In this paper, an improved boundary element approach for 2D elastodynamics in time-domain is presented. This approach consists in the truncation of time integrations, based on the rapid decrease of the fundamental solutions with time. It is shown that an important reduction of the computation time as well as the storage requirement can be achieved. Moreover, for half-plane problems, the size of boundary element (BE) meshes and the computation time can be significantly reduced. The proposed approach is used to study the seismic response of slopes subjected to incident SV waves. It is found that large amplifications take place on the upper surface close to the slope, while attenuations are produced on the lower surface. The results also show that surface motions become very complex when the incident wavelength is comparable with the size of the slope or when the slope is steep

We present approximate equations for qP-wave ray tracing and paraxial ray tracing in inhomogeneous layered weakly transversely isotropic (TI) media. Inside layers, the symmetry axis direction of the TI medium is allowed to vary continuously. Approximate equations are based on perturbation theory in which deviations of anisotropy from isotropy are considered to be first-order quantities. For qP-waves propagating in a TI medium, the approximate ray-tracing and paraxial ray-tracing equations depend on three parameters and two angles defining the direction of the symmetry axis. We also present the boundary conditions at interfaces for first-order rays and paraxial rays and compute reflection/transmission coefficients to the first order. All the quantities required for evaluation of the Green’s function are calculated to the first order, except the traveltime that is calculated to the second order. The accuracy of the presented algorithm is verified on simple models with respect to exact ray-tracing results. For anisotropy of about [Formula: see text], considered in the examples presented, the relative errors in traveltime and amplitude are less than [Formula: see text] and [Formula: see text], respectively. We then consider media where the symmetry axis is conformable with the structure, named structural transverse isotropy (STI). The method is applied to simple STI models and to a realistic overthrust model, showing significant differences with vertical transverse isotropy (VTI) models not only for traveltimes, but also for amplitudes.