The Optimal Use of Horizontal-to-Vertical Spectral Ratios of Earthquake Motions for Velocity Inversions Based on Diffuse-Field Theory for Plane Waves

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

“…Early, in a pioneering study for 1-D problem, Claerbout (1968) established the relationship between energy density and Green's function. This fact was explicitly pointed out by Kawase et al (2011) in their successful study of H/V for earthquake data having little or no surface waves. The theoretical H/V that explained data has only the contribution of body waves.…”

“…When considering the contribution of all the surface waves (black dashed line), oscillations appear at high frequencies and the overall amplitude of the spectral ratio increases in comparison with the previous case (see figure 4-a). When the diffuse field is dominated by body waves, as it is the case of the codas of deep earthquakes in Japan, the H/V ratio presents clear resonances at high frequencies (Kawase et al 2011). In fact, the H/V ratio considering only the body waves contributions (see figure 4-a) is very similar to the transfer function for vertical S waves, in partial agreement with Nakamura's (1989) interpretation.…”

Statistical properties of the seismic noise field: influence of soil heterogeneities

“…Although it has been shown that a perfectly diffuse and equipartitioned wavefield is a necessary and sufficient condition to retrieve the exact Green's function (Sánchez-Sesma et al 2008) and although this hypothesis has been used to interpret some experimental features of the seismic noise wavefield there had already been some conjectures that the noise wavefield might not be totally equipartitioned and diffuse but anyhow dominated by this feature (e.g. Kawase et al 2011;Sánchez-Sesma et al 2011;Hillers et al 2012). As shown by Matsushima et al (2014), it is easy to theoretically construct a diffuse field for an inhomogeneous medium but, on the contrary, equipartition would not be realized for the case of a medium with distinctive geometrical features, even under the strong scattering situation or random wave incidences.…”

“…Complementary to a 1-D description of the wave propagation for a diffusive field (e.g. Kawase et al 2011) and the influence of the 2-D geometric structure on seismic noise (Matsushima et al 2014), this enables us to also quantify the 2-D variability and the multiple scattering required to produce a diffusive wavefield.…”

A Review and Some New Issues on the Theory of the H/V Technique for Ambient Vibrations

“…This means that seismic waves propagate in every (three-dimensional) spatial direction in a uniform and isotropic way and that a specific energetic proportion between P and S waves exists, which is the same whenever and wherever. This theory, initially developed in a full-space (Sánchez-Sesma and Campillo 2006), has been afterwards applied to an half-space and to a layered half-space Kawase et al 2011). The link between the H/V curve and the subsoil configuration is simply given by the Green's function, computed for source and receiver located in the same position: its imaginary part, in the spectral domain, is proportional to the average spectralpower of the ambient-vibration ground-motion.…”