Scattering of anti-plane (SH) waves by a semi-elliptical hill: II—deep hill

The ground motion and wave propagation resulting from the scattering of anti-plane (SH) waves by a deep semi-elliptical hill on an elastic half-space are investigated. The solution is the closed-form one based on the method of wave-function expansion, and the expansion of elliptical sine and cosine over the half-range [−π/2, π/2]. The analysis shows that the interference of ground motion depends on several factors such as frequency of the incident waves, incident angle, and the aspect ratio of elliptical hills. Similar to part I: Shallow Hill, numerical results when semi-elliptical tends to semi-circular are compared with the work done by Lee et al. [17].