Geometrical focusing as a mechanism for significant amplification of ground motion in sedimentary basins: analytical and numerical study

We study the geometrical and material conditions which lead to focusing of seismic waves traveling across a concave velocity interface representing the boundary of a sedimentary basin within a denser rock. We approximate, using geometrical analysis for plane-waves, the combination of interface eccentricities and velocity ratios for which the seismic rays converge to a near surface region of the basin. 2-D finite difference modeling is used to compute Peak Ground Velocity (PGV) and spectral amplification across the basin. We show that effective geometrical focusing occurs for a narrow set of eccentricities and velocity ratios, where seismic energy is converged to a region of $pm $ 0.5 km from surface. This mechanism leads to significant amplification of PGV at the center of the basin, up to a factor of 3; frequencies of the modeled spectrum are amplified up to the corner frequency of the source. Finally, we suggest a practical method for evaluating the potential for effective geometrical focusing in sedimentary basins.