A Predictive Equation for the Vertical-to-Horizontal Ratio of Ground Motion at Rock Sites Based on Shear-Wave Velocity Profiles from Japan and Switzerland

Abstract

Abstract Ratios of vertical-to-horizontal ( V / H ) ground motion are important for the computation of scenario-compatible vertical design spectra. They are therefore a crucial aspect of seismic hazard analysis. We characterize the V / H ratio at rock sites in terms of the recording site’s average quarter-wavelength velocity. A predictive equation is presented, which can be used for reconstructing the expected V / H ratio of the 5%-damped response and Fourier spectra for rock sites, given a known shear-wave velocity profile. The equation is based on the regression analysis of two datasets: one from Switzerland and one from Japan. The two datasets allow us to analyze well-characterized hard-rock sites in Switzerland using small earthquakes ( M w >2), while the magnitude range is increased up to events of M w 7.3 using strong-motion recordings from Japan’s KiK-net seismic network. It is shown that a correlation exists between the quarter-wavelength velocity at a given frequency and the V / H ground-motion ratio. Small differences, possibly due to velocity measurement bias or topographical and basin effects, existed when analyzing the individual regional datasets. Apart from near-source distances ( R V / H , no clear magnitude- or distance-dependence of the V / H ratios is present in either of the datasets of earthquake recordings. We show that the same correlation exists for response spectra and Fourier spectra of recorded ground motion. A similar correlation was derived for ambient vibrations recorded at Swiss station sites, resulting in larger values of V / H at a given frequency and thereby indicating that V / H is sensitive to the composition of the wave field. Finally, uncertainties in the V / H models are presented. We separate the sources of uncertainty into source and site-specific components and present the single-site sigma uncertainty measure for site-specific hazard analyses.