Scattering of SH waves by a circular sectorial canyon

Abstract

The scattering of plane SH waves incident on a circular sectorial canyon is considered. An accurate region-matching technique is applied to derive a rigorous series solution. Appropriate wavefunctions are employed to describe antiplane motions. Judicious basis functions, involving Gegenbauer polynomials, are well utilized to correctly capture the singular behaviour in stress fields near the canyon bottom. The enforcement of matching conditions on the auxiliary boundary leads to the determination of unknown coefficients. Plotted results demonstrate the influence of pertinent parameters on surface and subsurface motions. Both steady-state and transient results are included. The solution technique proposed achieves a considerable reduction in the computational effort, facilitating benchmark computations. The derived series solution enriches the limited list of series solutions presently known for canyon problems related to SH-wave scattering. © The Authors 2013 Published by Oxford University Press on behalf of The Royal Astronomical Society.