Theoretical HVSR from the full wave field modelling of ambient vibrations in a weakly dissipative layered Earth

Ambient vibrations generated by anthropic activity in the range of frequencies of engineering interest ($0.5div20$ Hz) were modelled as the wavefield generated by a continuous distribution of random, independent point-like sources acting at the surface of a weakly dissipative layered Earth. A full wavefield solution was deduced analytically and used to evaluate major properties of Horizontal to Vertical Spectral Ratios (HVSR) in a representative set of selected cases of observed subsoil configurations. The results obtained confirmed -- on a more coherent analytical basis -- several statements deduced from empirical observations and numerical simulations which are of great importance for practical applications. It was confirmed that HVSR cannot be considered representative of the S-wave response function but as concerns the possibility of detecting the presence of 1-D resonance phenomena and of identifying the resonance frequency associated with the shallowest strong impedance contrast in the subsoil. The model enables evaluations of the reliability of HVSR interpretations provided in the surface-wave approximation that can be considered valid in the frequency range above the resonance frequency. At the resonance frequency, HVSR values prove sensitive to the strength of sources in the near proximity of the receiver (within a few tens of metres) and this suggests caution in the interpretation of HVSR peaks in terms of subsoil properties only.