Comparison using different models between theoretical and experimental HVSR curves.

The ambient vibration Horizontal to Vertical Spectral Ratios (HVSR) is a widely used technique to identify the seismic resonance phenomena induced by the presence of seismic impedance contrasts at depth. Moreover, the HVSR curve can be used to constrain the shear wave velocity (Vs) profile in numerical inversion procedures: for this purpose, different HVSR forward modeling were developed in the last decades, which differ from each other both for the basic theoretical assumptions related to the ambient vibration wavefield simulation and for the phases of the involved seismic waves. Recently, some works showed that strong similarities between these HVSR models exist. In particular, these approach were considered: one based on vertically propagating body waves; one based on the ellipticity of the fundamental mode of Rayleigh waves; one based on the contribution of uniformly distributed random sources at the surface and the full wavefield and one based on a diffuse random wavefield assumption. As concerns the last two models, full wavefield and surface wave only were taken into account. In view of these conclusions, the aim of this work is to perform a comparison of the different theoretical HVSR modeling with experimental HVSR curves. To accomplish this purpose, HVSR measurements were carried out at test sites belonging to the down-hole database of the Tuscany Region administration (Central Italy; https://www.regione.toscana.it/-/banca-dati-vel). In particular, more than 50 sites with Vs profiles characterized by the presence of the seismic bedrock (Vs≥800m/s) and strong impedance contrasts were selected. Velocimetric acquisitions were carried out using the three-directional 24-bit digital tromograph Tromino™ (https://moho.world/) and the ambient vibrations were acquired for 20 min with a sampling frequency of 128 Hz. In particular, the spectra of the single components were computed by averaging 20-s-long non-overlapping windows; a detrend and a 5% cosine taper were applied to each window, and the spectra were smoothed by using a triangular moving window with a frequency-dependent half-width (10% of central frequency). The horizontal components were combined with the geometric average. Theoretical HVSR curves were simulated considering the models mentioned above and taking into account the Vs and Vp profiles of the selected down-holes; density values were deduced from Vp by empirical relationships and, for not purely elastic models, damping values for Vp and Vs are assumed equal to 0.01 for all the layers. Finally, these curves were compared with the respective experimental ones in order to evaluate the differences in terms of frequency and peak amplitude as well as of overall trend.