## 2 DoV Estimation: Description of the Methods
### Determination of DoV from the ITALGEO2005 Model
According to the procedure used for the computation of the residual gravity anomalies ITALGEO2005 [24; 35], the (\(\xi\), \(\eta\))\({}_{RTC}\) were computed using the TC program of the GRAVSOFT package [38]. Therefore, the RTC effect in term of DoV components was evaluated modeling by prisms the topography between the Italian Digital Terrain Model, based on the SRTM3 data, and  
For the GNSS-LEV method, the data required for the application of Equation (5) and resulting directly from the GNSS and high precision spirit leveling observations described in Section 2.1 are given in Table S1 (Supplementary Materials). The standard deviations of the (\(\xi\), \(\eta\)) components were estimated by variance propagation as described in [41; 42]. In the QDaedalus survey, several sets of measurements were taken at every station over a 2 h period. The observation of each of the stars was repeated at least five times. Overall, each set of measurements comprised at least 180 observations. First, each set was adjusted individually (see Table S2 in Supplementary Materials); then, the final values were computed weighting the results of each adjustment according to the respective a-posteriori variance. The standard deviation of the averaged components was less than 0.5 arcsec for every station. In order to make direct comparisons, the grid of ITALGEO2005 was examined both at the station points of the QDaedalus system and at the intersection points of the measurement directions of the GNSS-LEV method (see Figures 5 and 6). In order to compare the two kinds of DoV obtained by the three techniques (geometric and gravimetric, it would be necessary to consider the curvature of the plumb line. The corrections calculated by the formula reported in [27] for the two sites are, respectively, 0.01 arcsec in Noto and 0.002 arcsec in Medicina, negligible with respect to the accuracy of ITALGEO2005 model. Although to a different level of precision, the three independent methods show, overall, an excellent agreement. Our DoV estimates also confirm what could be expected from an analysis of the geo-morphological features at the two sites. At Medicina site, low values of the DoV components were found. Differently, at Noto site, the DoV components were found to be more than twice larger over the entire area. This is consistent with what could be expected from the topographical surface features and the tectonic setting of the site areas. The ITALGEO2005 DoV contour maps (Figures 5 and 6) also confirm a smoother and homogeneous variability for Medicina site and rather abrupt variations at Noto site; again, these results are consistent with the sites' geo-morphological properties. According to the standard deviations reported in Tables 1 and 2 the precision of the GNSS-LEV method and the QDaedalus system satisfied the 1-arcsec precision threshold, the latter having the best performances in terms of precision. Conversely, the standard deviations of ITALGEO2005 are larger (2.5 arcsec) and, thus, greater than the limit required for high precision purposes. The ITALGEO2005 \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Medicine**} & \multicolumn{2}{c}{**GNSS-LEV**} & \multicolumn{2}{c}{**QDaedalus**} & \multicolumn{2}{c}{**ITALGEO2005**} \\ \cline{2-7}  & \(\xi\) **(arcsec)** & \(\eta\) **(arcsec)** & \(\xi\) **(arcsec)** & \(\eta\) **(arcsec)** & \(\xi\) **(arcsec)** & \(\eta\) **(arcsec)** \\ \hline GNSS-LEV & \(-\)5.4 (0.5) & \(-\)2.0 (0.5) & & & \(-\)4.6 (2.5) & \(-\)3.8 (2.5) \\ point & \(-\)5.0 (0.1) & \(-\)2.0 (0.1) & \(-\)4.4 (2.5) & \(-\)3.7 (2.5) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Components of the DoV obtained by the three methods for the Medicina site; standard deviations are given in brackets.