Abstract
Under the diffuse field approximation, the full-wave (FW) microtremor H/V spectral ratio (H/V) is modeled as the square root of the ratio of the sum of imaginary parts of the Green’s function of the horizontal components to that of the vertical one. For a given layered medium, the FW H/V can be well approximated with only surface waves (SW) H/V of the “cap-layered” medium which consists of the given layered medium and a new larger velocity half-space (cap layer) at large depth. Because the contribution of surface waves can be simply obtained by the residue theorem, the computation of SW H/V of cap-layered medium is faster than that of FW H/V evaluated by discrete wavenumber method and contour integration method. The simplified computation of SW H/V was then applied to identify the underground velocity structures at six KiK-net strong-motion stations. The inverted underground velocity structures were used to evaluate FW H/Vs which were consistent with the SW H/Vs of corresponding cap-layered media. The previous study on surface waves H/Vs proposed with the distributed surface sources assumption and a fixed Rayleigh-to-Love waves amplitude ratio for horizontal motions showed a good agreement with the SW H/Vs of our study. The consistency between observed and theoretical spectral ratios, such as the earthquake motions of H/V spectral ratio and spectral ratio of horizontal motions between surface and bottom of borehole, indicated that the underground velocity structures identified from SW H/V of cap-layered medium were well resolved by the new method.
Highlights
The microtremor H/S-wave velocity (Vs) spectral ratio (H/V) is the most popular approach to estimate the predominant period of a site (Nakamura 1989, 2000; Lermo and Chávez-García 1993)
In the framework of surface waves (SW) H/V, we investigate the differences between SW H/V of our approach and SW H/V of the previous study on microtremor H/V spectral ratio developed by Arai and Tokimatsu (2004)
Based on the aforementioned discussions, we conclude that the FW H/V of target layered medium should be well approximated with SW H/V of cap-layered medium in the period range, e.g., 0.1Tp0–5Tp0, under the following conditions: The impedance ratio of target layered medium is not larger than 6, and the S-wave velocity of cap layer is about twice as large as that in the half-space of target layered medium, the depth of upper interface of cap layer is about (5–10)λ0
Summary
The microtremor H/V spectral ratio (H/V) is the most popular approach to estimate the predominant period of a site (Nakamura 1989, 2000; Lermo and Chávez-García 1993). Based on the aforementioned discussions, we conclude that the FW H/V of target layered medium should be well approximated with SW H/V of cap-layered medium in the period range, e.g., 0.1Tp0–5Tp0, under the following conditions: The impedance ratio of target layered medium is not larger than 6, and the S-wave velocity of cap layer is about twice as large as that in the half-space of target layered medium, the depth of upper interface of cap layer is about (5–10)λ0. Thick black curves denote the observed H/Vs, dashed curves show the observed H/V within one standard deviation, thin black curves denote the ellipticity of fundamental mode of Rayleigh waves, cyan curves denote the FW H/Vs, blue curves denote the SW H/Vs of layered media consisting of PS logging data, and red curves denote the SW H/Vs of cap-layered media
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