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

Summary 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 memory limitations arising when solving the boundary conditions with a frequency‐domain approach. This formulation is flexible because it allows one to make an adaptive use of the Green’s function time translation properties: the boundary conditions solving scheme can be chosen as a trade‐off between memory 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 workstation computer. We obtain good results with four points per minimum wavelength discretization for various topographies and plane wave excitations. This implementation can be used for two different aims: the time‐domain approach allows an easier implementation of the BEM in hybrid methods (e.g. coupling with finite differences), and it also allows one to run simple BEM models with reasonable computer requirements. In order to keep reasonable computation times, we do not introduce any interface and we only consider homogeneous models. Results are shown for different configurations: an explosion near a flat free surface, a plane wave vertically incident on a Gaussian hill and on a hemispherical cavity, and an explosion point below the surface of a Gaussian hill. Comparison is made with other numerical methods, such as finite difference methods (FDMs) and spectral elements.