In-plane seismic response of inhomogeneous alluvial valleys with vertical gradients of velocities and constant Poisson ratio

The propagation of seismic P and SV waves within inhomogeneous alluvial valleys has been investigated using the indirect boundary element method (IBEM). An improvement on the formulae published early, for the 2D Green's functions in an inhomogeneous medium is presented in this work. A modification has been done over these functions in view of its connection to the ray theory. An accuracy analysis validates these modified Green's functions computing the relative error in frequency domain for the SH case, and with a quantitative analysis obtaining envelope and phase misfits of the solution in time domain, for the P–SV case.We used these analytical expressions for the Green's functions to simulate the wave propagation in semi-circular alluvial valleys with constant gradient of wave velocities. Our results for various inhomogeneous soft deposits displayed complex amplification patterns in space and frequency. We compared these results with those calculated using homogeneous material within the basins. The impedance contrast (relative to halfspace) is not constant in all sediments of the valley (i.e. is dependent upon depth). Indeed, the lowest wave velocities are on the free surface of our model. This induces significant lateral reflections of surface waves that have great influence on the free surface displacements, in comparison with the homogeneous models. The graded media completely modifies the response and produces a complex behavior due to body and surface waves that have a tendency to trapping energy at the shallowest region. In some cases, the heterogeneous deep basin behaves effectively as a shallower homogeneous basin.