Wavefield decomposition methods, apparatus, equipment, and media based on wavefront phase direction

Abstract

This application provides a wavefield decomposition method, apparatus, device, and medium based on wavefront phase direction, belonging to the field of geophysical exploration technology. The method includes: determining a wavefield decomposition operator based on the original wavefield and Thomsen parameters; the wavefield decomposition operator is a first-order pseudo-Helmholtz decomposition operator based on the wavefront phase direction; determining the wavenumber domain wavefield obtained after transforming the original wavefield to the wavenumber domain; performing computational processing based on the wavenumber domain wavefield and wavenumber, followed by inverse Fourier transform to obtain multiple intermediate quantities constituting an auxiliary wavefield; determining the auxiliary wavefield based on the multiple intermediate quantities and Thomsen parameters through an auxiliary wavefield expression; and performing wavefield decomposition based on anisotropic wavefield decomposition formula to achieve P-wave and S-wave separation, obtaining the P-wave and S-wave wavefields. This method not only achieves P-wave and S-wave vector wavefield separation and reduces imaging crosstalk noise, but also reduces computational load, balancing wavefield decomposition effect and computational efficiency.

Description

Technical Field

[0001] This application relates to the field of geophysical exploration technology, and in particular to a wavefield decomposition method, apparatus, equipment and medium based on wavefront phase direction. Background Technology

[0002] Migration imaging is a core step in seismic data processing, primarily utilizing the propagation characteristics of seismic waves in the subsurface medium to convert seismic wave data into structural images of the subsurface medium. Wavefield separation is a crucial step in elastic wave reverse-time migration imaging, enabling the differentiation of different waves from mixed seismic signals, facilitating separate imaging of each wave type in subsequent steps. Currently, wavefield separation in anisotropic media is typically achieved by solving the anisotropic Poisson equation in the spatial domain to obtain an auxiliary wavefield. However, this method is computationally intensive and inefficient. Summary of the Invention

[0003] This application provides a wavefield decomposition method, apparatus, device, and medium based on wavefront phase direction. It not only achieves P-wave and S-wave vector wavefield separation, providing P-wave and S-wave input data for elastic wave reverse-time migration and reducing imaging crosstalk noise, but also reduces computational load, balancing wavefield decomposition effect and computational efficiency. The technical solution is as follows:

[0004] On the one hand, a wavefield decomposition method based on wavefront phase direction is provided, the method comprising:

[0005] Based on the original wave field and Thomsen parameters, a wave field decomposition operator is determined. The original wave field is a displacement wave field or a particle vibration velocity wave field. The Thomsen parameters include anisotropy parameters and longitudinal and transverse wave velocities along the direction of the medium's symmetry axis. The wave field decomposition operator is a first-order pseudo-Helmholtz decomposition operator based on the wavefront phase direction.

[0006] Based on the original wave field, determine the wavenumber domain wave field obtained after transforming the original wave field into the wavenumber domain;

[0007] Based on the wavenumber domain wavefield and wavenumber, the calculations are performed, and then an inverse Fourier transform is performed to obtain multiple intermediate quantities that constitute the auxiliary wavefield.

[0008] Based on the multiple intermediate quantities and the Thomsen parameters, the auxiliary wavefield is determined through an auxiliary wavefield expression, which is obtained by approximating the square of the modulus of the wavefield decomposition operator in the wavenumber domain.

[0009] Wave field decomposition is performed based on the anisotropic wave field decomposition formula to achieve separation of P-waves and S-waves, and obtain the P-wave field and the S-wave field.

[0010] In some embodiments, determining the wavefield decomposition operator based on the original wavefield and Thomsen parameters includes:

[0011] The wavefront phase direction is determined based on the original wave field obtained from the TI medium forward modeling simulation.

[0012] Based on the Thomsen parameters, the spatial function in the wave field decomposition operator is determined;

[0013] The wavefield decomposition operator is determined based on the wavefront phase direction and the spatial function.

[0014] In some embodiments, the auxiliary wave field expression is represented as:

[0015]

[0016] Where w(x) represents the auxiliary wavefield; ε and δ represent the anisotropy parameters; v p and v s These respectively represent the longitudinal and transverse wave velocities along the direction of the medium's axis of symmetry;

[0017] Where u1, u2, and u3 represent intermediate quantities constituting the auxiliary wave field, respectively expressed as:

[0018]

[0019] Among them, FFT -1 Represents the inverse fast Fourier transform; U represents the wavenumber domain wavefield obtained after the original wavefield is transformed into the wavenumber domain; k x Indicates the wave number in the x-direction; k z This represents the wave number in the z-direction.

[0020] In some embodiments, the anisotropic wavefield decomposition formula requires applying a pseudo-divergence operator, a pseudo-gradient operator, and a pseudo-curl operator to the auxiliary wavefield. The pseudo-divergence operator is used to extract longitudinal waves in the original wavefield, and the pseudo-curl operator is used to extract transverse waves in the original wavefield.

[0021] In some embodiments, the step of performing wave field decomposition based on anisotropic wave field decomposition formula to achieve P-wave and S-wave separation and obtain P-wave and S-wave fields includes:

[0022] The pseudo-divergence operator and the pseudo-gradient operator are applied to the auxiliary wave field to obtain the longitudinal wave field.

[0023] The pseudo-curl operator is applied to the auxiliary wave field to obtain the transverse wave field.

[0024] In some embodiments, the equations used in the process of performing wavefield decomposition based on anisotropic wavefield decomposition formulas to separate P-waves and S-waves and obtain the P-wave and S-wave fields are expressed as follows:

[0025]

[0026] Among them, u p and u s The P-wave field and the S-wave field, respectively, are calculated from the original wave field; w represents the auxiliary wave field. This represents a pseudo-gradient operator; Indicates the pseudo-divergence operator; This represents the pseudo-curl operator.

[0027] On the other hand, a wavefield decomposition device based on wavefront phase direction is provided, the device comprising:

[0028] The operator determination module is used to determine the wave field decomposition operator based on the original wave field and Thomsen parameters. The original wave field is a displacement wave field or a particle vibration velocity wave field. The Thomsen parameters include anisotropy parameters and longitudinal and transverse wave velocities along the direction of the medium's symmetry axis. The wave field decomposition operator is a first-order pseudo-Helmholtz decomposition operator based on the wavefront phase direction.

[0029] An auxiliary wavefield determination module is used to determine the wavenumber domain wavefield obtained after transforming the original wavefield to the wavenumber domain, based on the original wavefield; perform calculations based on the wavenumber domain wavefield and wavenumber, and then perform an inverse Fourier transform to obtain multiple intermediate quantities constituting the auxiliary wavefield; and determine the auxiliary wavefield based on the multiple intermediate quantities and the Thomsen parameters through an auxiliary wavefield expression, wherein the auxiliary wavefield expression is obtained by approximating the square of the modulus of the wavefield decomposition operator in the wavenumber domain.

[0030] The wave field decomposition module is used to decompose the wave field based on the anisotropic wave field decomposition formula, realize the separation of P-waves and S-waves, and obtain the P-wave wave field and the S-wave wave field.

[0031] In some embodiments, the operator determination module is used to determine the wavefront phase direction based on the original wavefield obtained from the forward modeling of the TI medium; determine the spatial function in the wavefield decomposition operator based on the Thomsen parameters; and determine the wavefield decomposition operator based on the wavefront phase direction and the spatial function.

[0032] In some embodiments, the auxiliary wave field expression is represented as:

[0033]

[0034] Where w(x) represents the auxiliary wavefield; ε and δ represent the anisotropy parameters; vp and v s These respectively represent the longitudinal and transverse wave velocities along the direction of the medium's axis of symmetry;

[0035] Where u1, u2, and u3 represent intermediate quantities constituting the auxiliary wave field, respectively expressed as:

[0036]

[0037] Among them, FFT -1 Represents the inverse fast Fourier transform; U represents the wavenumber domain wavefield obtained after the original wavefield is transformed into the wavenumber domain; k x Indicates the wave number in the x-direction; k z This represents the wave number in the z-direction.

[0038] In some embodiments, the anisotropic wavefield decomposition formula requires applying a pseudo-divergence operator, a pseudo-gradient operator, and a pseudo-curl operator to the auxiliary wavefield. The pseudo-divergence operator is used to extract longitudinal waves in the original wavefield, and the pseudo-curl operator is used to extract transverse waves in the original wavefield.

[0039] In some embodiments, the wave field decomposition module is used to apply the pseudo-divergence operator and the pseudo-gradient operator to the auxiliary wave field to obtain the longitudinal wave field; and to apply the pseudo-curl operator to the auxiliary wave field to obtain the transverse wave field.

[0040] In some embodiments, the equations used by the wave field decomposition module are expressed as follows:

[0041]

[0042] Among them, u p and u s The P-wave field and the S-wave field, respectively, are calculated from the original wave field; w represents the auxiliary wave field. This represents a pseudo-gradient operator; Indicates the pseudo-divergence operator; This represents the pseudo-curl operator.

[0043] On the other hand, a computer device is provided, the computer device including a processor and a memory, the memory being used to store at least one computer program, the at least one computer program being loaded and executed by the processor to implement the wavefield decomposition method based on wavefront phase direction in the embodiments of this application.

[0044] On the other hand, a computer-readable storage medium is provided, wherein at least one computer program is stored in the computer-readable storage medium, and the at least one computer program is loaded and executed by a processor to implement the wavefield decomposition method based on wavefront phase direction in the embodiments of this application.

[0045] On the other hand, a computer program product is provided, including a computer program that is executed by a processor to implement the wavefield decomposition method based on wavefront phase direction in the embodiments of this application.

[0046] This application provides a wavefield decomposition method based on wavefront phase direction. In this method, a wavefield decomposition operator is determined based on the original wavefield and Thomsen parameters. This operator is a first-order pseudo-Helmholtz decomposition operator based on the wavefront phase direction. Then, an auxiliary wavefield is obtained using a Fourier transform through an auxiliary wavefield expression. Finally, pseudo-gradient, pseudo-divergence, and pseudo-curl operators are applied to the obtained auxiliary wavefield to achieve wavefield separation from the original wavefield, thus obtaining the P-wave and S-wave fields. This method not only achieves P-wave and S-wave vector wavefield separation, providing P-wave and S-wave input data for elastic wave reverse time migration and reducing imaging crosstalk noise, but also reduces computational load by using an approximate auxiliary wavefield expression to calculate the auxiliary wavefield, balancing wavefield separation effect and computational efficiency. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is a schematic diagram of an implementation environment provided in an embodiment of this application;

[0049] Figure 2 This is a flowchart of a wavefield decomposition method based on wavefront phase direction provided in an embodiment of this application;

[0050] Figure 3 This is a flowchart illustrating the determination of wavefield decomposition equations provided in an embodiment of this application;

[0051] Figure 4 This is a schematic diagram of the wave field decomposition result of a homogeneous anisotropic medium provided in an embodiment of this application;

[0052] Figure 5 This is a schematic diagram of the model parameters of a test model provided in an embodiment of this application;

[0053] Figure 6 This is a schematic diagram of the horizontal and vertical components of the wave field of a test model provided in an embodiment of this application;

[0054] Figure 7 This is a schematic diagram of the wave field decomposition result of a test model provided in an embodiment of this application;

[0055] Figure 8 This is a block diagram of a wavefield decomposition device based on wavefront phase direction provided in an embodiment of this application;

[0056] Figure 9 This is a schematic diagram of the structure of a terminal provided in an embodiment of this application;

[0057] Figure 10 This is a schematic diagram of the structure of a server provided in an embodiment of this application. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0059] In this application, the terms "first," "second," etc., are used to distinguish identical or similar items with essentially the same function. It should be understood that there is no logical or temporal dependency between "first," "second," and "nth," nor are there any restrictions on quantity or execution order.

[0060] In this application, the term "at least one" means one or more, and "multiple" means two or more.

[0061] The following is a brief introduction to the terminology used in this application.

[0062] Elastic wave reverse time migration: Elastic wave reverse time migration is based on the two-way elastic wave equation and uses seismic wave field information to achieve imaging of complex subsurface media.

[0063] Wavefront phase direction: This refers to the direction in which the phase of vibration at various points on the wavefront points during the propagation of a seismic wave. The wavefront phase direction is not an actual physical direction, but rather describes the vibration state of various points on the wavefront. The wavefront is the surface formed by particles that have just begun to displace at a certain moment when a seismic wave propagates in a medium.

[0064] Wavefield decomposition and P-wave / S-wave decomposition: Wavefield decomposition refers to distinguishing different wave types from a mixed seismic wavefield to better understand the propagation characteristics of seismic waves and the structure of the subsurface medium. Wavefield separation is a key step in elastic wave reverse-time migration. After wavefield separation, multiple waves can be imaged separately, which can suppress crosstalk artifacts between waves and improve image quality. In addition, wavefield separation in full waveform inversion can suppress multi-parameter crosstalk and nonlinear problems, improving inversion accuracy. P-wave / S-wave decomposition is a form of wavefield decomposition. P-wave / S-wave decomposition refers to separating the P-wave and S-wave components from a mixed seismic wave signal.

[0065] Longitudinal waves (P-waves) and transverse waves (S-waves): Longitudinal waves are waves in which the direction of particle vibration is the same as the direction of wave propagation. That is, longitudinal waves are compression waves that vibrate along the direction of wave propagation. Transverse waves are waves in which the direction of particle vibration is perpendicular to the direction of wave propagation. That is, transverse waves are shear waves and their vibration direction is perpendicular to the direction of wave propagation.

[0066] Isotropic and anisotropic media: An isotropic media are media in which the properties are identical in all directions. In an isotropic medium, the propagation direction of the wave is the same as the polarization direction of the longitudinal wave and perpendicular to the polarization direction of the transverse wave. Anisotropic media are media in which the properties change with direction. In anisotropic media, the propagation direction of the wave is neither parallel nor perpendicular to the polarization directions of the transverse and longitudinal waves. Therefore, in anisotropic media, the wave field needs to be projected onto the polarization directions of the transverse and longitudinal waves to achieve the decomposition of longitudinal and transverse waves in anisotropic media.

[0067] Vertically transversely isotropic medium (VTI medium): It is a transversely isotropic medium with a vertical axis of symmetry, which is perpendicular to the surface of the medium.

[0068] Spatial domain and wavenumber domain: The spatial domain refers to the space composed of image pixels. In the spatial domain, pixels are analyzed and processed using length as the variable. In the wavenumber domain, the image's spectrum is analyzed and processed using wavenumber as the variable. Wavenumber is the reciprocal of wavelength, representing the number of waves per unit length. The spatial domain and wavenumber domain can be converted using Fourier transform, transforming signals in the spatial domain into spectral information in the wavenumber domain.

[0069] Velocity wave field and displacement wave field: When seismic waves propagate through the Earth's medium, the particles in the medium vibrate under the influence of the waves. The vibration velocity of these particles forms a certain distribution in space, which is the velocity wave field. The displacement wave field describes the initial displacement of the particles during the wave. The initial displacement refers to the initial displacement of a particle relative to its equilibrium position during the wave.

[0070] It should be noted that all information (including but not limited to user device information, user personal information, etc.), data (including but not limited to data used for analysis, stored data, displayed data, etc.), and signals involved in this application are authorized by the user or fully authorized by all parties, and the collection, use, and processing of related data must comply with the relevant laws, regulations, and standards of the relevant countries and regions. For example, the original wavefield data involved in this application was obtained with full authorization.

[0071] Figure 1 This is a schematic diagram of an implementation environment provided in an embodiment of this application. See also... Figure 1 The implementation environment includes terminal 101 and server 102. Terminal 101 and server 102 can be connected directly or indirectly via wired or wireless communication, which is not limited herein.

[0072] Among them, terminal 101 can be various types of terminals such as mobile phones, desktop computers, laptops, and tablets. Server 102 can be an independent physical server, or a server cluster or distributed system composed of multiple physical servers. It can also be a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN (Content Delivery Network), and big data and artificial intelligence platforms.

[0073] Optionally, the wavefield decomposition method based on wavefront phase direction provided in this application embodiment can be executed by terminal 101 alone, by server 102 alone, or by terminal 101 and server 102 interacting.

[0074] In some embodiments, when the terminal 101 executes the method alone, the terminal 101 can read the wavefield data of the original wavefield from local storage space or a storage server, and perform wavefield decomposition on the original wavefield using a preset auxiliary wavefield expression. Alternatively, when the server 102 executes the method alone, the server 102 can perform data analysis and calculation based on the wavefield data of the original wavefield uploaded to the server 102 by other devices, thereby achieving wavefield decomposition of the original wavefield. The server 102 can also store the result data of the wavefield decomposition in the server 102, or send the result data of the wavefield decomposition to other devices for display to relevant personnel, or continue to perform other data calculations based on the result data of the wavefield decomposition, without limitation.

[0075] In some embodiments, when the terminal 101 and server 102 interactively execute the method, the terminal 101 and server 102 are associated, and the server 102 provides background services to the terminal 101. Optionally, the server 102 undertakes the main computational work, and the terminal 101 undertakes the secondary computational work; or, the server 102 undertakes the secondary computational work, and the terminal 101 undertakes the main computational work; or, the server 102 and the terminal 101 use a distributed computing architecture for collaborative computation. For example, the server 102 performs wavefield decomposition operator calculations and auxiliary wavefield data calculations based on the original wavefield data. The server 102 sends the computational results to the terminal 101, and the terminal 101 performs wavefield decomposition on the original wavefield based on the received computational results to obtain P-wave data and S-wave data.

[0076] It should be noted that in the following embodiments, the wavefield decomposition method based on wavefront phase direction proposed in the embodiments of this application will be used as an example for illustration when the terminal executes the method alone.

[0077] Figure 2 This is a flowchart of a wavefield decomposition method based on wavefront phase direction provided in an embodiment of this application, executed by a terminal. See [link / reference]. Figure 2 The method includes the following steps:

[0078] 201. The terminal determines the wave field decomposition operator based on the original wave field and Thomsen parameters. The original wave field is either a displacement wave field or a particle vibration velocity wave field. The Thomsen parameters include anisotropy parameters and longitudinal and transverse wave velocities along the direction of the medium's symmetry axis. The wave field decomposition operator is a first-order pseudo-Helmholtz decomposition operator based on the wavefront phase direction.

[0079] In this embodiment, the wavefield decomposition operator is a pseudo-derivative operator determined in the spatial domain. The calculation method of this wavefield decomposition operator is the same as that of the decomposition operator in the first-order pseudo-Helmholtz decomposition method based on the wavefront phase direction.

[0080] The calculation method for the wave field decomposition operator is shown in Formula 1 below.

[0081] Formula 1:

[0082]

[0083] in, This indicates taking the first spatial derivative along the x-direction; This represents the first spatial derivative along the z-direction. r(x) represents an intermediate coefficient, the calculation of which is shown in Formula 2 below.

[0084] Formula 2:

[0085]

[0086] Where, n x This represents the component of the wavefront phase direction in the horizontal x-direction; n z The z-axis represents the component of the wavefront phase direction; r1(x), r2(x), r3(x), and r4(x) refer to multiple spatial functions.

[0087] The calculation method for the wavefront phase direction is shown in Formula 3 below.

[0088] Formula 3:

[0089]

[0090] Where n represents the wavefront phase direction; k represents the wave number; This indicates that gradient calculation is being performed; u represents the horizontal or vertical component of the displacement or particle vibration velocity wave field in the spatial domain.

[0091] The calculation methods for multiple spatial functions are shown in Formula 4 below.

[0092] Formula 4:

[0093]

[0094] Where ε and δ are the anisotropy parameters of the medium corresponding to the original wave field; v p and v s It refers to the longitudinal and transverse wave velocities along the axis of symmetry of the medium; where the displacement or particle vibration velocity wave field corresponds to the VTI medium.

[0095] In some embodiments, the step of the terminal determining the wavefield decomposition operator based on the original wavefield and Thomsen parameters includes: determining the wavefront phase direction based on the original wavefield obtained by forward modeling of the TI medium according to the calculation method indicated by Formula 3; determining the spatial function in the wavefield decomposition operator based on the Thomsen parameters according to the calculation method indicated by Formula 4; and determining the wavefield decomposition operator based on the wavefront phase direction and the spatial function according to the calculation methods indicated by Formula 2 and Formula 1.

[0096] Steps 202 to 204 below are the steps by which the terminal performs calculations on the auxiliary wavefield expression to obtain the auxiliary wavefield. Specifically, this is an exemplary way for the terminal to determine the auxiliary wavefield based on the original wavefield, Fourier transform, and Thomsen parameters.

[0097] 202. The terminal determines the wavenumber domain wavefield obtained after the original wavefield is converted to the wavenumber domain, based on the original wavefield.

[0098] In this embodiment of the disclosure, the terminal performs a Fast Fourier Transform (FFT) on the original wave field to transform the original wave field in the spatial domain to the wavenumber domain, thereby obtaining a wavenumber domain wave field.

[0099] 203. The terminal performs calculations based on the wavenumber domain wavefield and wavenumber, and then performs an inverse Fourier transform to obtain multiple intermediate quantities that constitute the auxiliary wavefield.

[0100] In this embodiment of the disclosure, the terminal performs an inverse fast fourier transform (FFT). -1 This transforms the intermediate quantities related to the original wavefield from the wavenumber domain to the spatial domain. The calculation methods for multiple intermediate quantities are shown in Formula 5 below.

[0101] Formula 5:

[0102]

[0103] Where u1, u2, and u3 represent multiple intermediate quantities that constitute the auxiliary wave field. FFT -1 Represents the inverse fast Fourier transform; U represents the wavenumber domain wavefield obtained after transforming the original wavefield to the wavenumber domain; k x Indicates the wave number in the x-direction; k z This represents the wave number in the z-direction.

[0104] 204. The terminal determines the auxiliary wavefield based on multiple intermediate quantities and Thomsen parameters through the auxiliary wavefield expression. The auxiliary wavefield expression is obtained by approximating the square of the modulus of the wavefield decomposition operator in the wavenumber domain.

[0105] In this embodiment of the disclosure, the terminal determines the auxiliary wavefield based on multiple intermediate quantities and Thomsen parameters according to the auxiliary wavefield expression indicated by Formula 6 below.

[0106] Formula Six:

[0107]

[0108] Where w represents the auxiliary wave field. ε and δ both represent anisotropy parameters; v p and v s The values ​​represent the longitudinal and transverse wave velocities along the axis of symmetry, and u1, u2, and u3 represent intermediate quantities that constitute the auxiliary wave field.

[0109] It should be noted that steps 202 to 204 above can be summarized as solving for the auxiliary wavefield in the space-wavenumber domain. In this process, solving for the auxiliary wavefield in the space-wavenumber domain differs from the traditional method of obtaining the auxiliary wavefield through the anisotropic Poisson equation. Traditional methods require solving the anisotropic Poisson equation in the spatial domain to obtain the auxiliary wavefield, while the auxiliary wavefield proposed in this application is approximated in the wavenumber domain. Therefore, it involves performing a Fast Fourier Transform (FFT) on the original wavefield to transform it from the spatial domain to the wavenumber domain, and also involves performing an inverse FFT to transform intermediate quantities related to the original wavefield from the wavenumber domain to the spatial domain. Because the auxiliary wavefield expression is approximated, the computational load is significantly reduced while lowering the computational accuracy of the auxiliary wavefield, thus improving computational efficiency.

[0110] 205. The terminal performs wave field decomposition based on the anisotropic wave field decomposition formula to achieve separation of longitudinal and transverse waves, and obtain the longitudinal wave field and the transverse wave field.

[0111] In this embodiment, the original wavefield is decomposed by applying a pseudo-divergence operator, a pseudo-gradient operator, and a pseudo-curl operator to the auxiliary wavefield, resulting in a P-wave field and a S-wave field. The pseudo-divergence operator is used to extract the P-waves from the original wavefield, and the pseudo-curl operator is used to extract the S-waves. The wavefield decomposition operator is also called the pseudo-gradient operator.

[0112] The equations used to decompose the original wavefield by applying pseudo-divergence, pseudo-gradient, and pseudo-curl operators to the auxiliary wavefield are shown in Formula 7 below.

[0113] Formula 7:

[0114]

[0115] Among them, u p and u s These represent the P-wave field and S-wave field calculated from the original wave field, respectively; w represents the auxiliary wave field. This represents a pseudo-gradient operator; This indicates the pseudo-divergence operator; This represents the pseudo-curl operator.

[0116] In some embodiments, the step of applying a pseudo-divergence operator, a pseudo-gradient operator, and a pseudo-curl operator to the auxiliary wavefield to decompose the original wavefield into a longitudinal wavefield and a transverse wavefield includes: applying a pseudo-divergence operator and then a pseudo-gradient operator to the auxiliary wavefield according to the calculation method indicated by Formula 7 to obtain the longitudinal wavefield; and applying a pseudo-curl operator twice to the auxiliary wavefield according to the calculation method indicated by Formula 7 to obtain the transverse wavefield.

[0117] This application provides a wavefield decomposition method based on wavefront phase direction, and more specifically, a fast decomposition method for P-waves and S-waves in VTI media based on wavefront phase direction, to quickly achieve anisotropic wavefield separation. It primarily utilizes the bivariate first-order Taylor approximation to solve for the auxiliary wavefield in the space-wavenumber domain, as reflected in the auxiliary wavefield expression. This method requires only one fast Fourier transform and three inverse fast Fourier transforms for each component at each time step to obtain the auxiliary wavefield, thereby achieving anisotropic wavefield separation and obtaining the P-wave and S-wave fields. This approach not only achieves P-wave and S-wave vector wavefield separation, providing P-wave and S-wave input data for elastic wave reverse time migration and reducing imaging crosstalk noise, but also reduces computational load by calculating the auxiliary wavefield in the space-wavenumber domain, balancing wavefield decomposition effect and computational efficiency. This method is more efficient than solving the anisotropic Poisson equation in the space domain to obtain the auxiliary wavefield, significantly improving computational efficiency. Furthermore, compared with existing anisotropic wave field decomposition methods, this method strikes a good balance between wave field decomposition effect and computational efficiency, which is of great significance for wave field separation and elastic wave migration imaging.

[0118] The above Figure 2 The flowchart of the wavefield decomposition method based on wavefront phase direction is introduced. See below. Figure 3 As shown, the process of determining the equations used in this method is introduced, including the process of determining the auxiliary wave field expression. Figure 3 This is a flowchart of a method for determining wavefield decomposition equations provided in an embodiment of this application. The method includes the following steps:

[0119] 301. Construct a wavefield decomposition operator, which is a first-order pseudo-Helmholtz decomposition operator based on the wavefront phase direction.

[0120] In this embodiment, the calculation method of the wavefield decomposition operator is shown in Equations 1 to 4 in step 201 above. It should be noted that the traditional calculation method for elastic wavefield decomposition of VTI media is shown in Equation 7 in step 203 above. However, the calculation method for the auxiliary wavefield in the traditional method differs from that proposed in this application. In the traditional method, the auxiliary wavefield is calculated by solving the anisotropic Poisson equation in the spatial domain, and its calculation method is shown in Equation 8 below.

[0121] Formula 8:

[0122]

[0123] Where w represents the auxiliary wave field; r This represents a spatial coefficient, the calculation method of which is shown in Formula 2 in step 201 above; This indicates taking the first spatial derivative along the x-direction; This indicates taking the first spatial derivative along the z-direction; u represents the original wave field.

[0124] 302. Perform a binary first-order Taylor approximation on the reciprocal of the square of the modulus of the wave field decomposition operator in the wavenumber domain, and return to the spatial domain to obtain the auxiliary wave field expression.

[0125] In some embodiments, when the wave field decomposition operator has been determined, the steps for determining the auxiliary wave field expression are shown in (1)-(3) below.

[0126] (1) Transform the anisotropic Poisson equation satisfied by the auxiliary wave field in the spatial domain to the wavenumber domain to obtain the expression of the auxiliary wave field in the wavenumber domain.

[0127] First, the anisotropic Poisson equation satisfied by the auxiliary wavefield in the spatial domain is shown in Equation 8 above. Transforming Equation 8 to the wavenumber domain yields the expression for the auxiliary wavefield; that is, the calculation method for the auxiliary wavefield is shown in Equation 9 below.

[0128] Formula Nine:

[0129]

[0130] Where W corresponds to w in the spatial domain, representing the wave field after transforming the auxiliary wave field in the spatial domain to the wavenumber domain; U corresponds to u in the spatial domain, representing the wave field after transforming the original wave field in the spatial domain to the wavenumber domain; k x Indicates the wave number in the horizontal x-direction; k z This represents the wave number in the z-direction. r represents an air-varying coefficient. Since the wavefront phase direction is defined by the wave number, the calculation method for this intermediate coefficient is shown in Formula 10 below.

[0131] Formula 10:

[0132]

[0133] Where r1, r2, r3, and r4 correspond to multiple spatial functions r1(x), r2(x), r3(x), and r4(x) in the spatial domain, respectively. The calculation methods for these spatial functions are shown in Formula 4 in step 201 above; k x Indicates the wave number in the horizontal x-direction; k z This represents the wave number in the z-direction.

[0134] Therefore, the reference auxiliary wavefield expression in the wavenumber domain can be represented by Equation 11 below. That is, the calculation method for the reference auxiliary wavefield is shown in Equation 11 below.

[0135] Formula 11:

[0136] W = -FU

[0137] Where W corresponds to w in the spatial domain, representing the wave field after transforming the auxiliary wave field in the spatial domain to the wave number domain; U corresponds to u in the spatial domain, representing the wave field after transforming the original wave field in the spatial domain to the wave number domain. F is a space-varying function related to the anisotropy parameter, and its calculation method is shown in Formula XII below.

[0138] Formula 12:

[0139]

[0140] Here, r1, r2, r3, and r4 correspond to multiple spatial functions r1(x), r2(x), r3(x), and r4(x) in the spatial domain, respectively. The calculation methods for the multiple spatial function values ​​are shown in Formula 4 in step 201 above. Since the multiple spatial function values ​​are related to the anisotropic parameters, the intermediate variable F also contains anisotropic parameters, and therefore can be expressed as F(ε,δ).

[0141] (2) Based on the space-varying function F(ε,δ), the auxiliary wave field expression is approximated to obtain the approximate auxiliary wave field in the wavenumber domain.

[0142] Accordingly, a two-dimensional first-order Taylor approximation is performed on F in the wavenumber domain to obtain the approximate F; in the auxiliary wavefield expression, F is replaced with the approximate expression to obtain the approximate auxiliary wavefield expression in the wavenumber domain.

[0143] For F(ε,δ), a two-dimensional first-order Taylor expansion is performed at F(0,0) to obtain an approximate intermediate variable. The calculation method is shown in Formula XIII below.

[0144] Formula Thirteen:

[0145]

[0146] Where, k x Indicates the wave number in the horizontal x-direction; k z Indicates the wave number in the z-direction; v p Corresponding to v in the spatial domain p (x); v s Corresponding to v in the spatial domain s (x); ε corresponds to ε(x) in the spatial domain; δ corresponds to δ(x) in the spatial domain.

[0147] Substituting Formula 13 into Formula 11 yields an approximate auxiliary wave field in the wavenumber domain.

[0148] (3) Transform the approximate auxiliary wave field expression to the spatial domain to obtain the auxiliary wave field in the spatial domain. The auxiliary wave field expression is shown in Formula 5 and Formula 6 above.

[0149] 303. Based on the wave field decomposition operator and auxiliary wave field expression, construct the wave field decomposition formula.

[0150] In this embodiment of the application, it can be seen from Formulas 6 and 7 that the VTI medium wave field decomposition formula is shown in Formula 14 below.

[0151] Formula Fourteen:

[0152]

[0153] in, This represents the wave field decomposition operator, also known as the pseudo gradient operator; Indicates the pseudo-divergence operator; represents the pseudo-curl operator; w represents the auxiliary wave field.

[0154] Therefore, by applying pseudo-divergence, pseudo-curl, and pseudo-gradient operators to the auxiliary wave field using Formula 14 above, the wave field decomposition of the VTI medium can be achieved, yielding the longitudinal and transverse waves in the original wave field.

[0155] This application provides a method for determining wavefield decomposition, which lays the foundation for wavefield decomposition methods based on wavefront phase direction. More specifically, it lays the foundation for a rapid decomposition method of longitudinal and transverse waves in VTI media based on wavefront phase direction, and can be used to quickly achieve anisotropic wavefield separation.

[0156] Through the following Figures 4-7 The image shown demonstrates the effectiveness of the wavefield decomposition method based on wavefront phase direction proposed in this application.

[0157] Figure 4 This is a schematic diagram illustrating the wave field decomposition results of a homogeneous anisotropic medium provided in an embodiment of this application. See also... Figure 4 As shown, Figure 4 In the figures, the horizontal axis represents distance, and the vertical axis represents depth. Figure 4 Figure (a) shows the horizontal component of the particle vibration velocity wave field, which is an original wave field; Figure 4 Figure (b) shows the vertical component of the particle vibration velocity wave field, which is another original wave field. After performing wave field decomposition on the two original wave fields respectively, the wave field decomposition results are as follows. Figure 4 Figure (c) shows the horizontal component of the longitudinal wave; Figure 4 The middle (d) diagram represents the vertical component of the longitudinal wave; Figure 4 Figure (e) shows the horizontal component of the transverse wave; Figure 4 The middle (d) diagram represents the vertical component of the transverse wave.

[0158] Figure 5 This is a schematic diagram of the model parameters of a test model provided in an embodiment of this application. The test model is the widely used Hess model for testing VTI medium wavefield separation algorithms. See also... Figure 5 As shown, Figure 5 In the figures, the horizontal axis represents distance, and the vertical axis represents depth. Figure 5 Figure (a) shows the P-wave velocity in the Hess model; Figure 5 Figure (b) shows the density of the Hess model; Figure 5 Figure (c) shows the anisotropy parameter ε; Figure 5 The figure in (d) represents the anisotropy parameter δ.

[0159] Figure 6 This is a schematic diagram of the horizontal and vertical components of the wave field of a test model provided in an embodiment of this application. The horizontal and vertical components of the particle vibration velocity are simulated using the traditional elastic wave equation for anisotropic media. The results are shown in [reference needed]. Figure 6 As shown. Figure 6 In the figures, the horizontal axis represents distance, and the vertical axis represents depth. Figure 6 Figure (a) shows the horizontal component of the particle vibration velocity wave field; Figure 6 Figure (b) shows the vertical component of the particle vibration velocity wave field. It can be seen that in the horizontal and vertical components of the particle vibration velocity wave field, the longitudinal wave and the transverse wave are coupled together, resulting in a complex wave field, which is not conducive to subsequent processing.

[0160] Figure 7 This is a schematic diagram of the wavefield decomposition result of a test model provided in an embodiment of this application. The method of this application is used to separate the P-waves and S-waves in the wavefield; the separation result is shown below. Figure 7 As shown in the figure. The horizontal axis of each graph represents distance, and the vertical axis represents depth. Among them, Figure 7 Figure (a) shows the horizontal component of the longitudinal wave; Figure 7 Figure (b) shows the vertical component of the longitudinal wave; Figure 7 Figure (c) shows the horizontal component of the transverse wave; Figure 7 Figure (d) shows the vertical component of the transverse wave. It can be seen that the longitudinal and transverse waves are effectively separated in the horizontal and vertical components of the particle vibration velocity wave field, providing a decoupled longitudinal and transverse wave field for subsequent elastic wave reverse time migration, and significantly reducing imaging crosstalk noise.

[0161] In this application, addressing the issues of P-wave and S-wave decomposition effectiveness and computational complexity in VTI media in the spatial domain, an auxiliary wavefield is solved in the space-wavenumber domain, combined with a first-order pseudo-Helmholtz decomposition operator in the wavefront phase direction, achieving rapid decomposition of P-waves and S-waves in VTI media. This is primarily achieved using the bivariate first-order Taylor approximation to solve the auxiliary wavefield in the space-wavenumber domain. This approach not only achieves P-wave and S-wave vector wavefield separation, providing P-wave and S-wave input data for elastic wave reverse-time migration and reducing imaging crosstalk noise, but also reduces computational complexity by calculating the auxiliary wavefield in the space-wavenumber domain, balancing wavefield decomposition effectiveness and computational efficiency. This method is more efficient than methods that obtain the auxiliary wavefield by solving the anisotropic Poisson equation in the spatial domain, significantly improving computational efficiency. Furthermore, compared to existing anisotropic wavefield decomposition methods, this method achieves a good balance between wavefield decomposition effectiveness and computational efficiency, which is of great significance for both wavefield separation and elastic wave migration imaging.

[0162] Figure 8 This is a block diagram of a wavefield decomposition device based on wavefront phase direction provided in an embodiment of this application. This device is used to execute the steps of the aforementioned wavefield decomposition method based on wavefront phase direction. See [link to relevant documentation]. Figure 8 The wavefield decomposition device based on wavefront phase direction includes: operator determination module 801, auxiliary wavefield determination module 802, and wavefield decomposition module 803.

[0163] The operator determination module 801 is used to determine the wave field decomposition operator based on the original wave field and Thomsen parameters. The original wave field is a displacement wave field or a particle vibration velocity wave field. The Thomsen parameters include anisotropy parameters and longitudinal and transverse wave velocities along the direction of the medium's symmetry axis. The wave field decomposition operator is a first-order pseudo-Helmholtz decomposition operator based on the wavefront phase direction.

[0164] The auxiliary wavefield determination module 802 is used to determine the wavenumber domain wavefield obtained after the original wavefield is transformed into the wavenumber domain, based on the original wavefield; to perform calculations based on the wavenumber domain wavefield and wavenumber, and then to perform an inverse Fourier transform to obtain multiple intermediate quantities that constitute the auxiliary wavefield; based on the multiple intermediate quantities and the Thomsen parameter, the auxiliary wavefield is determined through the auxiliary wavefield expression, which is obtained by approximating the square of the modulus of the wavefield decomposition operator in the wavenumber domain;

[0165] The wave field decomposition module 803 is used to decompose the wave field based on the anisotropic wave field decomposition formula, realize the separation of P-waves and S-waves, and obtain the P-wave wave field and the S-wave wave field.

[0166] In some embodiments, the operator determination module 801 is used to determine the wavefront phase direction based on the original wavefield obtained by forward modeling of the TI medium; determine the spatial function in the wavefield decomposition operator based on the Thomsen parameters; and determine the wavefield decomposition operator based on the wavefront phase direction and the spatial function.

[0167] In some embodiments, the auxiliary wave field expression is as follows:

[0168]

[0169] Where w(x) represents the auxiliary wavefield; ε and δ represent the anisotropy parameters; v p and v s These represent the longitudinal and transverse wave velocities along the axis of symmetry of the medium, respectively.

[0170] Where u1, u2, and u3 represent intermediate quantities constituting the auxiliary wave field, respectively expressed as:

[0171]

[0172] Among them, FFT -1 Represents the inverse fast Fourier transform; U represents the wavenumber domain wavefield obtained after transforming the original wavefield to the wavenumber domain; k x Indicates the wave number in the x-direction; k z This represents the wave number in the z-direction.

[0173] In some embodiments, the anisotropic wave field decomposition formula requires the application of a pseudo-divergence operator, a pseudo-gradient operator, and a pseudo-curl operator to the auxiliary wave field. The pseudo-divergence operator is used to extract the longitudinal waves in the original wave field, and the pseudo-curl operator is used to extract the transverse waves in the original wave field.

[0174] In some embodiments, the wave field decomposition module 803 is used to apply the pseudo-divergence operator and the pseudo-gradient operator to the auxiliary wave field to obtain the longitudinal wave field; and to apply the pseudo-curl operator to the auxiliary wave field to obtain the transverse wave field.

[0175] In some embodiments, the equations used by the wavefield decomposition module are expressed as follows:

[0176]

[0177] Among them, u p and u s These represent the P-wave field and S-wave field calculated from the original wave field, respectively; w represents the auxiliary wave field. This represents a pseudo-gradient operator; Indicates the pseudo-divergence operator; This represents the pseudo-curl operator.

[0178] This application provides a wavefield decomposition device based on wavefront phase direction. It determines the wavefield decomposition operator based on the original wavefield and Thomsen parameters. This operator is a first-order pseudo-Helmholtz decomposition operator based on the wavefront phase direction. Then, an auxiliary wavefield is determined by combining the original wavefield, Fourier transform, and Thomsen parameters with the auxiliary wavefield expression. During this process, forward and inverse Fourier transforms are performed on the original and intermediate wavefields to obtain the auxiliary wavefield. By applying pseudo-divergence, pseudo-gradient, and pseudo-curl operators to the auxiliary wavefield, wavefield decomposition of the original wavefield can be achieved, resulting in the P-wave and S-wave fields. This device not only achieves P-wave and S-wave vector wavefield separation, providing P-wave and S-wave input data for elastic wave reverse time migration and reducing imaging crosstalk noise, but also reduces computational load by calculating the auxiliary wavefield in the space-wavenumber domain, balancing wavefield decomposition effect and computational efficiency.

[0179] It should be noted that the wavefield decomposition device based on wavefront phase direction provided in the above embodiments is only illustrated by the division of the above functional modules when running the application. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the terminal can be divided into different functional modules to complete all or part of the functions described above. In addition, the wavefield decomposition device based on wavefront phase direction provided in the above embodiments and the wavefield decomposition method embodiments based on wavefront phase direction belong to the same concept, and the specific implementation process can be found in the method embodiments, which will not be repeated here.

[0180] Figure 9 This is a schematic diagram of the structure of a terminal provided in an embodiment of this application. The terminal 900 can be a portable mobile terminal, such as a smartphone, tablet computer, laptop computer, or desktop computer. The terminal 900 may also be referred to as user equipment, portable terminal, laptop terminal, desktop terminal, or other names.

[0181] Typically, terminal 900 includes a processor 901 and a memory 902.

[0182] Processor 901 may include one or more processing cores, such as a quad-core processor, a nine-core processor, etc. Processor 901 may be implemented using at least one hardware form selected from DSP (Digital Signal Processing), FPGA (Field-Programmable Gate Array), and PLA (Programmable Logic Array). Processor 901 may also include a main processor and a coprocessor. The main processor, also known as a CPU (Central Processing Unit), is used to process data in the wake-up state; the coprocessor is a low-power processor used to process data in the standby state. In some embodiments, processor 901 may integrate a GPU (Graphics Processing Unit), which is responsible for rendering and drawing the content to be displayed on the screen. In some embodiments, processor 901 may also include an AI (Artificial Intelligence) processor, which is used to handle computational operations related to machine learning.

[0183] The memory 902 may include one or more computer-readable storage media, which may be non-transitory. The memory 902 may also include high-speed random access memory and non-volatile memory, such as one or more disk storage devices or flash memory devices. In some embodiments, the non-transitory computer-readable storage media in the memory 902 are used to store at least one computer program, which is executed by the processor 901 to implement the wavefront phase direction-based wavefield decomposition method provided in the method embodiments of this application.

[0184] In some embodiments, the terminal 900 may also optionally include a peripheral device interface 903 and at least one peripheral device. The processor 901, memory 902, and peripheral device interface 903 can be connected via a bus or signal line. Each peripheral device can be connected to the peripheral device interface 903 via a bus, signal line, or circuit board. Specifically, the peripheral device includes at least one of the following: a radio frequency circuit 904, a display screen 905, a camera assembly 906, an audio circuit 907, and a power supply 908.

[0185] Peripheral device interface 903 can be used to connect at least one I / O (Input / Output) related peripheral device to processor 901 and memory 902. In some embodiments, processor 901, memory 902 and peripheral device interface 903 are integrated on the same chip or circuit board; in some other embodiments, any one or two of processor 901, memory 902 and peripheral device interface 903 can be implemented on separate chips or circuit boards, which is not limited in this embodiment.

[0186] The radio frequency (RF) circuit 904 is used to receive and transmit RF (Radio Frequency) signals, also known as electromagnetic signals. The RF circuit 904 communicates with communication networks and other communication devices via electromagnetic signals. The RF circuit 904 converts electrical signals into electromagnetic signals for transmission, or converts received electromagnetic signals back into electrical signals. In some embodiments, the RF circuit 904 includes: an antenna system, an RF transceiver, one or more amplifiers, a tuner, an oscillator, a digital signal processor, a codec chipset, a user identity module card, etc. The RF circuit 904 can communicate with other terminals through at least one wireless communication protocol. This wireless communication protocol includes, but is not limited to: the World Wide Web, metropolitan area networks, intranets, various generations of mobile communication networks (2G, 3G, 4G, and 5G), wireless local area networks, and / or WiFi (Wireless Fidelity) networks. In some embodiments, the RF circuit 904 may also include circuitry related to NFC (Near Field Communication), which is not limited in this application.

[0187] Display screen 905 is used to display a UI (User Interface). This UI may include graphics, text, icons, videos, and any combination thereof. When display screen 905 is a touch display screen, it also has the ability to collect touch signals on or above its surface. These touch signals can be input as control signals to processor 901 for processing. In this case, display screen 905 can also be used to provide virtual buttons and / or a virtual keyboard, also known as soft buttons and / or a soft keyboard. In some embodiments, there may be one display screen 905, disposed on the front panel of terminal 900; in other embodiments, there may be at least two display screens 905, disposed on different surfaces of terminal 900 or in a folded design; in other embodiments, display screen 905 may be a flexible display screen, disposed on a curved or folded surface of terminal 900. Furthermore, display screen 905 may be configured as a non-rectangular irregular shape, i.e., a non-rectangular screen. Display screen 905 may be made of materials such as LCD (Liquid Crystal Display) or OLED (Organic Light-Emitting Diode).

[0188] The camera assembly 906 is used to acquire images or videos. In some embodiments, the camera assembly 906 includes a front-facing camera and a rear-facing camera. Typically, the front-facing camera is located on the front panel of the terminal, and the rear-facing camera is located on the back of the terminal. In some embodiments, there are at least two rear-facing cameras, which are any one of a main camera, a depth-sensing camera, a wide-angle camera, and a telephoto camera, to achieve background blurring by fusion of the main camera and the depth-sensing camera, panoramic shooting by fusion of the main camera and the wide-angle camera, VR (Virtual Reality) shooting, or other fusion shooting functions. In some embodiments, the camera assembly 906 may also include a flash. The flash can be a single-color temperature flash or a dual-color temperature flash. A dual-color temperature flash refers to a combination of a warm-light flash and a cool-light flash, which can be used for light compensation at different color temperatures.

[0189] The audio circuit 907 may include a microphone and a speaker. The microphone is used to collect sound waves from the user and the environment, converting them into electrical signals that are input to the processor 901 for processing, or to the radio frequency circuit 904 for voice communication. For stereo sound acquisition or noise reduction purposes, multiple microphones may be used, each positioned at a different location on the terminal 900. The microphone may also be an array microphone or an omnidirectional microphone. The speaker is used to convert electrical signals from the processor 901 or the radio frequency circuit 904 into sound waves. The speaker may be a conventional diaphragm speaker or a piezoelectric ceramic speaker. When the speaker is a piezoelectric ceramic speaker, it can convert electrical signals not only into audible sound waves but also into inaudible sound waves for purposes such as distance measurement. In some embodiments, the audio circuit 907 may also include a headphone jack.

[0190] Power supply 908 is used to power the various components in terminal 900. Power supply 908 can be AC ​​power, DC power, a disposable battery, or a rechargeable battery. When power supply 908 includes a rechargeable battery, the rechargeable battery can support wired or wireless charging. The rechargeable battery can also be used to support fast charging technology.

[0191] Those skilled in the art will understand that Figure 9 The structure shown does not constitute a limitation on terminal 900 and may include more or fewer components than shown, or combine certain components, or use different component arrangements.

[0192] Figure 10 This is a schematic diagram of a server structure provided in an embodiment of this application. The server 1000 can vary significantly due to different configurations or performance. It may include one or more Central Processing Units (CPUs) 1001 and one or more memories 1002. The memories 1002 store at least one computer program, which is loaded and executed by the processor 1001 to implement the wavefield decomposition method based on wavefront phase direction provided in the various method embodiments described above. Of course, the server may also have wired or wireless network interfaces, a keyboard, and input / output interfaces for input and output. The server may also include other components for implementing device functions, which will not be elaborated here.

[0193] This application also provides a computer-readable storage medium storing at least one computer program, which is loaded and executed by a processor to implement the wavefield decomposition method based on wavefront phase direction described in the above embodiments. For example, the computer-readable storage medium may be a read-only memory (ROM), a random access memory (RAM), a compact disc read-only memory (CD-ROM), magnetic tape, floppy disk, or optical data storage device, etc.

[0194] This application also provides a computer program product, including a computer program that is executed by a processor to implement the wavefield decomposition method based on wavefront phase direction in this application.

[0195] Those skilled in the art will understand that all or part of the steps of the above embodiments can be implemented by hardware or by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as a read-only memory, a disk, or an optical disk.

[0196] The above description is merely an optional embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A wavefield decomposition method based on wavefront phase direction, characterized in that, The method includes: Based on the original wave field and Thomsen parameters, a wave field decomposition operator is determined. The original wave field is a displacement wave field or a particle vibration velocity wave field. The Thomsen parameters include anisotropy parameters and longitudinal and transverse wave velocities along the direction of the medium's symmetry axis. The wave field decomposition operator is a first-order pseudo-Helmholtz decomposition operator based on the wavefront phase direction. Based on the original wave field, determine the wavenumber domain wave field obtained after transforming the original wave field into the wavenumber domain; Based on the wavenumber domain wavefield and wavenumber, the calculations are performed, and then an inverse Fourier transform is performed to obtain multiple intermediate quantities that constitute the auxiliary wavefield. Based on the multiple intermediate quantities and the Thomsen parameters, the auxiliary wavefield is determined through an auxiliary wavefield expression, which is obtained by approximating the square of the modulus of the wavefield decomposition operator in the wavenumber domain. Wave field decomposition is performed based on the anisotropic wave field decomposition formula to achieve separation of P-waves and S-waves, and obtain the P-wave field and the S-wave field.

2. The method according to claim 1, characterized in that, The determination of the wavefield decomposition operator based on the original wavefield and Thomsen parameters includes: The wavefront phase direction is determined based on the original wave field obtained from the TI medium forward modeling simulation. Based on the Thomsen parameters, the spatial function in the wave field decomposition operator is determined; The wavefield decomposition operator is determined based on the wavefront phase direction and the spatial function.

3. The method according to claim 1, characterized in that, The auxiliary wavefield expression is as follows: Where w(x) represents the auxiliary wavefield; ε and δ represent the anisotropy parameters; v p and v s These respectively represent the longitudinal and transverse wave velocities along the direction of the medium's axis of symmetry; Where u1, u2, and u3 represent intermediate quantities constituting the auxiliary wave field, respectively expressed as: Among them, FFT -1 Represents the inverse fast Fourier transform; U represents the wavenumber domain wavefield obtained after the original wavefield is transformed into the wavenumber domain; k x Indicates the wave number in the x-direction; k z This represents the wave number in the z-direction.

4. The method according to claim 1, characterized in that, The anisotropic wavefield decomposition formula requires applying a pseudo-divergence operator, a pseudo-gradient operator, and a pseudo-curl operator to the auxiliary wavefield. The pseudo-divergence operator is used to extract the longitudinal waves in the original wavefield, and the pseudo-curl operator is used to extract the transverse waves in the original wavefield.

5. The method according to claim 4, characterized in that, The wave field decomposition based on the anisotropic wave field decomposition formula, which separates the P-wave and S-wave, to obtain the P-wave field and the S-wave field, includes: The pseudo-divergence operator and the pseudo-gradient operator are applied to the auxiliary wave field to obtain the longitudinal wave field. The pseudo-curl operator is applied to the auxiliary wave field to obtain the transverse wave field.

6. The method according to claim 1, characterized in that, The equations used in the process of performing wavefield decomposition based on the anisotropic wavefield decomposition formula to separate the P-wave and S-wave fields and obtain the P-wave and S-wave fields are expressed as follows: Among them, u p and u s The P-wave field and the S-wave field, respectively, are calculated from the original wave field; w represents the auxiliary wave field. This represents a pseudo-gradient operator; Indicates the pseudo-divergence operator; × represents the pseudo-curl operator.

7. A wavefield decomposition device based on wavefront phase direction, characterized in that, The device includes: The operator determination module is used to determine the wave field decomposition operator based on the original wave field and Thomsen parameters. The original wave field is a displacement wave field or a particle vibration velocity wave field. The Thomsen parameters include anisotropy parameters and longitudinal and transverse wave velocities along the direction of the medium's symmetry axis. The wave field decomposition operator is a first-order pseudo-Helmholtz decomposition operator based on the wavefront phase direction. An auxiliary wavefield determination module is used to determine the wavenumber domain wavefield obtained after transforming the original wavefield to the wavenumber domain, based on the original wavefield; perform calculations based on the wavenumber domain wavefield and wavenumber, and then perform an inverse Fourier transform to obtain multiple intermediate quantities constituting the auxiliary wavefield; and determine the auxiliary wavefield based on the multiple intermediate quantities and the Thomsen parameters through an auxiliary wavefield expression, wherein the auxiliary wavefield expression is obtained by approximating the square of the modulus of the wavefield decomposition operator in the wavenumber domain. The wave field decomposition module is used to decompose the wave field based on the anisotropic wave field decomposition formula, realize the separation of P-waves and S-waves, and obtain the P-wave wave field and the S-wave wave field.

8. A computer device, characterized in that, The computer device includes a processor and a memory, the memory being used to store at least one computer program, the at least one computer program being loaded by the processor and executed as described in any one of claims 1 to 6, the wavefield decomposition method based on wavefront phase direction.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store at least one computer program for executing the wavefield decomposition method based on wavefront phase direction as described in any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, The computer program, when executed by a processor, implements the wavefield decomposition method based on wavefront phase direction as described in any one of claims 1 to 6.

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