CN-122017962-A - High-precision seismic elastic wave field forward modeling method, device, equipment and storage medium

CN122017962ACN 122017962 ACN122017962 ACN 122017962ACN-122017962-A

Abstract

The embodiment of the application provides a high-precision seismic elastic wave field forward modeling method, device, equipment and storage medium, wherein the method comprises the steps of dispersing wave equations in an elastic medium by jointly applying an improved time-high-order implicit staggered grid differential method, and obtaining two types of time-space domain dispersion relations about P waves and S waves based on plane wave finishing simplification; the method comprises the steps of combining a least square method and a Taylor series expansion method to solve two types of time-space domain dispersion relations of P waves and S waves to obtain high-order differential coefficients corresponding to the P waves and the S waves, calculating a P wave field component by using the high-order differential coefficients corresponding to the P waves based on a wave field separation technology, calculating an S wave field component by using the high-order differential coefficients corresponding to the S waves, and superposing the components to obtain a high-precision full-elastic wave field. According to the technical scheme, better simulation precision can be generated under the same parameter condition, so that an effective wave field prolongation scheme is provided for subsequent elastic wave migration imaging and waveform inversion.

Inventors

WEI ZHEFENG
ZHU CHENGHONG

Assignees

中国石油化工股份有限公司
中国石油化工股份有限公司石油勘探开发研究院

Dates

Publication Date: 20260512
Application Date: 20241112

Claims (10)

1. The high-precision seismic elastic wave field forward modeling method is characterized by comprising the following steps of: The improved time-high-order implicit staggered grid differential method is jointly applied to discrete wave equations in an elastic medium, and two types of time-space domain dispersion relations about P waves and S waves are obtained based on plane wave sorting and simplification; Solving two types of time-space domain dispersion relations of the P wave and the S wave by combining a least square method and a Taylor series expansion method to obtain high-order differential coefficients corresponding to the P wave and the S wave; Based on wave field separation technology, the P wave field component is calculated by using the high-order difference coefficient corresponding to the P wave, the S wave field component is calculated by using the high-order difference coefficient corresponding to the S wave, and the components are overlapped to obtain the high-precision full-elastic wave field.
2. The method of claim 1, wherein the wave equation in the elastic medium is as follows: Where v x and v z are the velocity components, τ xx 、τ zz and τ xz are the stress components, ρ is the density, And V p and v s are longitudinal and transverse wave velocities, respectively, t is a time term, x is a spatial transverse coordinate, and z is a spatial longitudinal coordinate, which are Ramez constants.
3. The method of claim 2, wherein the wave equation in the elastic medium is discretized by jointly applying a modified time-high order implicit staggered grid differencing method, resulting in a discrete form of the wave equation in the elastic medium that is: in the above formula, Δt is a time sampling interval; The lower corner marks i and j in the space x direction and the grid index in the z direction, the upper corner mark o is a time grid index, f 1 ,f 3 ,g 1 ,g 3 ,p 1 ,q 1 ,w 1 ,w 3 is hidden format differential solution, f 2 ,f 4 ,g 2 ,g 4 ,p 2 ,q 2 ,w 2 ,w 4 is explicit format differential solution, and the specific form is as follows: Wherein h is the space grid step length, d m 、d m,n is the higher-order differential coefficient involved in the improved discrete format, M is half of the length of the space differential operator, N is half of the length of the time differential operator, M is the grid index of the space differential operator M, N is the grid index of the time differential operator N, b is the differential coefficient in the hidden format, and the method comprises the following steps Wherein X is any wavefield component; The method is a wave field value at any moment, wherein lower corner marks i and j are grid indexes in the x direction and the z direction of space, and upper corner mark o is a time grid index; the sign is determined for the second partial derivative along the x-direction.
4. A method according to claim 3, characterized in that the two types of time-space domain dispersion relation for P-waves and S-waves are as follows: Wherein, the Omega is angular frequency, deltat is time sampling interval, r p ＝v p deltat/h is P wave kurtosis, v p is longitudinal wave velocity, h is space grid step length, r s ＝v s deltat/h is S wave kurtosis, v s is transverse wave velocity, d m 、d m,n is higher order differential coefficient involved in the improved discrete format, M is half of the length of the spatial differential operator, N is half of the length of the temporal differential operator, M is the index of the spatial differential operator M, N is the index of the temporal differential operator N, k x is wave number in x direction, b is differential coefficient in hidden format, and k z is wave number in z direction.
5. The method of claim 1, wherein the calculation formula of the high order differential coefficients corresponding to the P-wave and the S-wave is as follows: The corresponding P-wave differential coefficient in the improved time high-order implicit staggered grid differential method can be obtained by solving the equations (34) - (37), the corresponding S-wave differential coefficient in the improved time high-order implicit staggered grid differential method can be obtained by solving the equations (34) - (38), wherein epsilon, delta, f ε,δ 、f δ,ε 、w ε+δ 、γ、w γ , Are all intermediate variables.
6. The method of claim 1, wherein the P-wave wavefield component is: Wherein, the As a component of velocity associated with the P-wave, For the stress component related to the P-wave, ρ is the density, v p is the longitudinal wave velocity, v x and v z are the velocity components, t is the time term, x is the spatial transverse coordinate, and z is the spatial longitudinal coordinate.
7. The method of claim 1, wherein the S-wave wavefield component is: Wherein, the As a velocity component associated with the S-wave, For stress components related to S-waves, ρ is density, v s is transverse wave velocity, v x and v z are velocity components, t is a time term, x is a spatial transverse coordinate, and z is a spatial longitudinal coordinate.
8. High accuracy seismic elastic wave field forward device, characterized by, include: The two types of time-space domain dispersion relation construction modules are used for dispersing wave equations in the elastic medium by jointly applying an improved time-high-order implicit staggered grid differential method, and two types of time-space domain dispersion relation about P waves and S waves are obtained based on plane wave finishing reduction; The high-order differential coefficient acquisition module is used for solving the time-space domain dispersion relation by combining a least square method and a Taylor series expansion method to obtain high-order differential coefficients corresponding to the P wave and the S wave; The high-precision full-elastic wave field acquisition module is used for calculating a P wave field component by adopting a high-order difference coefficient corresponding to the P wave based on a wave field separation technology, calculating an S wave field component by adopting a high-order difference coefficient corresponding to the S wave, and overlapping the components to obtain the high-precision full-elastic wave field.
9. An electronic device, comprising: A processor; a memory; and a computer program, wherein the computer program is stored in the memory, the computer program comprising instructions that, when executed by the processor, cause the electronic device to perform the method of any one of claims 1 to 7.
10. A computer readable storage medium, characterized in that the computer readable storage medium comprises a stored program, wherein the program, when run, controls a device in which the computer readable storage medium is located to perform the method of any one of claims 1 to 7.

Description

High-precision seismic elastic wave field forward modeling method, device, equipment and storage medium Technical Field The application relates to the field of geophysical exploration seismic forward modeling, in particular to a high-precision seismic elastic wave field forward modeling method, device and equipment and a storage medium. Background The high-precision seismic wave field prolongation technology is the basis and key of seismic migration imaging and waveform inversion. The core of the seismic wave field continuation is to carry out discrete solution on the wave equation by adopting a numerical algorithm, and among a plurality of seismic wave field numerical solution algorithms, a finite difference method is popular because of simplicity, easiness and high calculation efficiency. How to improve the numerical discrete accuracy, stability and flexibility is a long-term research goal of finite difference methods. The higher order analog accuracy in the spatial domain can be achieved by increasing the finite difference operator length (Dablain, 1986; virieux,1986; dong Liangguo et al, 2000; pei Zhenglin, 2004; du Qizhen et al, 2010; liu Yang, 2014; yin Xingyao et al, 2015), but its analog accuracy in the time domain is still second order. The idea of replacing higher order time derivatives with a combination of spatial derivatives can effectively improve the time accuracy (Dablain, 1986; chen, 2011), but the scheme belongs to a spatial domain method, and the accuracy still needs to be further improved. Liu and Sen (2009) developed a time-space domain finite difference method, and the difference coefficient calculated by the method depends on wave field propagation parameters, so that the time simulation precision can be effectively improved on the premise of ensuring the space simulation precision. Further, liu and Sen (2013) developed a time-space domain finite difference scheme based on a diamond-shaped difference method, which introduces paraxial nodes on the basis of a traditional cross-shaped difference method to achieve high-order simulation accuracy in time-space. Based on this idea, by introducing additional grid nodes on the basis of the traditional finite difference method to jointly approximate different partial derivatives in the wave equation and adopting a taylor expansion or optimization algorithm to solve the corresponding time-space domain dispersion relation, the novel combined difference method can obtain high-order space and time simulation precision (Tan and Huang,2014; wang et al 2016; zhang Baoqing et al 2016; chen et al 2017; ren et al 2017). However, the existing time high-order differential method mainly adopts an explicit differential method to discrete partial derivatives in the wave equation, and compared with the explicit differential, the implicit differential can obtain higher simulation precision under the condition that operator lengths are consistent. Therefore, in order to further improve the time and space precision of the finite difference method in solving the wave equation, it is necessary to develop a time-high-order implicit finite difference method for the wave equation in the elastic medium, and the method has important research significance on the elastic wave reverse time migration and waveform inversion. Disclosure of Invention In view of this, in order to improve the accuracy of forward modeling of the seismic wave field, the present application provides a high-accuracy forward modeling method, device, apparatus and storage medium for the seismic elastic wave field based on the high-accuracy elastic wave field numerical modeling of the improved hidden-format time-based high-order differential method, which can enable the elastic wave numerical modeling to obtain higher time and space accuracy at the same time, generate more accurate seismic wave field response, and further provide more effective seismic wave field extrapolation tools for seismic wave field migration imaging and full waveform inversion. In a first aspect, an embodiment of the present application provides a high-precision seismic elastic wave field forward modeling method, including: The improved time-high-order implicit staggered grid differential method is jointly applied to discrete wave equations in an elastic medium, and two types of time-space domain dispersion relations about P waves and S waves are obtained based on plane wave sorting and simplification; Solving two types of time-space domain dispersion relations of the P wave and the S wave by combining a least square method and a Taylor series expansion method to obtain high-order differential coefficients corresponding to the P wave and the S wave; Based on wave field separation technology, the P wave field component is calculated by using the high-order difference coefficient corresponding to the P wave, the S wave field component is calculated by using the high-order difference coefficient corresponding to the S wave, and the