Scattering and focusing of SH waves by a convex circular-arc topography

Abstract

SUMMARY The scattering problem of plane SH waves by convex circular-arc topography is investigated. The series solution corresponding to this problem is derived via the wavefunction expansion method, combining with the region-matching technique. For the semi-circular case, the proposed formulation can be reduced to a simpler form than that given in the literature and consequently is easier to calculate. Both the steady-state and transient responses for some parameters are evaluated and discussed. Besides, based on the theory of geometric optics, for a concave mirror the focusing of light will take place, implying that analogous phenomenon may arise in the case of present topography. Such a focusing phenomenon will cause localized concentration of high amplitude of wave motion, which may have a great influence on underground structures. Therefore, the focusing effect by convex circular-arc surface is further examined in both the frequency and time domains. Numerical results show that the geometry under consideration is indeed capable of focusing wave energy, which is a significant contributor to the amplification behaviour.