Amplification of elastic waves by a three dimensional valley. Part 2: Transient response

Abstract Transient response of three dimensional dipping layers of different shapes subjected to incident P, SV, SH and Rayleigh waves is investigated. The time domain response is constructed from steady state solutions through the Fourier synthesis. An indirect boundary integral equation method is applied to calculate the required steady state solutions. The material of the half‐space and the layer is assumed to be linear, weakly inelastic, homogeneous and isotropic. Numerical results show that the maximum amplification of motion is strongly dependent upon the type of incident wave, the shape of the basin and signal frequency. The change in the shape of the valley from hemispherical to semi‐prolate causes a significant increase in the amplitude of surface waves near the edges; however, the maximum amplification of motion near the centre of the valley decreases. This phenomenon is especially apparent for the case of an incident P wave. In comparison to the corresponding two dimensional responses, the amplitude of motion near the centre of the valley is in general higher for three dimensional models.