Difference of horizontal-to-vertical spectral ratios of observed earthquakes and microtremors and its application to S-wave velocity inversion based on the diffuse field concept

We have been discussing the validity of using the horizontal-to-vertical spectral ratios (HVRs) as a substitute for S-wave amplifications after Nakamura first proposed the idea in 1989. So far a formula for HVRs had not been derived that fully utilized their physical characteristics until a recent proposal based on the diffuse field concept. There is another source of confusion that comes from the mixed use of HVRs from earthquake and microtremors, although their wave fields are hardly the same. In this study, we compared HVRs from observed microtremors (MHVR) and those from observed earthquake motions (EHVR) at one hundred K-NET and KiK-net stations. We found that MHVR and EHVR share similarities, especially until their first peak frequency, but have significant differences in the higher frequency range. This is because microtremors mainly consist of surface waves so that peaks associated with higher modes would not be prominent, while seismic motions mainly consist of upwardly propagating plain body waves so that higher mode resonances can be seen in high frequency. We defined here the spectral amplitude ratio between them as EMR and calculated their average. We categorize all the sites into five bins by their fundamental peak frequencies in MHVR. Once we obtained EMRs for five categories, we back-calculated EHVRs from MHVRs, which we call pseudo-EHVRs (pEHVR). We found that pEHVR is much closer to EHVR than MHVR. Then we use our inversion code to invert the one-dimensional S-wave velocity structures from EHVRs based on the diffuse field concept. We also applied the same code to pEHVRs and MHVRs for comparison. We found that pEHVRs yield velocity structures much closer to those by EHVRs than those by MHVRs. This is natural since what we have done up to here is circular except for the average operation in EMRs. Finally, we showed independent examples of data not used in the EMR calculation, where better ground structures were successfully identified from pEHVRs again. Thus we proposed here a simple empirical method to estimate S-wave velocity structures using single-station microtremor records, which is the most cost-effective method to characterize the site effects.[Figure not available: see fulltext.].