## 4 Field Tests of the GFZ-WISE
### Data Recording, Analysis and Results
In particular, Figure 7a,b, upper panels, show snapshots of the theoretical Bessel function fitting procedure with the experimental spatial correlation values, when plotted as a function of distance \(r\), together with the root mean square values for the velocity explored during the grid search procedure. The high quality of the fitting results indicates that reliable phase velocity estimates were retrieved. In fact, in the case the GFZ-WSUs were not perfectly synchronized and the very small amplitude frequencies higher than 1 Hz properly recorded, it would have been impossible to obtain phase differences among all the couple of sensors in the array in a relation each other that allow estimating the velocity of the Rayleigh waves transmitting throughout the array. Moreover, Figure 7a,b, lower panels, provide an example of the phase velocity values estimated during the real-time analysis. A real-time analysis of the data allows the operator to observe in real time both the quality of the space-correlation values fitting procedure, and the evolution of velocity estimates with the increasing of the frequency. Figure 8 shows the final result of the ESAC analysis together with theoretical limits for the spatial aliasing and spatial resolution estimated from the array response function [42]. The RWDC is characterized by a quite regular increase in the Rayleigh wave phase velocities from about 15 Hz down to 2.5 Hz, which indicates a regular and smooth increase of the S-wave velocities with depth in the subsoil. It is worth noting that the limits of the dispersion curve at both high and low frequencies are very well correlated with the predicted resolution and spatial aliasing constraints. That is, at low frequencies the phase velocities can be estimated until 2.5 Hz, which is in agreement with the resolution boundary estimated considering the maximum inter-station distance [4]. Similarly, the linear trend of velocities increasing with frequency from about 10 Hz onwards is clearly related to the spatial aliasing [4]. The H/V spectral ratios [43] were computed using for all stations the same time-window length adopted for the estimation of the dispersion curve. The Fourier spectra were computed for each noise component and smoothed using a Hanning window of 10% relative bandwidth. This ensures the reduction of numerical instabilities while preserving the major features of the spectra. The resulting spectral ordinates relative to the horizontal components were geometrically averaged and divided by the vertical spectral ordinate to compute the H/V function. Finally, H/V ratios obtained by considering the resultant time windows were then averaged to compute the final H/V curves along with the relevant 95% confidence interval. Figure 8, inner inset, shows the example of one estimated H/V. In agreement with the results about the subsoil structure provided by the RWDC, the H/V is flat and indicates that down to the first few tens of meters depth under the site there are no high-impedance contrast  
Figure 7: Real-time fitting procedure for Rayleigh-wave velocity estimation. (a) Analysis for the frequency 2.49 Hz. In the _upper-right panel_ is shown the comparison between the observed spatial correlation function (_black dots_) and the theoretical Bessel function values for the best-fit velocities (_gray dots and line_). In the _upper-left panel_ is shown the RMS for the tested velocities. In the _lower panels_ are shown the evolutionary, real-time dispersion curve estimations, where the Rayleigh-wave velocities for the actual (_black dot_) and previous (_gray dots_) analyzed frequencies are shown. (b) same as (a) but for the frequency 5.9 Hz. boundaries. A large impedance contrast might be expected at greater depths, requiring the identification of a peak in the H/V ratio curve at frequencies well below those have to be exploited from data recorded by the GFZ-WSU. Finally, the inversion procedure was carried out in order to retrieve the S-wave velocity profile.