Horizontal-to-vertical spectral ratios from a full-wavefield model of ambient vibrations generated by a distribution of spatially correlated surface sources

A new effective model is presented to compute horizontal-to-vertical spectral ratios (HVSR) relative to ambient vibrations, under the assumption that these are originated by a distribution of spatially correlated random surface sources. The major novelty of this model lies in the description of both ground displacement and sources as stochastic fields defined on the Earth's surface, stationary in time and homogeneous in space. In this frame, the power spectral density of the displacement stochastic field can be written as a function of the power spectral density of the force stochastic field and of the subsoil properties, through the relevant Green's function. Spatial correlation between ambient vibration sources is shown to be a necessary condition to warrant convergence of the integrals defining the frequency power spectra of the displacement field that make up the HVSR curve. Furthermore, it is shown that this HVSR curve may be significantly affected by the effective range of the force-field correlation on the Earth's surface. This formalization reduces computational efforts with respect to the previous version of the model based on distributed surface sources and may provide synthetic HVSR-curve patterns that are in line with those given by that computationally more troublesome version, as well as with those deduced under the assumption that the ambient vibrations constitute a diffuse wavefield.