Numerical Simulation of Ground Rotations along 2D Topographical Profiles under the Incidence of Elastic Plane Waves

The surface displacement field along a topographical profile of an elastic half-space subjected to the incidence of elastic waves can be computed using different numerical methods. The method of fundamental solutions (MFS) is one of such techniques in which the diffracted field is constructed by means of a representation in terms of the Green's functions for discrete forces located outside the domain of interest. From the enforcement of boundary conditions, such forces can be computed; thus, the ground motion can be calculated. One important advantage of MFS over boundary integral techniques is that singularities are avoided. The computation of ground-motion rotations implies the application of the rotational operator to the displacement field. This can be done using either numerical derivatives or analytical expressions to compute the rotational Green's tensor. We validate the method using exact analytical solutions in terms of both displacement and rotation, which are known for simple geometries. To demonstrate the accuracy for generic geometries, we compare results against those obtained using the spectral-element method. We compute surface rotations for incoming plane waves (P, SV, and Rayleigh) near a topographical profile. We point out the effects of topography on rotational ground motion in both frequency and time domains.