SH-wave diffraction by a semi-circular hill revisited: A null-field boundary integral equation method using degenerate kernels

Abstract

Following the success of seismic analysis of a canyon [1], the problem of SH-wave diffraction by a semi-circular hill is revisited using the null-field boundary integral equation method (BIEM). To fully utilize the analytical property in the null-field boundary integral equation approach in conjunction with degenerate kernels for solving the semi-circular hill scattering problem, the problem is decomposed into two regions to produce circular boundaries using the technique of taking free body. One is the half-plane problem containing a semi-circular boundary. This semi-infinite problem is imbedded in an infinite plane with an artificial full circular boundary such that degenerate kernel can be fully applied. The other is an interior problem bounded by a circular boundary. The degenerate kernel in the polar coordinates for two subdomains is utilized for the closed-form fundamental solution. The semi-analytical formulation along with matching boundary conditions yields six constraint equations. Instead of finding admissible wave expansion bases, our null-field BIEM approach in conjunction with degenerate kernels have five features over the conventional BIEM/BEM: (1) free from calculating principal values, (2) exponential convergence, (3) elimination of boundary-layer effect, (4) meshless and (5) well-posed system. All the numerical results are comparing well with the available results in the literature. It is interesting to find that a focusing phenomenon is also observed in this study.