适用于声波方程数值模拟的时间-空间域隐式有限差分算子优化方法

声波方程数值模拟已广泛应用于理论地震计算,同时构成了地震逆时偏移成像技术的基础.对于有限差分法而言,在满足一定的稳定性条件时,普遍存在着因网格化而形成的数值频散效应.如何有效地缓解或压制数值频散是有限差分方法研究的关键所在.有限差分格式分为显式有限差分和隐式有限差分.隐式有限差分能够进一步压制数值频散效应.因此本文提出了给定频率范围满足时间-空间域隐式有限差分频散关系的方法,并根据震源频率、波速和网格间距确定波数范围,在此基础上建立方程确定了相应的隐式有限差分系数,使得差分系数能在更大频率范围符合波场传播规律.通过频散分析和正演模拟,验证了本文方法的有效性.

Acoustic wave equation modeling based on implicit finite difference operators in the time-space domain

Numerical simulation of acoustic wave equation is widely used to synthesize seismograms theoretically, and is also the basis of reverse time migration. With some stability conditions, dispersion often appears when time and the spatial derivatives in the wave equation are gridded. How to suppress such grid dispersion is therefore a key problem for finite difference approaches. Finite-difference formulations of partial differential equations are either explicit or implicit. Implicit formulations can suppress the grid dispersion further and the stability condition is better. Therefore, we propose to satisfy the time-space domain dispersion relationship in a proper range of frequencies. Dispersion analysis and seismic numerical simulation demonstrate the effectiveness of the proposed method.