Exact solution to scattering of SH waves by an elliptic-arc canyon in the corner of an elastic quarter space

Herein, we investigate the dynamic anti-plane problem of an elliptic-arc canyon in the corner of an elastic quarter space. The method of wavefunction expansions and the method of images are applied to derive an exact analytical solution for plane-wave incidence. Values of field quantities are evaluated via closed-form expressions involving Mathieu functions. Results are given as benchmarks for numerical studies.