变网格有限差分弹性波方程数值模拟方法

Numeric simulation by grid-various finite-difference elastic wave equation

研究复杂介质中地震波传播规律及地震响应特征,需要在细小网格剖分下进行弹性波方程数值模拟计算,而小网格下的数值模拟计算将带来巨大的计算量问题,采用变网格计算是减少计算量的有效途径。本文给出一种变网格差分计算的实现方法,在局部复杂介质区域采用细网格计算,其余区域采用粗网格计算,在两种网格的过渡区通过改变差分算子和波场插值实现波传播的过渡衔接。理论分析和数值模拟结果表明,变网格时在粗细网格的过渡区不会对地震波传播模拟带来影响,从而达到了既减少计算量又保证计算精度的目的。

Studying seismic wave propagating rule and seismic response in complex medium needs carrying out numeric simulation of elastic wave equation under tiny grid separation,which brings an issue of giant computational works,and using grid-various computation is effective way to reduce computational works.The paper gives a method for implementing grid-various finite-difference computation: the computation in tiny grid is used in local complex medium area,the computation in gross grid is carried out in rest area.In transitional area between two grids,the transitional link is finished by changing differential operator and wavefield interpolation.The theoretical analysis and numeric simulation showed that it does not affect the simulation of seismic wave propagation in the transitional area between the gross and tiny grid,which attained the goal both reducing computational works and guaranteeing the precision.