计算分层大地媒质中格林函数的模拟镜像方法

Simulated image method for green's function of multi-layer earth media

为了快速精确计算分层大地媒质中格林函数,提出了模拟镜像方法.该方法将点源格林函数表示成有限个经典镜像与模拟镜像之和.模拟镜像的位置由经典镜像方法给出,其强度通过广义逆方法逼近格林函数的截断误差部分来确定.对于两层大地媒质问题,3～5个模拟镜像即可达到上千个经典镜像的计算精度.与复镜像法不同,模拟镜像的位置和强度均为实数,因此其物理意义比复镜像法更合理,同时,数学处理也更简便,是快速精确计算分层大地媒质中点源格林函数的一个很好的候选方法.

In order to calculate Green's function of multi-layer earth media (GFMEM) rapidly and accurately, the simulated image method is presented. GFMEM is analytically expressed by the finite number of classical images and the simulated images. The location of simulated images are given by the classical image method, and their intensity are determined by approximating the truncation error of Green's function using the generalized inversion method based on the singularity value decomposition. For the problem of two-layer earth media, the three to five simulated images can obtain more than one thousand classical images.