Abstract
Microtremors 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.
Highlights
Site conditions can generate significant changes in earthquake ground motion producing concentrated damage (Sanchez-Sesma 1987; Aki 1988)
The Green’s function (GF) can be retrieved from averaging cross correlations of the recorded motions (Campillo & Paul 2003; Sanchez-Sesma et al 2008)
A remarkable characteristic of the noise we recorded at Texcoco is the consistency of spectral measurements
Summary
Site conditions can generate significant changes in earthquake ground motion producing concentrated damage (Sanchez-Sesma 1987; Aki 1988). The noise H/V spectral ratio (NHV) has been studied to explain its strengths and limitations (Bonnefoy-Claudet et al 2006; Cadet 2007; Bard 2008; Pilz et al 2009; Lunedei & Albarello 2010). We assume that the noise is a diffuse wavefield containing all types of elastic waves This may provide deep physical insight and explain the success of one of the most used techniques nowadays. We express the NHV as the square root of the ratio of the corresponding imaginary parts of Green’s tensor components (Sanchez-Sesma et al 2010) We use this theory to explain results from an experiment at Texcoco, a site near Mexico City within the ancient lake bed
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