Scattering of Anti-Plane (SH) Waves by a Shallow Semi-Elliptical Hill with a Concentric Elliptical Tunnel

A closed-form wave function analytic solution of two-dimensional scattering and diffraction of incident plane SH-waves by a shallow semi-elliptical hill with a concentric elliptical tunnel on an elastic half-space is presented. This research extends the previous solution by authors in 2013 which addressed only the semi-elliptical hill, to a hill-tunnel system. Ground surface displacement near the hill are studied and exhibited. It was observed from the results that the aspect ratio of hill and tunnel profiles, frequency of incident waves, and incident angles are the primary factors that may affect the surface ground motion amplitudes near the hill-tunnel system.