SH波地表散射的局域边界元模拟  

Localized Boundary Element method for seismic wave surface scattering problems:2D SH case

作　　者：盖增喜[1] 陈晨旭 GE ZengXi;CHEN ChenXu(School of Earth and Space Sciences,Peking University,Beijing 100871,China)

机构地区：[1]北京大学地球与空间科学学院,北京100871

出　　处：《地球物理学报》2020年第6期2274-2280,共7页Chinese Journal of Geophysics

基　　金：国家重点研发项目(2018YFC1504203);中国地质调查局地质调查项目(DD20160082)资助.

摘　　要：本文提出了一种计算不规则起伏地形中SH波散射的有效方法——局域边界元法.本方法基于传统边界元法,为计算复杂地表散射问题提供了一种更加高效的解决方案.根据地震波满足的边界积分方程中牵引力格林函数的特性,我们将自由边界分解成水平部分和起伏部分.通过公式推导,可将水平部分的位移由起伏部分的位移通过格林函数线性叠加表示,因此只需对起伏部分的位移进行直接求解,从而极大地减少了待求解的未知数个数,显著提高了计算效率.通过与半圆形山谷SH波平面波入射的解析解比较,验证了方法的正确性.数值模型比较显示,局域边界元模拟结果与传统边界元数值解完全吻合,但是大幅提高了计算效率.因此,局域边界元法可以作为模拟不规则地形中地震波散射的有效工具.In this paper an efficient approach,Localized Boundary Element Method,is proposed to study the scattering problem of SH waves by an irregular topography in 2D model.This method is based on the traditional Boundary Element method which can provide accurate solutions for surface scattering problems.In the new approach,by taking account in the characteristic of the Green′s function of tractions between the elements along the flat part of the surface,the displacements of the nodes on the flat part can be expressed as linear superposition of the displacements of the nodes along the irregular part.Thus only the unknowns along the irregular part of surface topography need to be directly solved.Therefore,the number of unknowns is greatly reduced which in turn improve the efficiency significantly.Comparison the computed displacement of a semi-circular canyon with analytical solution and full boundary element method shows that the new approach has exactly the same accuracy as the full boundary element method but much higher efficiency.Thus the new method can serve as a useful tool in simulating the seismic wave scattering problems by irregular topography.

关 键 词：地震波传播 起伏表面散射 边界元法 局域化模拟 

分 类 号：P315[天文地球—地震学]