Seismic response of three-dimensional topographies using a time-domain boundary element method

We present a time-domain implementation for a boundary element method (BEM) to compute the diffraction of seismic waves by 3-D topographies overlying a homogeneous half-space. This implementation is chosen to overcome the mem ory limitations arising when solving the boundary conditions with a frequen cy-domain approach. This formulation is flexible because it allows one to m ake an adaptive use of the Green's function time translation properties: th e boundary conditions solving scheme can be chosen as a trade-off between m emory and cpu requirements. We explore here an explicit method of solution that requires little memory but a high cpu cost in order to run on a workst ation computer. We obtain good results with four points per minimum wavelen gth discretization for various topographies and plane wave excitations. Thi s implementation can be used for two different aims: the time-domain approa ch allows an easier implementation of the BEM in hybrid methods (e.g. coupl ing with finite differences), and it also allows one to run simple BEM mode ls with reasonable computer requirements. In order to keep reasonable compu tation times, we do not introduce any interface and we only consider homoge neous models. Results are shown for different configurations: an explosion near a flat free surface, a plane wave vertically incident on a Gaussian hi ll and on a hemispherical cavity, and an explosion point below the surface of a Gaussian hill. Comparison is made with other numerical methods, such a s finite difference methods (FDMs) and spectral elements.