Applicability of Theoretical Horizontal-to-Vertical Ratio of Microtremors Based on the Diffuse Field Concept to Previously Observed Data

Abstract

Horizontal-to-vertical spectral ratios of microtremors (MHVRs) have been interpreted as representing either the Rayleigh-wave ellipticity or the amplitude ratio of the sum of Rayleigh and Love waves in a horizontally layered structure. However, based on the recently established diffuse field concept, the theoretical form of MHVR has been proposed to be the square root of the ratio between the imaginary part of the horizontal Green's function on the surface and that of the vertical one. The theory assumes that the energy of a wavefield inside the earth will be equipartitioned among the various states in 3D space. In the case of microtremors, this may occur for randomly applied point-force loadings on the surface after sufficient lapse time to allow multiple scattering. Recent works on diffuse fields suggest that equipartition may arise in several ways, but understanding the emergence of equipartition in realistic settings requires further scrutiny. In the meantime, the resulting formula is quite simple, and its meaning has theoretical support from deterministic exact solutions. As references, we use observed microtremor data from several sites that were reported previously and validate the diffuse field method (DFM) as an alternative method to explain observed MHVR. We use only sites with reliable velocity structures to compare different methods quantitatively. As a result, we found that the DFM solutions with the corresponding 1D layered structures well explain the observed MHVRs for most of the sites. Thus, we believe that MHVR can be used to invert a 1D velocity structure by using DFM as a theoretical tool.

Application of a simplified calculation for full-wave microtremor H/V spectral ratio based on the diffuse field approximation to identify underground velocity structures

“…On the other hand, the amplitudes of DSS-SW H/Vs at peaks are a bit smaller than those of SW H/Vs. It agrees with the study of Kawase et al (2015) who compared the DSS-SW and FW H/Vs by use of underground velocity structures identified from DSS-SW H/Vs. The constant Rayleigh-to-Love waves amplitude ratio for horizontal motions (R/L) in a period range of 0.1-5 s which is assumed to by Arai and Tokimatsu (2004) suggests that the shape of DSS-SW H/V is the same as H/V evaluated from the medium responses of fundamental and higher modes of Rayleigh waves, and the different amplitude between them only relies on the value of R/L.…”

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

“…Unfortunately, it is quite difficult to provide direct evidence of the diffusivity using the observed data since we cannot observe wave field under controlled condition in the real field. For example isotropic nature of energy distribution in three-dimensional space, that is equipartition of seismic energy, cannot be easily observed because of the complex site effects near the observation point (See reviews in Kawase et al 2015).…”

“…The DFC theory for MHVR can be used for the velocity structure inversion. The validation studies of this DFC interpretation of MHVR can be found in Salinas et al (2014), Kawase et al (2015), and Lontsi et al (2015). Recently García-Jerez et al (2016) show a new calculation scheme using residue integrals, which is much more efficient in computing Green's functions and so they used it for velocity inversion.…”

The inversion of spectral ratio H/V in a layered system using the diffuse field assumption (DFA)

“…In this communication, we explore the main features of H/V under the DFA. The applicability issue of DFA was dealt with in Kawase et al (2015). They compared the results of Arai and Tokimatsu (2004) with the DFA calculations with excellent agreement.…”