Direct evaluation of S-wave amplification factors from microtremor H/V ratios: Double empirical corrections to “Nakamura” method

Abstract

The Horizontal-to-Vertical spectral ratios of microtremors (MHVR) have been utilized as a convenient tool to extract a predominant frequency at a target site. The so-called “Nakamura” method, which was proposed by Nakamura in 80's, assumed that MHVR provides us directly the S-wave amplification factor of earthquake in the horizontal component, that is, Horizontal-to-Horizontal spectral ratio (HHR) with respect to the bedrock, although the validity of the method had never been proved. Recently, based on the diffuse field concept (DFC) proposed by Sánchez-Sesma and others in 2011 MHVRs are found to correspond to the square root of the ratio of the imaginary part of the displacement for a unit harmonic load in the horizontal direction with respect to the corresponding one in the vertical direction. With the same DFC for body waves Horizontal-to-Vertical spectral ratios of earthquake (EHVR) correspond to the ratio of the horizontal motion for a vertical incidence of S wave with respect to the vertical correspondent of P wave, as revealed by Kawase and others in 2011. Thus there should be a systematic difference between EHVR and MHVR because of the difference in their primary contribution of wave types. We first calculated the ratios of EHVR with respect to MHVR (EMR) at 100 strong motion stations in Japan. Then we normalized frequency by the fundamental peak frequency at each site and calculated the average of EMRs for five categories based on their fundamental peak frequencies. Once we got empirical EMRs for five categories we transformed MHVRs into pseudo EHVRs. At the same time we calculated the average Vertical-to-Vertical spectral ratios (VVRs) for the same sites using the generalized spectral inversion technique (GIT) of Nakano et al. (2015) [16]. Finally the S-wave amplification factor, HHR, of earthquake ground motion at the site were calculated from MHVR with double corrections using EMR and VVR for the corresponding category. We compared these final empirical prediction with the observed HHRs from GIT to find quite high correlations and small overall residuals. The proposed method to get HHR from MHVR with these double empirical corrections can be considered as a natural but significant extension to the so-called “Nakamura” method.