Method and device for processing singularity of shear wave in elastic wave forward modeling of fluid-solid boundary coupling medium

Abstract

The present invention discloses a method and device for handling shear wave singularities in the forward modeling of elastic waves in fluid-solid boundary coupled media. The method comprises: constructing a two-dimensional elastic wave equation for seismic waves; constructing an analytical domain elastic wave equation based on the two-dimensional elastic wave equation; establishing a non-split PML boundary analytical domain elastic wave equation based on the analytical domain elastic wave equation and a predetermined non-split PML boundary region differential operator; and constructing a non-split PML boundary analytical domain high-order difference format for the elastic wave equation based on the non-split PML boundary analytical domain elastic wave equation and predetermined time difference operators and spatial high-order finite difference operators for forward modeling wave propagation in seawater layers. This technical solution, by introducing complex velocity processing in the analytical domain, avoids the shear wave singularity that occurs when using the elastic wave equation to forward model wave propagation in seawater layers without increasing computer memory usage.

Description

Technical Field

[0001] The present invention relates to the technical field of geophysical exploration of oil and natural gas resources, and in particular to a method and device for processing shear wave singularities in elastic wave forward modeling of a fluid-solid boundary coupling medium. Background Art

[0002] The field of oil and gas exploration is gradually moving towards two deep areas, deep waters and deep formations, and two new areas, polar new areas and unconventional oil and gas. Marine oil and gas exploration is expanding into deep waters and deep formations, and we will continue to increase our exploration efforts to push new reserves to a peak and ensure national energy security.

[0003] Oil and gas seismic exploration focuses on heterogeneous oil and gas reservoirs in complex salt bodies located deep within the formations. These reservoirs are characterized by complex lithologies, typically composed of igneous and metamorphic rocks. This violates the traditional assumptions of sedimentary layered reservoirs, resulting in dramatic lateral variations in geophysical characteristics and significant exploration challenges. The complex seismic response of these heterogeneous salt reservoirs necessitates the development of seismic forward and inversion models tailored to complex deepwater reservoirs. In deepwater oil and gas seismic exploration, seismic waves propagate through a complex medium consisting of a coupled seawater layer, elastic strata, and complex salt bodies. The velocity and density parameters of the seawater layer medium in deep water areas will change with depth, and it has the characteristics of a continuous medium. However, the seawater layer medium does not propagate shear waves, and the shear wave velocity is zero; the elastic parameters of the sedimentary formations vary little laterally, and stratification occurs vertically, which can be equivalent to an elastic layered medium; complex salt bodies are highly heterogeneous, and the elastic parameters have spatially varying characteristics, that is, the elastic parameters are a function of the spatial coordinates. Such complex coupled media will lead to wave field aliasing problems.

[0004] How to establish an elastic wave equation that can accurately describe the seismic wave propagation process in complex salt media and avoid shear wave singularities is a key issue in deepwater complex salt oil and gas seismic exploration. Summary of the Invention

[0005] The present invention provides a method and device for processing shear wave singularities in the forward modeling of elastic waves in a fluid-solid boundary coupled medium. By introducing complex velocities to process the problem in the analytical domain, the shear wave singularity phenomenon that occurs when using the elastic wave equation to forward model wave propagation in the seawater layer is avoided without increasing computer memory usage.

[0006] According to one aspect of the present invention, a method for processing shear wave singularities in elastic wave forward modeling of a fluid-solid boundary coupled medium is provided, the method comprising:

[0007] Construct the two-dimensional elastic wave equation in seismic waves;

[0008] According to the two-dimensional elastic wave equation, an analytical domain elastic wave equation is constructed; wherein the analytical domain elastic wave equation includes a wave equation for propagation of a real wave field in a seawater layer medium and a wave equation for propagation of an imaginary wave field in a seawater layer medium;

[0009] Establishing a non-split PML boundary analytic domain elastic wave equation according to the analytic domain elastic wave equation and a predetermined non-split PML boundary region differential operator; wherein the non-split PML boundary region differential operator includes a first-order differential operator, a cross-term differential operator, and a second-order differential operator;

[0010] According to the non-split PML boundary analytical domain elastic wave equation and predetermined time difference operators and spatial high-order finite difference operators, a non-split PML boundary analytical domain elastic wave equation high-order difference format is constructed for forward simulation of wave propagation in seawater layer medium;

[0011] Among them, the spatial high-order finite difference operator includes a first-order differential operator high-order difference format, a second-order differential operator high-order difference format and a cross-term differential operator high-order difference format; the non-split PML boundary analytical domain elastic wave equation high-order difference format includes an elastic displacement x-component high-order difference format and an elastic displacement z-component high-order difference format.

[0012] According to another aspect of the present invention, a device for processing shear wave singularities in elastic wave forward modeling of a fluid-solid boundary coupled medium is provided, the device comprising:

[0013] Two-dimensional elastic wave equation construction module, used to construct the two-dimensional elastic wave equation in seismic waves;

[0014] An analytical domain elastic wave equation construction module is used to construct an analytical domain elastic wave equation based on the two-dimensional elastic wave equation; wherein the analytical domain elastic wave equation includes a wave equation for propagation of a real wave field in a seawater layer medium and a wave equation for propagation of an imaginary wave field in a seawater layer medium;

[0015] a non-split PML boundary analytical domain elastic wave equation establishment module, configured to establish the non-split PML boundary analytical domain elastic wave equation according to the analytical domain elastic wave equation and a predetermined non-split PML boundary region differential operator; wherein the non-split PML boundary region differential operator includes a first-order differential operator, a cross-term differential operator, and a second-order differential operator;

[0016] A non-split PML boundary analytical domain elastic wave equation high-order difference format construction module is used to construct a non-split PML boundary analytical domain elastic wave equation high-order difference format based on the non-split PML boundary analytical domain elastic wave equation and predetermined time difference operators and spatial high-order finite difference operators for forward simulation of wave propagation in seawater layer media;

[0017] Among them, the spatial high-order finite difference operator includes a first-order differential operator high-order difference format, a second-order differential operator high-order difference format and a cross-term differential operator high-order difference format; the non-split PML boundary analytical domain elastic wave equation high-order difference format includes an elastic displacement x-component high-order difference format and an elastic displacement z-component high-order difference format.

[0018] The technical solution of the embodiment of the present invention constructs a two-dimensional elastic wave equation for seismic waves; constructs an analytical domain elastic wave equation based on the two-dimensional elastic wave equation; establishes a non-split PML boundary analytical domain elastic wave equation based on the analytical domain elastic wave equation and a predetermined non-split PML boundary region differential operator; and constructs a high-order difference format for the non-split PML boundary analytical domain elastic wave equation based on the non-split PML boundary analytical domain elastic wave equation and predetermined time difference operators and spatial high-order finite difference operators for forward modeling of wave propagation in seawater layers. This technical solution avoids the shear wave singularity that occurs when using the elastic wave equation to forward model wave propagation in seawater layers by introducing complex velocities to handle the problem in the analytical domain, without increasing computer memory usage.

[0019] It should be understood that the content described in this section is not intended to identify the key or important features of the embodiments of the present invention, nor is it intended to limit the scope of the present invention. Other features of the present invention will become readily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0021] Figure 1 Flowchart of a method for processing singularities in shear wave forward modeling of elastic waves in fluid-solid boundary coupling media according to the first embodiment of the present invention;

[0022] Figure 2 The deep-water layered elastic medium model provided in Example 1 of this application;

[0023] Figure 3 The deep-water layered elastic medium model seismic forward observation system provided in Example 1 of the present application;

[0024] Figure 4 The elastic wave u provided in Example 1 of this application x Component forward modeling singularity phenomenon;

[0025] Figure 5 The elastic wave u provided in Example 1 of this applicationz Component forward modeling singularity phenomenon;

[0026] Figure 6 The analytical domain elastic wave u provided in the first embodiment of the present application x Component forward wavefield snapshot;

[0027] Figure 7 The analytical domain elastic wave u provided in the first embodiment of the present application z Component forward wavefield snapshot;

[0028] Figure 8 The analytical domain elastic wave u provided in the first embodiment of the present application x Component forward record;

[0029] Figure 9 The analytical domain elastic wave u provided in the first embodiment of the present application z Component forward record;

[0030] Figure 10 The longitudinal wave velocity of the complex salt body model in deep water provided in Example 1 of the present application;

[0031] Figure 11 The shear wave velocity of the complex salt body model in deep water provided in Example 1 of the present application;

[0032] Figure 12 The complex salt body model provided in the first embodiment of the present application is the analytical domain elastic wave u x Component forward wavefield snapshot;

[0033] Figure 13 The complex salt body model provided in the first embodiment of the present application is the analytical domain elastic wave u z Component forward wavefield snapshot;

[0034] Figure 14 The complex salt body analytical domain elastic wave u provided in Example 1 of this application x Component forward record;

[0035] Figure 15 The complex salt body analytical domain elastic wave u provided in Example 1 of this application z Component forward record;

[0036] Figure 16 A schematic diagram of the structure of a device for processing shear wave singularities in elastic wave forward modeling of a fluid-solid boundary coupled medium provided in the second embodiment of the present invention;

[0037] Figure 17 The present invention is a schematic diagram of the structure of an electronic device for implementing the method for processing singularities of shear waves in elastic wave forward modeling of a fluid-solid boundary coupled medium according to an embodiment of the present invention. DETAILED DESCRIPTION

[0038] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0039] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0040] Example 1

[0041] Figure 1 This is a flow chart of a method for processing the singularity of shear waves in elastic wave forward modeling of fluid-solid boundary coupled media provided in accordance with the first embodiment of the present invention. This embodiment can be applied to the situation where elastic wave equations in the analytical domain of fluid-solid boundary coupled media are established to solve the shear wave singularity problem in the fluid phase medium of the seawater layer. This method can be executed by a fluid-solid boundary coupled medium elastic wave forward modeling shear wave singularity processing device. The fluid-solid boundary coupled medium elastic wave forward modeling shear wave singularity processing device can be implemented in the form of hardware and / or software. The fluid-solid boundary coupled medium elastic wave forward modeling shear wave singularity processing device can be configured in an electronic device. Figure 1 As shown, the method includes:

[0042] S110. Construct a two-dimensional elastic wave equation for seismic waves.

[0043] In this embodiment, during seismic exploration of complex salt-body oil and gas reservoirs in deepwater areas, a seismic source is excited in the seawater layer and propagates downward through a complex path through coupled media, such as the overlying seawater layer and the subsurface elastic strata, returning to the seawater layer for reception. Because the shear wave velocity in the seawater layer is zero, using the elastic wave equation to simulate wave propagation in fluid-solid boundary coupled media can lead to shear wave singularities, resulting in instability in the numerical simulation algorithm. To improve the stability of the forward modeling algorithm for the elastic wave equation in fluid-solid boundary coupled media, an analytical domain method for handling shear wave singularities in elastic wave forward modeling of fluid-solid boundary coupled media is established. Furthermore, considering the non-split PML (perfectly matched layer) boundary condition, a high-order difference scheme for the elastic wave equation in the non-split PML boundary analytical domain is constructed without increasing memory consumption. This not only improves the stability of the finite difference method and avoids shear wave singularities, but also enhances the accuracy of seismic forward modeling of seawater layer media. Furthermore, the elastic wave equation has only three displacement components, which, when implemented technically, reduces computer memory consumption and significantly reduces the amount of computation.

[0044] In this scheme, the two-dimensional elastic wave equation in seismic wave dynamics can be established based on the three basic equations in elastic mechanics, that is, the two-dimensional elastic wave equation in seismic wave dynamics is established using the geometric equation, the constitutive equation, and the Newtonian motion differential equation:

[0045]

[0046] Among them, V P and are the propagation speeds of longitudinal and shear waves in elastic media, u x and u z They are the horizontal component and vertical component of the elastic wave respectively. In a uniform isotropic perfectly elastic medium, the propagation of elastic waves is decoupled.

[0047] Furthermore, using the Helmholtz potential eddy current decomposition theory, the scalar potential φ and vector potential ψ are defined as Helmholtz potential, and the elastic wave displacement field is decomposed into Thus, the decoupling equation of elastic wave propagation can be obtained. Among them, the decoupling equation of elastic wave propagation includes longitudinal wave propagation and shear wave propagation.

[0048] The following formula is used to describe the propagation of longitudinal waves:

[0049]

[0050] The following formula is used to describe shear wave propagation:

[0051]

[0052] Among them, u P and u Srepresent the longitudinal wave field and the shear wave field, respectively. represents the Laplace operator.

[0053] When seismic waves propagate in the seawater layer, the shear wave modulus of the seawater layer is zero, resulting in the shear wave propagation speed in the seawater layer being zero, that is, the denominator V s =0, but the numerator is not zero, so the algebraic expression The result of the division loses its uniqueness, and the infinite value makes it impossible to deal with the problem of seismic wave propagation normally. However, the propagation of seismic waves in the space-time domain meets the physical feasibility and the excitation energy is limited, that is, Therefore, we can get:

[0054] or

[0055] The above formula is used to describe the analysis of the singularity of shear wave propagation in the seawater layer medium. That is, when seismic waves propagate in the seawater layer medium, the shear wave singularity phenomenon occurs when the shear wave propagates in the seawater layer medium. Specifically, it manifests as instability in the numerical solution of the elastic wave equation.

[0056] S120. Construct an analytical domain elastic wave equation based on the two-dimensional elastic wave equation; wherein the analytical domain elastic wave equation includes a wave equation for propagating a real wave field in a seawater layer medium and a wave equation for propagating a virtual wave field in a seawater layer medium.

[0057] In this embodiment, the elastic wave equation is used to describe the wave propagation process in the seawater layer medium. Through singularity analysis, it is known that there are shear wave singularities in the seawater layer medium. This leads to instability in the numerical simulation of the wave propagation process in the seawater layer medium and the underground elastic medium using the elastic wave equation. If the displacement-stress equation is used for simulation, although the shear wave singularity can be avoided, it takes up a lot of memory space and is difficult to use in engineering applications. According to the above shear wave singularity analysis, an abnormal function appears in the real number domain, which is difficult to solve this problem in the real number domain. The shear wave singularity problem can be solved in the analytical domain defined by complex numbers. Therefore, the complex velocity is introduced into the shear wave velocity in the seawater layer medium as follows:

[0058]

[0059] Among them, the real part of the shear wave velocity V S =0, imaginary part of shear wave velocity 0<α S ≤1, generally α S The value of is 1, and the shear wave velocity of the seawater layer in the analytical domain is The shear wave velocity singularity is avoided in the analytical domain.

[0060] Furthermore, based on the two-dimensional elastic wave equation and complex velocity, the analytical domain elastic wave equation can be constructed:

[0061]

[0062] The above equation is the extended elastic wave equation. By introducing complex shear wave velocity, the elastic wave equation can be stably solved in the analytical domain to avoid the occurrence of shear wave singularities. By establishing the elastic wave equation in the analytical domain, the concept of complex wave field is expanded compared with the original wave equation.

[0063] Furthermore, the analytical domain elastic wave equation is used to describe the propagation process of seismic waves in the seawater layer medium, which is divided into two parts. That is, the wave equation for the real wave field propagation in the seawater layer medium and the wave equation for the imaginary wave field propagation in the seawater layer medium can be used to describe the propagation process of seismic waves in the seawater layer medium respectively.

[0064] The wave equation for the propagation of real wave field in seawater layer medium is:

[0065]

[0066] The wave equation for the propagation of virtual wave field in seawater layer medium is:

[0067]

[0068] The above analytical domain elastic wave equation is applied to numerically simulate the wave propagation process of the coupled medium between the seawater layer medium and the underground elastic formation medium. After the numerical simulation is completed, the real part of the complex wave field can be directly obtained to complete the simulation of the elastic wave propagation of the coupled medium.

[0069] S130. Establish a non-split PML boundary analytic domain elastic wave equation based on the analytic domain elastic wave equation and a predetermined non-split PML boundary region differential operator; wherein the non-split PML boundary region differential operator includes a first-order differential operator, a cross-term differential operator, and a second-order differential operator.

[0070] In this embodiment, boundary issues must be considered to better simulate elastic wave propagation in coupled media. A non-split PML boundary condition, also known as a convolutional PML boundary condition, is introduced to solve the elastic wave equation in the analytical domain. This avoids the large amount of variable memory consumed by traditional numerical simulations of the elastic wave equation with a split PML boundary. By introducing a non-split PML boundary in the computational boundary region, using the x-direction and the cross term xz as examples, a time-space partial differential operator is introduced to obtain a non-split PML boundary region differential operator.

[0071] The first-order differential operator is:

[0072]

[0073] The cross-term differential operator is:

[0074]

[0075] The second-order differential operator is:

[0076]

[0077] in, k x (x) and The parameter k represents the attenuation of the evanescent wave in the x direction. z (z) and represents the parameter of the evanescent wave in the z direction, ξ x (t) and ξ z (t) represents the intermediate variable between the x-direction and the z-direction.

[0078] Furthermore, based on the first-order differential operator, cross-term differential operator, second-order differential operator and the elastic wave equation in the analytical domain, the elastic wave equation in the non-split PML boundary analytical domain is constructed as follows:

[0079]

[0080] S140. According to the non-split PML boundary analytical domain elastic wave equation and the predetermined time difference operator and spatial high-order finite difference operator, a non-split PML boundary analytical domain elastic wave equation high-order difference format is constructed for forward simulation of seawater layer medium wave propagation; wherein the spatial high-order finite difference operator includes a first-order differential operator high-order difference format, a second-order differential operator high-order difference format and a cross-term differential operator high-order difference format; the non-split PML boundary analytical domain elastic wave equation high-order difference format includes an elastic displacement x-component high-order difference format and an elastic displacement z-component high-order difference format.

[0081] In this scheme, the elastic wave equation in the analytical domain is used to establish a high-order difference format for the elastic wave equation in the analytical domain with a non-split PML boundary. Here, the time domain uses the second-order difference format, and the space domain uses the high-order difference format. First, the time grid difference format is determined, and the Taylor expansion method is used to obtain:

[0082]

[0083] Secondly, the spatial grid adopts a high-order difference format and defines the spatial grid difference operator according to the order of the differential operator.

[0084] The high-order difference format of the first-order differential operator is:

[0085]

[0086] The high-order difference format of the second-order differential operator is:

[0087]

[0088] The high-order difference format of the cross-term differential operator is:

[0089]

[0090] Among them, D x 、 D xz Differential operators are and The high-order finite difference operator, c n represents the differential coefficient of the nth point from the center, x represents the xth point, n represents the order of spatial difference, ω0 represents the differential coefficient of the center position, ω n represents the differential coefficient of the nth point from the center, △x represents the spatial sampling interval in the x direction, Represents the differential coefficient of the nth point from the center in the x direction, Indicates the differential coefficient of the nth point from the center in the z direction.

[0091] Furthermore, a high-order difference format for the elastic wave equation in the non-split PML boundary analytic domain is constructed based on the time difference operator, the spatial high-order finite difference operator and the elastic wave equation in the non-split PML boundary analytic domain.

[0092] Specifically, the following formula is used to construct the high-order difference format of the elastic displacement x component:

[0093]

[0094] The following formula is used to construct the high-order difference format of the elastic displacement z component:

[0095]

[0096] By establishing an analytical domain processing method for shear wave singularities in elastic wave forward modeling of fluid-solid boundary coupled media and considering non-split PML boundary conditions, a high-order difference format for the elastic wave equation in the non-split PML boundary analytical domain is constructed without increasing memory consumption. This not only improves the stability of the finite difference method and avoids shear wave singularities, but also improves the accuracy of seismic forward modeling of seawater media.

[0097] The technical solution of the embodiment of the present invention constructs a two-dimensional elastic wave equation in seismic waves; constructs an analytical domain elastic wave equation based on the two-dimensional elastic wave equation; establishes a non-split PML boundary analytical domain elastic wave equation based on the analytical domain elastic wave equation and a predetermined non-split PML boundary region differential operator; and constructs a non-split PML boundary analytical domain elastic wave equation high-order difference format based on the non-split PML boundary analytical domain elastic wave equation and predetermined time difference operators and spatial high-order finite difference operators for forward modeling of wave propagation in seawater layers. By implementing this technical solution, complex velocities are introduced to process the problem in the analytical domain, avoiding the shear wave singularity phenomenon that occurs when using the elastic wave equation to forward model wave propagation in seawater layers without increasing computer memory usage.

[0098] In this plan, Figure 2 The deep water layered elastic medium model provided in Example 1 of this application is as follows: Figure 2 As shown in the figure, a four-layer, three-interface model and a coupled-medium complex rock model were constructed. The four-layer, three-interface model consists of a seawater layer as the overlying fluid medium and a sedimentary elastic stratum as the underlying medium. This deepwater layered elastic medium model can be used to validate shear wave singularity analysis and the effectiveness of forward seismic modeling of complex rock masses in deepwater areas. The coupled-medium complex rock model consists of a seawater layer, a sedimentary stratum, and a complex rock layer.

[0099] Specifically, the first step is to build a two-dimensional fluid-solid coupling medium model

[0100] In order to analyze the shear wave singularity and solve the shear wave singularity effect in the simulation process, a four-layer three-interface fluid-solid coupling medium model was constructed, such as Figure 2 As shown, the overlying seawater layer has a longitudinal wave velocity of 1500 m / s and a transverse wave velocity of 0 m / s; the underlying sedimentary layer has a longitudinal wave velocity of 2200 m / s and a transverse wave velocity of 1100 m / s; the second sedimentary layer has a longitudinal wave velocity of 2800 m / s and a transverse wave velocity of 1400 m / s; the sedimentary basement layer has a longitudinal wave velocity of 3200 m / s and a transverse wave velocity of 1600 m / s.

[0101] Step 2: Analysis of shear wave singularity in seawater layer

[0102] Using the four-layer three-interface fluid-solid boundary coupling medium model constructed above, the elastic wave equation is directly used for forward simulation. Figure 3 The deep-water layered elastic medium model seismic forward observation system provided in Example 1 of the present application, ★ is the excitation position, is the detector position. Figure 4 The elastic wave u provided in Example 1 of this application x Component forward modeling singularity phenomenon; Figure 5The elastic wave u provided in Example 1 of this application z Component forward modeling singularity phenomenon; such as Figure 4 and Figure 5 As shown in the figure, the shear wave singularity phenomenon of the wave field is clearly seen, which is caused by the zero shear wave velocity. Since the shear wave velocity is zero, the shear wave singularity appears near the earthquake source. This is achieved by forward simulation of the shear wave singularity through the elastic wave equation of the fluid-solid boundary coupling medium.

[0103] Step 3: Establish a high-order difference scheme for the elastic wave equation in the analytical domain

[0104] By using the above-mentioned analytical domain elastic wave equation and considering the non-split PML boundary conditions, the non-split PML boundary analytical domain elastic wave equation is constructed. This can avoid the large amount of variable memory consumed by the traditional split PML boundary elastic wave equation numerical simulation, and at the same time solve the shear wave singularity problem of the elastic wave equation in simulating the propagation of seismic waves in the fluid phase medium. Then, the Taylor expansion method is used to establish the time grid and the space grid using a high-order difference format. The high-order difference format of the first-order differential operator, the second-order differential operator and the cross-term differential operator is considered to establish a stable high-order difference format of the analytical domain elastic wave equation to simulate the propagation of seismic waves in the coupled medium of seawater layer + elastic stratum, and solve the instability problem caused by the shear wave singularity.

[0105] Figure 6 The analytical domain elastic wave u provided in the first embodiment of the present application x Component forward wave field snapshot, Figure 7 The analytical domain elastic wave u provided in the first embodiment of the present application z Component forward wave field snapshot, such as Figure 6 and Figure 7 As shown in the figure, the elastic wave field u at t = 2.0 seconds is simulated using the high-order difference format of the analytical domain elastic wave equation in the four-layer three-interface fluid-solid boundary coupling medium model. x Component and u z A snapshot of the wave field of the component shows the obvious effect of the high-order difference scheme of the elastic wave equation in the analytical domain in resolving the shear wave singularity.

[0106] Figure 8 The analytical domain elastic wave u provided in the first embodiment of the present application x Component forward record, Figure 9 The analytical domain elastic wave u provided in the first embodiment of the present application z Component forward record, such as Figure 8 and Figure 9 As shown in the figure, there is an obvious earthquake simulation recording effect, which eliminates the shear wave singularity phenomenon.

[0107] Step 4: Forward simulation of complex salt body model in deep waters

[0108] Using the above-mentioned high-order difference scheme of the elastic wave equation in the analytical domain, forward simulation of a complex salt body model in deep waters was carried out. The complex salt body model consists of deep water layers, sedimentary strata, and complex salt bodies. Figure 10 The longitudinal wave velocity of the complex salt body model in deep water provided in Example 1 of this application is: Figure 11 The shear wave velocity of the complex salt body model in deep water provided in Example 1 of this application, the seismic observation system reference Figure 3 As shown, it is also excited by the seawater layer medium and received by the seawater layer medium. Figure 12 The complex salt body model provided in the first embodiment of the present application is the analytical domain elastic wave u x Component forward wave field snapshot, Figure 13 The complex salt body model provided in the first embodiment of the present application is the analytical domain elastic wave u z Component forward wave field snapshot, Figure 12 、 Figure 13 They are the elastic wave u of the complex salt body model at t = 2.0 seconds x Component and u z The wave field snapshot of the component uses a stable high-order finite difference format of the analytical domain elastic wave equation, so a more stable wave field can be obtained, avoiding the shear wave singularity problem, and then obtaining a high-precision deep-water complex salt body model seismic forward simulation record. Figure 14 The complex salt body analytical domain elastic wave u provided in Example 1 of this application x Component forward record, Figure 15 The complex salt body analytical domain elastic wave u provided in Example 1 of this application z Component forward record, such as Figure 14 、 Figure 15 As shown, they are elastic wave u x Component and u z The component seismic forward modeling records have laid a foundation for seismic forward modeling of complex salt bodies in deep waters.

[0109] Example 2

[0110] Figure 16 This is a schematic diagram of the structure of the device for processing the singularity of elastic wave forward modeling of shear waves in fluid-solid boundary coupling medium provided by the second embodiment of the present invention. Figure 16 As shown, the device includes:

[0111] A two-dimensional elastic wave equation construction module 1610 is used to construct a two-dimensional elastic wave equation in seismic waves;

[0112] The analytical domain elastic wave equation construction module 1620 is used to construct an analytical domain elastic wave equation based on the two-dimensional elastic wave equation; wherein the analytical domain elastic wave equation includes a wave equation for propagation of a real wave field in the seawater layer medium and a wave equation for propagation of an imaginary wave field in the seawater layer medium;

[0113] A non-split PML boundary analytic domain elastic wave equation establishing module 1630 is configured to establish a non-split PML boundary analytic domain elastic wave equation based on the analytic domain elastic wave equation and a predetermined non-split PML boundary region differential operator; wherein the non-split PML boundary region differential operator includes a first-order differential operator, a cross-term differential operator, and a second-order differential operator;

[0114] A non-split PML boundary analytic domain elastic wave equation high-order difference format construction module 1640 is used to construct a non-split PML boundary analytic domain elastic wave equation high-order difference format based on the non-split PML boundary analytic domain elastic wave equation and predetermined time difference operators and spatial high-order finite difference operators for forward modeling of wave propagation in seawater layer media;

[0115] Among them, the spatial high-order finite difference operator includes a first-order differential operator high-order difference format, a second-order differential operator high-order difference format and a cross-term differential operator high-order difference format; the non-split PML boundary analytical domain elastic wave equation high-order difference format includes an elastic displacement x-component high-order difference format and an elastic displacement z-component high-order difference format.

[0116] Optionally, the two-dimensional elastic wave equation construction module 1610 is specifically used to:

[0117] The following formula is used to construct the two-dimensional elastic wave equation in seismic waves;

[0118]

[0119] Among them, V P and They are the longitudinal wave propagation speed and the shear wave propagation speed of the elastic medium, u x and u z They are the horizontal and vertical components of the elastic wave respectively.

[0120] Optionally, the analytical domain elastic wave equation construction module 1620 is specifically used to:

[0121] The elastic wave equation in the analytical domain is constructed using the following formula;

[0122]

[0123] in, Real part of shear wave velocity V S =0, imaginary part of shear wave velocity 0<α S ≤1.

[0124] Optionally, the analytical domain elastic wave equation construction module 1620 is further configured to:

[0125] The wave equation for the propagation of real wave fields in seawater layer media is constructed using the following formula;

[0126]

[0127] The wave equation for the propagation of virtual wave field in seawater layer medium is constructed using the following formula;

[0128]

[0129] Optionally, the non-split PML boundary analytical domain elastic wave equation establishment module 1630 is specifically used to:

[0130] The following formula is used to establish the first-order differential operator in the non-split PML boundary region differential operator;

[0131]

[0132] The following formula is used to establish the cross-term differential operator in the non-split PML boundary region differential operator;

[0133]

[0134] The following formula is used to establish the second-order differential operator in the non-split PML boundary region differential operator;

[0135]

[0136] in, k x (x) and The parameter k represents the attenuation of the evanescent wave in the x direction. z (z) and represents the parameter of the evanescent wave in the z direction, ξ x (t) and ξ z (t) represents the intermediate variable between the x-direction and the z-direction.

[0137] Optionally, the non-split PML boundary analytical domain elastic wave equation establishment module 1630 is further used to:

[0138] The following formula is used to establish the elastic wave equation of the non-split PML boundary analytical domain;

[0139]

[0140] Optionally, the non-split PML boundary analytic domain elastic wave equation high-order difference format construction module 1640 is specifically used to:

[0141] The time difference operator is constructed using the following formula;

[0142]

[0143] The following formula is used to construct the high-order difference format of the first-order differential operator in the spatial high-order finite difference operator:

[0144]

[0145] The following formula is used to construct the second-order differential operator space high-order difference format in the spatial high-order finite difference operator:

[0146]

[0147] The following formula is used to construct the spatial high-order difference format of the cross-term differential operator in the spatial high-order finite difference operator:

[0148]

[0149] Among them, D x 、 D xz Differential operators are and The high-order finite difference operator, c n represents the differential coefficient of the nth point from the center, x represents the xth point, n represents the order of spatial difference, ω0 represents the differential coefficient of the center position, ω n represents the differential coefficient of the nth point from the center, △x represents the spatial sampling interval in the x direction, Represents the differential coefficient of the nth point from the center in the x direction, Indicates the differential coefficient of the nth point from the center in the z direction.

[0150] Optionally, the non-split PML boundary analytic domain elastic wave equation high-order difference format building module 1640 is further used to:

[0151] The following formula is used to construct the high-order difference format of the elastic displacement x component:

[0152]

[0153] The following formula is used to construct the high-order difference format of the elastic displacement z component:

[0154]

[0155] The device for processing singularities of shear waves in the forward modeling of elastic waves in a fluid-solid boundary coupling medium provided in an embodiment of the present invention can execute the method for processing singularities of shear waves in the forward modeling of elastic waves in a fluid-solid boundary coupling medium provided in any embodiment of the present invention, and has functional modules and beneficial effects corresponding to the execution method.

[0156] Example 3

[0157] Figure 17A schematic diagram of the structure of an electronic device 10 that can be used to implement an embodiment of the present invention is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices (such as helmets, glasses, watches, etc.) and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present invention described and / or claimed herein.

[0158] like Figure 17 As shown, the electronic device 10 includes at least one processor 11 and a memory, such as a read-only memory (ROM) 12, a random access memory (RAM) 13, etc., which is communicatively connected to the at least one processor 11. The memory stores a computer program that can be executed by the at least one processor. The processor 11 can perform various appropriate actions and processes according to the computer program stored in the read-only memory (ROM) 12 or the computer program loaded from the storage unit 18 into the random access memory (RAM) 13. Various programs and data required for the operation of the electronic device 10 can also be stored in the RAM 13. The processor 11, ROM 12, and RAM 13 are connected to each other via a bus 14. An input / output (I / O) interface 15 is also connected to the bus 14.

[0159] Multiple components in the electronic device 10 are connected to the I / O interface 15, including an input unit 16, such as a keyboard, a mouse, etc.; an output unit 17, such as various types of displays, speakers, etc.; a storage unit 18, such as a magnetic disk, an optical disk, etc.; and a communication unit 19, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 19 allows the electronic device 10 to exchange information / data with other devices via a computer network such as the Internet and / or various telecommunication networks.

[0160] The processor 11 can be any general-purpose and / or specialized processing component with processing and computing capabilities. Some examples of the processor 11 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various specialized artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. The processor 11 executes the various methods and processes described above, such as the method for handling singularities in shear wave forward modeling of elastic waves in fluid-solid boundary coupled media.

[0161] In some embodiments, the method for processing singularities of shear waves in the forward modeling of elastic waves in a fluid-solid boundary coupled medium may be implemented as a computer program, which is tangibly contained in a computer-readable storage medium, such as a storage unit 18. In some embodiments, part or all of the computer program may be loaded and / or installed on the electronic device 10 via the ROM 12 and / or the communication unit 19. When the computer program is loaded into the RAM 13 and executed by the processor 11, one or more steps of the method for processing singularities of shear waves in the forward modeling of elastic waves in a fluid-solid boundary coupled medium described above may be executed. Alternatively, in other embodiments, the processor 11 may be configured to execute the method for processing singularities of shear waves in the forward modeling of elastic waves in a fluid-solid boundary coupled medium by any other appropriate means (for example, by means of firmware).

[0162] Various embodiments of the systems and techniques described herein can be implemented in digital electronic circuit systems, integrated circuit systems, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), system-on-chip systems (SOCs), programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments can include being implemented in one or more computer programs that are executable and / or interpreted on a programmable system that includes at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0163] Computer programs for implementing the methods of the present invention may be written in any combination of one or more programming languages. These computer programs may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when the computer program is executed by the processor, the functions / operations specified in the flowcharts and / or block diagrams are implemented. The computer program may be executed entirely on the machine, partially on the machine, as a stand-alone software package, partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0164] In the context of the present invention, computer-readable storage media can be tangible media that can contain or store a computer program for use with an instruction execution system, device or equipment or used in combination with an instruction execution system, device or equipment. Computer-readable storage media can include but are not limited to electronic, magnetic, optical, electromagnetic, infrared or semiconductor systems, devices or equipment, or any suitable combination of the foregoing. Alternatively, computer-readable storage media can be machine-readable signal media. More specific examples of machine-readable storage media can include electrical connections based on one or more lines, portable computer disks, hard disks, random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memory), optical fibers, portable compact disk read-only memories (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0165] To provide interaction with a user, the systems and techniques described herein can be implemented on an electronic device having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user can provide input to the electronic device. Other types of devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including acoustic input, voice input, or tactile input).

[0166] The systems and techniques described herein can be implemented in a computing system that includes back-end components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes front-end components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such back-end components, middleware components, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: a local area network (LAN), a wide area network (WAN), a blockchain network, and the Internet.

[0167] A computing system may include clients and servers. The clients and servers are typically remote from each other and typically interact via a communication network. This client-server relationship arises through computer programs running on the respective computers, creating a client-server relationship. The server may be a cloud server, also known as a cloud computing server or cloud host. This server is a hosting product within the cloud computing service ecosystem that addresses the management difficulties and limited scalability of traditional physical hosting and VPS services.

[0168] It should be understood that the various forms of the processes shown above can be used to reorder, add, or delete steps. For example, the steps described in the present invention can be performed in parallel, sequentially, or in a different order, as long as the desired results of the technical solution of the present invention can be achieved. This is not limited herein.

[0169] The above specific embodiments do not limit the scope of protection of the present invention. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

Claims

1. A method for processing singularities of shear waves in elastic wave forward modeling of fluid-solid boundary coupling medium, characterized by: include: Construct the two-dimensional elastic wave equation in seismic waves; According to the two-dimensional elastic wave equation, an analytical domain elastic wave equation is constructed; wherein the analytical domain elastic wave equation includes a wave equation for propagation of a real wave field in a seawater layer medium and a wave equation for propagation of an imaginary wave field in a seawater layer medium; Establishing a non-split PML boundary analytic domain elastic wave equation according to the analytic domain elastic wave equation and a predetermined non-split PML boundary region differential operator; wherein the non-split PML boundary region differential operator includes a first-order differential operator, a cross-term differential operator, and a second-order differential operator; According to the non-split PML boundary analytical domain elastic wave equation and predetermined time difference operators and spatial high-order finite difference operators, a non-split PML boundary analytical domain elastic wave equation high-order difference format is constructed for forward simulation of wave propagation in seawater layer medium; Among them, the spatial high-order finite difference operator includes a first-order differential operator high-order difference format, a second-order differential operator high-order difference format and a cross-term differential operator high-order difference format; the non-split PML boundary analytical domain elastic wave equation high-order difference format includes an elastic displacement x-component high-order difference format and an elastic displacement z-component high-order difference format.

2. The method according to claim 1, characterized in that Construct the two-dimensional elastic wave equation in seismic waves, including: The following formula is used to construct the two-dimensional elastic wave equation in seismic waves; Among them, V P and They are the propagation speed of longitudinal waves and shear waves in elastic media, u x and u z They are the horizontal and vertical components of the elastic wave respectively.

3. The method according to claim 2, characterized in that According to the two-dimensional elastic wave equation, an analytical domain elastic wave equation is constructed, including: The elastic wave equation in the analytical domain is constructed using the following formula; in, Real part of shear wave velocity V S =0, imaginary part of shear wave velocity 0<α S ≤1, V P and They are the propagation speed of longitudinal waves and shear waves in elastic media, u x and u z They are the horizontal and vertical components of the elastic wave respectively.

4. The method according to claim 1, wherein include: The following formula is used to establish the first-order differential operator in the non-split PML boundary region differential operator; The following formula is used to establish the cross-term differential operator in the non-split PML boundary region differential operator; The following formula is used to establish the second-order differential operator in the non-split PML boundary region differential operator; in, k x (x) and The parameter k represents the attenuation of the evanescent wave in the x direction. z (z) and represents the parameter of the evanescent wave in the z direction, ξ x (t) and ξ z (t) represents the intermediate variable between the x-direction and the z-direction.

5. The method according to claim 4, characterized in that According to the analytical domain elastic wave equation and a predetermined non-split PML boundary region differential operator, a non-split PML boundary analytical domain elastic wave equation is established, including: The following formula is used to establish the elastic wave equation of the non-split PML boundary analytical domain; Among them, V P and V S They are the real parts of the longitudinal wave propagation velocity and the shear wave propagation velocity of the elastic medium, u x and u z They are the horizontal and vertical components of the elastic wave, and the imaginary part of the shear wave velocity 0<α S ≤1.

6. The method according to claim 5, characterized in that include: The time difference operator is constructed using the following formula; The following formula is used to construct the high-order difference format of the first-order differential operator in the spatial high-order finite difference operator; The following formula is used to construct the second-order differential operator space high-order difference format in the space high-order finite difference operator; The following formula is used to construct the spatial high-order difference format of the cross-term differential operator in the spatial high-order finite difference operator; Among them, D x 、 D xz Differential operators are and The high-order finite difference operator, c n represents the differential coefficient of the nth point from the center, x represents the xth point, n represents the order of spatial difference, ω0 represents the differential coefficient of the center position, ω n represents the differential coefficient of the nth point from the center, △x represents the spatial sampling interval in the x direction, Represents the differential coefficient of the nth point from the center in the x direction, Indicates the differential coefficient of the nth point from the center in the z direction, u x is the horizontal component of the elastic wave, u z is the vertical component of the elastic wave.

7. The method according to claim 6, characterized in that According to the non-split PML boundary analytical domain elastic wave equation and predetermined time difference operators and spatial high-order finite difference operators, a non-split PML boundary analytical domain elastic wave equation high-order difference format is constructed, including: The following formula is used to construct the high-order difference format of the elastic displacement x component; The following formula is used to construct the high-order difference format of the elastic displacement z component; Among them, V P and V S are the real parts of the longitudinal wave propagation velocity and the shear wave propagation velocity of the elastic medium, k x (x) and The parameter k represents the attenuation of the evanescent wave in the x direction. z (z) and represents the parameter of the evanescent wave in the z direction, ξ x (t) and ξ z (t) represents the intermediate variable between the x-direction and the z-direction, and the imaginary part of the shear wave velocity 0<α S ≤1.

8. A device for processing singularities of shear waves in elastic wave forward modeling of fluid-solid boundary coupling medium, characterized by: include: Two-dimensional elastic wave equation construction module, used to construct the two-dimensional elastic wave equation in seismic waves; An analytical domain elastic wave equation construction module is used to construct an analytical domain elastic wave equation based on the two-dimensional elastic wave equation; wherein the analytical domain elastic wave equation includes a wave equation for propagation of a real wave field in a seawater layer medium and a wave equation for propagation of an imaginary wave field in a seawater layer medium; a non-split PML boundary analytical domain elastic wave equation establishment module, configured to establish the non-split PML boundary analytical domain elastic wave equation according to the analytical domain elastic wave equation and a predetermined non-split PML boundary region differential operator; wherein the non-split PML boundary region differential operator includes a first-order differential operator, a cross-term differential operator, and a second-order differential operator; A non-split PML boundary analytical domain elastic wave equation high-order difference format construction module is used to construct a non-split PML boundary analytical domain elastic wave equation high-order difference format based on the non-split PML boundary analytical domain elastic wave equation and predetermined time difference operators and spatial high-order finite difference operators for forward simulation of wave propagation in seawater layer media; Among them, the spatial high-order finite difference operator includes a first-order differential operator high-order difference format, a second-order differential operator high-order difference format and a cross-term differential operator high-order difference format; the non-split PML boundary analytical domain elastic wave equation high-order difference format includes an elastic displacement x-component high-order difference format and an elastic displacement z-component high-order difference format.

9. The device according to claim 8, characterized in that 2D elastic wave equation building blocks, specifically for: The following formula is used to construct the two-dimensional elastic wave equation in seismic waves; Among them, V P and They are the propagation speed of longitudinal waves and shear waves in elastic media, u x and u z They are the horizontal and vertical components of the elastic wave respectively.

Images