Modelling noise H/V spectral ratio in a laterally inhomogeneous layered medium

Central to the task of seismic hazard assessment is the evaluation of potential amplifications due to site effects. The horizontal-to-vertical spectral ratio (HVSR) of ambient seismic noise (ASN) is a widespread measurement to assess the predominant soil frequency of a given site and estimate the wave velocities of the subsoil stratigraphy using inversion schemes. In practice, the inversions are currently made, assuming flat layers. In fact, HVSR measurements may show significant lateral and azimuthal changes due to the spatial variations of local geology, which can introduce uncertainties into the characterization of a site. This suggests the importance of considering detailed measurements of lateral and angular variations in layered settings. Inversion of soil properties at depth for horizontally layered media has become feasible assuming that ASN constitutes a diffuse field, that is, produced by equi-partitioned uniform illumination and/or by random sources and the ensuing multiple scattering by heterogeneities. Under the diffuse field assumption (DFA), the HVSR have been modelled by calculating the imaginary parts of the Green's function (IMGs) when source and observer coincide at the same point. In this work we use the 3-D indirect boundary element method (IBEM) to model the HVSR for each independent horizontal direction referred to here as directional-HVSR for layered media with lateral inhomogeneity. The IMGs at the source required to get HVSR have locality properties that depend on frequency and may imply significant economies in the calculation. For simple models we modelled the IMGs approximately using an adaptive meshing scheme that accounts both for the locality of the problem and the diffraction properties of waves at low and high frequencies. The obtained directional-HVSR displays variations in both frequency and azimuth. The results also show that layer interface variations can lead to ‘spots’ of higher wave excitation associated to local resonant modes. This shows the importance of HVSR in forecasting earthquake response and suggests the need for denser field measurements to study lateral and azimuthal variability. In order to show the reality of directional-HVSR, field data from Chalco, a soft soil site at the southern part of the Valley of Mexico, have been preliminarily analysed.