Contribution of Rayleigh and Body Waves to Displacement Induced by a Vertical Point Force on a Layered Elastic Half-Space

A numerical method is presented for computing ground surface displacement induced by a vertical point force acting on a three-dimensional layered elastic half-space. The contribution of the residue of the Rayleigh poles and the branch line integrals, i.e., that of Rayleigh and body waves, to the ground displacement is computed for a two-layered medium, and its variation with the S-wave velocity ratio between the surface and base layers, V_ /V_ , is examined. It is shown that, when V_ /V_ is less than 1.5 or when V_ /V_ is greater than 1.5 and the normalized frequency is not close to 1, Rayleigh waves get to dominate as the normalized ditance is greater than at most 3〜4. When V_ /V_ is greater than 3 and the normalized frequency is close to 1, body waves dominate up to a normalized distance of 100, due to their peculiar attenuation characteristics which are very similar to those of Rayleigh waves.