Scattering of elastic spherical P, SV, and SH waves by three-dimensional hill in a layered half-space

In this paper, the method of combining indirect boundary element method (IBEM) with the region-matching technique is used to solve the seismic responses of a three-dimensional (3D) hill in a layered half-space subjected to spherical P, SV, and SH waves. The direct stiffness method and Hankel transform method are used to solve the free field of spherical wave source field, and the scattering field is constructed by Green's function in half-space. The correctness and accuracy of this method are verified by comparing with the results of several literatures. This method can be used to deal with arbitrary-shaped hill topography, and has the advantages of wide applicability, high accuracy and fast convergence. Taking Gaussian hill topography as an example, the scattering phenomenon of hill under the incidence of spherical P, SV and SH waves is studied, and the influences of hill topography, source location and frequency on site seismic responses are explored. The results show that: Existence of the hill topography has evident focusing effect, which significantly enlarges the seismic response on the hill surface, and the hill has evident isolation effect in the process of energy propagation; With higher frequency of the incident wave, the fluctuation amplitude of displacement on the hill surface increases; The fluctuation amplitude of horizontal displacement on the hill surface is SV wave > SH wave > P wave, and the vertical displacement is P wave > SV wave.