Linear optimization implicit time-space domain finite difference numerical simulation method based on acoustic wave equation

Abstract

The invention discloses a linear optimization implicit time-space domain finite difference numerical simulation method based on an acoustic wave equation, including the following steps: (1) reading parameters; (2) obtaining the time high-order discrete format of a time derivative based on a diamond difference operator and second-order time central difference; (3) solving a second-order spatial derivative by using a spatially implicit discrete format, and solving an implicit differential coefficient based on a spatial dispersion relation and an optimization method; (4) obtaining the time-spacedomain dispersion relation based on the time high-order discrete format and the spatial implicit discrete format; (5) solving the differential coefficient in the time high-order discrete format by using a linear optimization algorithm; (6) absorbing the boundary reflection by using a mixed absorption boundary condition and the obtained differential coefficient, performing recursion according to the wave equation to obtain the wave field at any time and an entire seismic record; and (7) recording a wave field snapshot, outputting the seismic record and ending the process. The finite differencenumerical simulation method has high accuracy, good stability and low dispersion errors.

Description

technical field [0001] The invention belongs to the technical field of seismic wave field numerical simulation, and relates to a high-precision, high-efficiency linear optimization implicit time-space domain finite difference numerical simulation method based on solving acoustic wave equations. Background technique [0002] At present, the reverse time migration method and the full waveform inversion technology have shown great potential in processing the imaging of complex structures such as salt domes and the inversion of reservoir parameters, and have been paid more and more attention by geophysicists. However, both reverse time migration and full waveform inversion methods involve the numerical solution of the wave equation. When the model is too large, especially when the model is three-dimensional, the computational complexity is large and time-consuming, which restricts the development of these two technologies to some extent. Therefore, high-precision, high-efficienc...

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Problems solved by technology

[0004] The purpose of the present invention is to provide a linear optimization implicit time-space domain finite difference numerical simulation method based on the acoustic wave equation in order to overcome the problems of low time accuracy, poor stability and easy dispersion of the traditional implicit spatial finite difference method, which has higher precision and better stability, under the premise of maintaining the spatial implicit differential accuracy, the present invention proposes a linear optimization time-space domain strategy that significantly suppresses time dispersion (that is, the fifth step in the claim), which can be reverse time migration and the full waveform inversion method provide a wave field with smaller dispersion and higher precision, and can help improve the accuracy and efficiency of the numerical simulation of the acoustic wave equation

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