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.