A theory for microtremor H/V spectral ratio: application for a layered medium

Abstract

International audienceMicrotremors are produced by multiple random sources close to the surface of the Earth. They may include the effects of multiple scattering, which suggests that their intensities could be well described by diffusion-like equations. Within this theoretical framework, the average autocorrelation of the motions at a given receiver, in the frequency domain, measures average energy density and is proportional to the imaginary part of the Green's function (GF) when both source and receiver are the same. Assuming the seismic field is diffuse we compute the H/V ratio for a surface receiver on a horizontally layered medium in terms of the imaginary part of the GF at the source. This theory links average energy densities with the GF in 3-D and considers the H/V ratio as an intrinsic property of the medium. Therefore, our approach naturally allows for the inversion of H/V, the well-known Nakamura's ratio including the contributions of Rayleigh, Love and body waves. Broad-band noise records at Texcoco, a soft soil site near Mexico City, are studied and interpreted using this theory

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

“…It has been established that if the H/V is defined as the square root of the ratio between the horizontal and the vertical energies of a Diffuse Field, it is then possible to express this ratio in terms of the imaginary components of the Green function (Sánchez-Sesma et al 2011a). In what follows, we summarize the arguments.…”

“…The second interpretation is due to Nakamura (1989;2000), who suggests that the ratio H/V is related to the transfer function for vertical incidence of SH waves; the success of the H/V measurements was spectacular but it came along with controversy about the interpretation of the resulting spectral ratios. On the other hand, Sánchez-Sesma et al (2010;2011a) have proposed recently that microtremors form a Diffuse Field containing all types of body (P and S) and surface waves (Love and Rayleigh). In a recent review, Lunedei and Malischewsky (2015) made a detailed description of the various theoretical models for the H/V spectral ratio developed in the last three decades.…”

“…Theory asserts that within a diffuse elastic wavefield the autocorrelation in frequency domain, at any point of the medium, is proportional to the imaginary part of the Green's function for coinciding source and receiver (Sánchez-Sesma et al 2011a).…”

“…The other line just studies the Rayleigh wave ellipticity. Regarding the first research line, there are two models of the ambient seismic wave field: the Distributed Surface Sources (DSS) model Lunedei & Albarello 2015) and the Diffuse Field Assumption (DFA) (Sánchez-Sesma et al 2011a). These models were compared recently (García-Jerez et al 2011;2012) and it was found that they provide similar results; particularly regarding the surface-wave behavior.…”

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.…”