A time-domain acoustic wave equation explicit finite-difference seismic response simulation method

Abstract

The invention relates to a time domain acoustic wave equation explicit finite difference seismic response simulation method. The method includes the following steps that: 1) the initial value and allowable maximum approximation error xi of spatial difference operator length 2M+1 are set; 2) on the basis of space-wave number domain function approximation-based spatial finite difference coefficient solving method, the difference coefficient and wave number domain error function value of an explicit finite difference formula which is built based on K-space operator compensation numerical value simulation error are solved according to the acoustic wave speed of a target region; 3) if the wave number domain error function value is larger than the allowable maximum approximation error xi, 1 is added to the value of M, and the method returns to step 2), if the wave number domain error function value is smaller than the allowable maximum approximation error xi, and M is larger than 1, 1 is subtracted from the value of M, and the method returns to step 2), otherwise, a minimum spatial difference operator length 2M+1 which satisfies the allowable maximum approximation error xi and a difference coefficient corresponding to the minimum spatial difference operator length 2M+1 are determined, a next step is continued; and 4) seismic response numerical value simulation is performed on the target region, so that the simulation seismic records or seismic waves of the target region can be obtained.

Description

technical field [0001] The invention relates to a seismic response simulation method of wave equation, in particular to a time domain acoustic wave equation explicit finite difference seismic response simulation method. Background technique [0002] Wave equation forward modeling is an important research direction in the field of exploration geophysics, and it is of great significance to the simulation of wave phenomena, the research and implementation of reverse time migration and full waveform inversion. At present, the wave equation forward modeling methods mainly include finite difference method, finite element method, boundary element method and pseudospectral method. Among many forward modeling methods, the finite difference method has smaller computational complexity and memory requirements than other methods, and can meet the computational speed and memory requirements of reverse time migration and full waveform inversion. Therefore, the finite difference method is ...

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Problems solved by technology

The third is to obtain the finite difference coefficient based on the optimization method. This method can still achieve high accuracy for high-frequency components, but the calculation amount is large. In some cases, it is easy to fall into the local optimum and cannot obtain the global optimum value.

Because reverse time migration and full waveform inversion require a lot of forward calculations, the current finite difference method still has a huge amount of calculation and memory requirements, and the calculation speed and efficiency are low, which limits the wide application of reverse time migration and full waveform inversion , so high-precision and high-efficiency finite-difference forward modeling is the key to the widespread implementation of reverse time migration and full waveform inversion

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