Amplification of elastic waves due to a point source in the presence of complex surface topography

This paper first presents the amplification or de-amplification in the three-dimensional wave scattering generated by the half-space when subjected to a dilatational point load placed at some point in the medium, when the free surface is changed to simulate a two-dimensional ridge or a valley deformation. This model is then extended to include the presence of a long, circular, buried cavity. The solution is formulated using the boundary elements method for a wide range of frequencies and spatially harmonic line loads, which are subsequently used to obtain time series by means of (fast) inverse Fourier transforms into space–time. Our simulation results indicate larger wave amplification and de-amplification in the time and frequency domains when the topographic surface includes a smooth ridge and canyon deformations. The presence of a buried inclusion further complicates the wave field displacement pattern, including additional reflections.