• Earthquake ground motions;
  • Earthquake interaction, forecasting, and prediction;
  • Wave scattering and diffraction


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