褶积微分算子法数值模拟的边界问题研究

STUDY ON THE BOUNDARY PROBLEM FOR THE NUMERICAL MODELING BY THE CONVOLUTION DIFFERENTIATOR METHOD

褶积微分算子法是一种全新的数值模拟方法,已被广泛应用于复杂介质的地震波场数值模拟,但是其边界反射问题一直没有解决。这里将最佳匹配层(PML)吸收边界条件引入到褶积微分算子法中,此方法是在研究区域的边界上加入吸收层,使边界上传入吸收层的波,随传播距离按指数规律衰减,不产生任何反射,以达到消除边界反射的目的。构造不同的模型,通过对比分析证明,PML吸收边界条件能比较好地解决褶积微分算子法的边界问题,从而验证了完全匹配层吸收效果的优越性。

The convolution differentiator method is a new numerical modeling method which is widely applied in complex media numerical modeling,but the boundary reflecting problem has not been resolved.This paper introduces perfect match layer(PML) absorbing boundary which was added on the boundary of the interesting region,no reflection is produced when wave propagates from boundary of studied region to absorbing layer and wave attenuates exponentially with propagation distance.By building different models and modeling,the numerical experiments demonstrate that the PML absorbing boundary can better resolve the boundary reflecting problems,Superiority of PML boundary condition was validated.