinal and transverse wave fields and the microstructure characteristics of the medium; it also establishes the longitudinal and transverse wave control equations and the corresponding phase velocity expressions under the modified couple stress theory, and establishes a decoupling separation scheme for the vector wave field under the modified couple stress theory. Based on the above settings, this application can effectively reflect the influence of the heterogeneity caused by the interaction of the fine microstructure in the medium on the longitudinal and transverse wave fields, and, using the proposed wave field separation scheme, the vector seismic wave field calculated under the modified couple stress theory can be effectively separated, which lays a research foundation for the subsequent realization of imaging and inversion considering the fine microstructure in the medium.

[0087] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Figure 7 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. The processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a wave field separation method considering the interaction of medium microstructures is implemented.

[0088] Those skilled in the art will understand that Figure 7 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components. In an exemplary embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and the processor implements the steps in the above-mentioned method embodiments when executing the computer program.

[0089] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0090] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0091] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0092] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0093] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0094] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A wave field separation method considering the interaction of medium microstructure, characterized in that: The wave field separation method considering the interaction of medium microstructures comprises: Under the modified couple stress theory, combined with the high-order moment balance relationship, a generalized wave equation is constructed; the medium characteristic scale parameter is used to characterize the medium microstructure characteristics; Based on the seismic wave field simulation task, a corresponding medium parameter model set and a task observation system are constructed; the medium parameter model set includes a longitudinal wave velocity model, a transverse wave velocity model, a density model and a medium characteristic scale parameter model; the task observation system includes the source location, source type, source main frequency and detection point location; According to the medium parameter model set and the mission observation system, the generalized wave equation is numerically simulated to obtain a vector seismic wave field that takes into account the interaction of medium microstructures; Based on the polarization characteristics of seismic longitudinal waves and seismic shear waves, the vector seismic wave field is decoupled and separated using a divergence operator and a curl operator to obtain corresponding longitudinal wave fields and shear wave fields.

2. The wave field separation method considering medium microstructure interaction according to claim 1, characterized in that: Under the modified couple stress theory, combined with the high-order moment balance relationship, the generalized wave equation is constructed, including: Under the modified couple stress theory, the equilibrium equations satisfied by the stress tensor and the couple stress tensor are determined according to the high-order moment equilibrium relation. Under the modified couple stress theory, a geometric equation is constructed; the geometric equation is used to characterize the relationship between the curvature tensor, the strain tensor and the displacement; Based on the work conjugation relation and generalized Hooke's law, the constitutive equation under the modified couple stress theory is determined; The geometric equation and the constitutive equation are substituted into the equilibrium equation under the modified couple stress theory to obtain the generalized wave equation.

3. The wave field separation method considering medium microstructure interaction according to claim 2, characterized in that: The equilibrium equation satisfied by the stress tensor and the couple stress tensor is: Wherein, τ is the stress tensor, e is the preset displacement symbol, m is the couple stress tensor, M is the body couple, F is the body force, u is the displacement vector, ρ is the density, and t is the time; the subscripts i, j, k, n, s represent different directional components, and each directional component has three values; when a variable has multiple directional vectors and there is no comma between the directional components, the multiple directional vectors represent the space; when a variable has multiple directional components and there is a comma between the directional components, the directional component after the comma represents the derivative of the variable in the direction corresponding to the directional component; The geometric equation is: Among them, ε is the strain tensor, χ is the curvature tensor, and ω is the rotation vector; The constitutive equation under the modified couple stress theory is: t ij =λδ ij e kk +2with ij ,m ij =2μl e 2 x ij =2h ij ; Among them, λ and μ are Lame constants, δ is the Kronecker symbol, l e is the characteristic scale parameter of the medium, μ is the shear modulus, and η is the parameter that characterizes the rotation characteristics of the medium microelement.

4. The wave field separation method considering medium microstructure interaction according to claim 3, characterized in that: The generalized wave equation is:

5. The wave field separation method considering medium microstructure interaction according to claim 1, characterized in that: When the generalized wave equation is numerically simulated according to the medium parameter model set and the mission observation system, the calculation method adopted is: finite difference method or finite element method.

6. The wave field separation method considering medium microstructure interaction according to claim 1, characterized in that: The function expressions of the divergence operator and the curl operator are respectively: Among them, P and S are the divergence operator and the curl operator respectively, and the divergence operator is used to characterize the separated longitudinal wave field, and the curl operator is used to characterize the separated shear wave field; u x is the x component of the vector wave field, u z is the z component of the vector wave field.

7. The wave field separation method considering medium microstructure interaction according to claim 1, characterized in that: The wave field separation method considering medium microstructure interaction also includes: Determining a vector expression corresponding to the generalized wave equation; Based on the Helmholtz decomposition theorem, the calculation functions of the irrotational scalar potential and the irscatterable vector potential obtained after wave field decomposition are determined; Substituting the calculation function of the irrotational scalar potential and the calculation function of the divergence-free vector potential into the vector expressions corresponding to the generalized wave equation, respectively, to determine the corresponding longitudinal wave control equation and transverse wave control equation; Based on the plane strain of the two-dimensional xoz surface, the longitudinal wave control equation and the shear wave control equation are rewritten; Define a two-dimensional xoz in-plane body wave solution, and substitute it into the rewritten longitudinal wave governing equation and the shear wave governing equation, respectively, to determine the corresponding longitudinal wave phase velocity equation and shear wave phase velocity equation; Obtain variable data sets corresponding to different media; each of the variable data sets includes a medium characteristic scale parameter; The variable data sets corresponding to the different media are respectively substituted into the longitudinal wave phase velocity equation and the transverse wave phase velocity equation to obtain the corresponding longitudinal wave phase velocity theoretical dispersion curve and transverse wave phase velocity theoretical dispersion curve; the longitudinal wave phase velocity theoretical dispersion curve is used to characterize the influence of the characteristic scale parameters and frequency of the medium on the longitudinal wave; the transverse wave phase velocity theoretical dispersion curve is used to characterize the influence of the characteristic scale parameters and frequency of the medium on the transverse wave.

8. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the wave field separation method considering medium microstructure interaction as described in any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the wave field separation method considering medium microstructure interaction described in any one of claims 1 to 7 is implemented.

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