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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SUMMARYAn evaluation of the wave passage e ects on the relevant dynamic properties of structures with exible foundation is presented. A simple soil-structure system similar to that used in practice to take into account the inertial interaction e ects by the soil exibility is studied. The kinematic interaction e ects due to non-vertically incident P, SV and Rayleigh waves are accounted for in this model. The e ective period and damping of the system are obtained by establishing an equivalence between the interacting system excited by the foundation input motion and a replacement oscillator excited by the free-ÿeld ground motion. In this way, the maximum structural response could be estimated from standard free-ÿeld response spectra using the period and damping of the building modiÿed by both the soil exibility and the travelling wave e ects. Also, an approximate solution for the travelling wave problem is examined over wide ranges of the main parameters involved. Numerical results are computed for a number of soil-structure systems to identify under which conditions the e ects of wave passage are important. It comes out that these e ects are generally negligible for the system period, but they may signiÿcantly change the system damping since the energy dissipation within the soil depends on both the wave radiation and the di raction and scattering of the incident waves by the foundation.

In order to explain damage and observed ground motions in Mexico City during the 1985 Michoacán earthquake, simultaneous consideration must be given to source, path, and site conditions. This is clear from teleseismic records and local vertical displacements. Incident waves had an important part of energy in the frequency band of 0.3-1 Hz. Damage distribution and observed motion in the lake bed zone cannot be satisfactorily explained using one-dimensional theory. The effects of lateral irregularities are required. To assess its effects we describe the stratigraphic setting of the valley and discuss some features of damage distribution with results for one- and two-dimensional wave propagation models. These are useful to establish on quantitative basis the importance of lateral heterogeneity.

It has been recently demonstrated that averaging the autocorrelations of fields produced by various almost-vertical incoming elastic body plane waves upon a layered system approximately leads to the imaginary part of the corresponding 1D Green's functions for deep sources located underneath the receiver . Thus, the ensemble of these waves from deep earthquakes recorded in a station located in the epicentral zone is interpreted as a diffuse field. In this short note, we extend the study to consider earthquakes recorded in a station located at epicentral distances of up to hundreds of kilometers. We consider the horizontal-to-vertical spectral ratio (HVSR) of the averaged P, S, and coda waves and full earthquake records at the Cibeles station (Mexico City Accelerometric Network) and compare these with the results obtained with the corresponding HVSR for the 1D (Kawase et al., 2011) and the 3D (Sánchez-Sesma, Rodríguez, et al., 2011) diffuse fields models. Using the signals of 90 earthquakes recorded at Cibeles, we find that the experimental results have distinctive features compatible with the 3D signature of a diffuse field. We interpret this result as a consequence of the multiple paths that seismic waves undergo from the subducting slab to the Mexico City valley and to the multiple scattering in a complex tectonic environment. Our study strongly suggests that we can use strongmotion records from earthquakes and apply similar techniques to the ones used to analyze the ambient seismic field.