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

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The elastodynamic Green function can be retrieved from the cross correlations of the motions of a diffuse field. To extract the exact Green function, perfect diffuseness of the illuminating field is required. However, the diffuseness of a field relies on the equipartition of energy, which is usually described in terms of the distribution of wave intensity in direction and polarization. In a full three dimensional (3D) elastic space, the transverse and longitudinal waves have energy densities in fixed proportions. On the other hand, there is an alternative point of view that associates equal energies with the independent modes of vibration. These two approaches are equivalent and describe at least two ways in which equipartition occurs. The authors gather theoretical results for diffuse elastic fields in a 3D full-space and extend them to the half-space problem. In that case, the energies undergo conspicuous fluctuations as a function of depth within about one Rayleigh wavelength. The authors derive diffuse energy densities from both approaches and find they are equal. The results derived here are benchmarks, where perfect diffuseness of the illuminating field was assumed. Some practical implications for the normalization of correlations for Green function retrieval arise and they have some bearing for medium imaging.

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Comprehensive studies in geophysics and seismology have dealt with scattering phenomena in unbounded elastic domains containing fractures or cavities. Other studies have been carried out to investigate scattering by discontinuities located near a free surface. In this last case, the presence of fractures and cavities significantly affects wave motion and, in some cases, large resonant peaks may appear. To study these resonant peaks and describe how they can be affected by the presence of other near-free-surface fractures or cavities we propose the use of the indirect boundary element method to simulate 2D scattering of elastic P and SV waves. The geometries considered are planar and elliptic cracks and cavities. This method establishes a system of integral equations that allows us to compute the diffracted displacement and traction fields. We present our results in both frequency and time domains. In the planar cracks located near the free surface, we validate the method by comparing results with those of a previously published study. We develop several examples of various fractures and cavities to show resonance effects and total scattered displacement fields, where one can observe conspicuous peaks in the frequency domain and important wave interactions in the time domain. Finally, we show how our dimensionless graphs can be used to deal with materials like clay, sand, or gravel and compare the response with finite-element analysis of elastic beams.