Difference of Horizontal-to-Vertical (H/V) Spectral Ratios of Microtremors and Earthquake Motions: Theory and Observation

Horizontal-to-vertical spectral ratios (HVRs) of microtremors have been traditionally interpreted theoretically as representing the Rayleigh wave ellipticity or just utilized a convenient tool to extract predominant periods of ground. However, based on the diffuse field theory (Sánchez-Sesma et al., 2011) the microtremor H/V spectral ratios (MHVRs) correspond to the square root of the ratio of the imaginary part of horizontal displacement for a horizontally applied unit harmonic load and the imaginary part of vertical displacement for a vertically applied unit load. The same diffuse field concept leads us to derive a simple formula for earthquake HVRs (EHVRs), that is, the ratio of the horizontal motion on the surface for a vertical incidence of S wave divided by the vertical motion on the surface for a vertical incidence of P wave with a fixed coefficient (Kawase et al., 2011). The difference for EHVRs comes from the fact that primary contribution of earthquake motions would be of plane body waves. Traditionally EHVRs are interpreted as the responses of inclined SV wave incidence only for their S wave portions. Without these compact theoretical solutions, EHVRs and MHVRs are either considered to be very similar/equivalent, or totally different in the previous studies. With these theoretical solutions we need to re-focus our attention on the difference of HVRs. Thus we have compared here HVRs at several dozens of strong motion stations in Japan. When we compared observed HVRs we found that EHVRs tend to be higher in general than the MHVRs, especially around their peaks. As previously reported, their general shapes share the common features. Especially their fundamental peak and trough frequencies show quite a good match to each other. However, peaks in EHVRs in the higher frequency range would not show up in MHVRs. When we calculated theoretical HVRs separately at these target sites, their basic characteristics correspond to these observed differences. At this stage of research we found that the underground structures that are optimized for EHVRs would not explain perfectly MHVRs. This strongly suggests that we need to optimize underground structures to explain both EHVRs and MHVRs at the same time.