Quantification of Percentage Conversion of Incident SV-Wave Energy, Spectral Bandwidth and Dominant Frequency of Generated Rayleigh Wave in Terms of Depth and Rise-Time of Earthquake

Abstract

Based on the analytical and numerical solutions as well as unexpected observed damages to the buildings and long-span structures in the epicentral zone of large shallow earthquakes, structural engineers have concluded that coseismic vertical ground motion play a major role in the damages. Recent researches have revealed the generation of high frequency Rayleigh wave with large amplitude in the epicentral zone of shallow earthquakes. Further, there is meta-response of a building at its longitudinal resonance frequency as compared to flexural resonance frequency during interaction with the Rayleigh waves. This paper presents the physics behind Rayleigh wave generation in the homogeneous half-space due to an incident SV-wave at the free surface and numerical quantification of variation of dominant frequency and spectral amplitudes of the generated Rayleigh waves with focal depth, Poisson's ratio and the rise-time of the point earthquake. It is concluded that the coupling of evanescence P-wave with the critically reflected SV-wave at/just after the critical point generates Rayleigh waves. Further, generation process is not immediate just after the critical point, but, it occurs over a span at least equal to one wavelength. A relation is established between depth of point earthquake and dominant wavelength of Rayleigh wave and this relation is unaffected by the change of Poisson’s ratio, rise-time and depth of point earthquake source. There is an exponential decrease of percentage conversion of the critically incident SV-wave energy in to the Rayleigh wave energy with an increase of focal-depth. Further, this percentage conversion increases with decrease of Poisson’s ratio and an increase of rise-time of the earthquake.