Scattering problems of SH wave by using the null-field boundary integral equation approach

Abstract

Scattering problem of seismic wave is an important issue for studying earthquake in seismology. In this talk, we employ the null-field boundary integral equation method (BIEM) in conjunction with degenerate kernels and eigenfunction expansion to solve the SH-wave scattering problems containing circular or elliptical boundary. The null-field BIEM was developed by NTOU/MSV group, Taiwan in 2003. Recent progress in this area is addressed. The fundamental solution is expanded by using the degenerate kernels, while the boundary density is approximated by using the Fourier series. Since circular and elliptical canyons or hills are considered, polar coordinates and elliptical coordinates are used. The semi-analytical formulation can be derived by using the null-field BIEM after matching of boundary conditions. We also provide semi-analytical solutions for benchmark examples such as single semi-circular or semi-elliptical canyon, two successive semi-circular canyons, a semi-circular or semi-elliptical hill and a semi-circular hill containing a circular inclusion. Besides, a shallow canyon and a shallow hill are also addressed. Numerical results are well compared with the available data in the literature.