Scattering and Focusing of SH Waves by a Lower Semielliptic Convex Topography

The SH-wave scattering induced by a lower semielliptic convex topography is studied here. A rigorous series solution is obtained via the region-matching technique. The method of separation of variables in elliptic coordinates is adopted to express the pertinent wave fields in terms of an infinite series containing products of radial and angular Mathieu functions with unknown coefficients. Steady-state responses for some parameters are calculated and discussed. Because the present surficial configuration may collect wave energy in much the same way as a concave mirror does with converging light waves, the potential focusing effects are further probed in the frequency domain. Numerical results demonstrate that the geometry under consideration is indeed capable of causing a localized high concentration of wave energy underground, which may have a great influence on the structures below the convex topography such as mountain tunnels.