## 5 Discussion  
HR data coming from tiltmeters and GNSS networks on Mt. Etna allowed us to investigate in detail the very rapid deformation accompanying each of the four paroxysmal episodes of the Voragine crater at Mt. Etna. From the time-series analysis it is evident that the four paroxysms produced decreasing ground displacements, both on GNSS and tilt  
Figure 10: SISTEM inversion results. In the first row the real East–West, North–South and Vertical components are reported; in the second and third row the corresponding Expected and Residual are reported, respectively; all the values are in mm. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline UTM Easting (m) & 500,055 \(\pm\) 59 \\ UTM Northing (m) & 4,179,769 \(\pm\) 19 \\ Depth b.s.l. (m) & 6530 \(\pm\) 22 \\ Radius (m) & 500 \(\pm\) 0 (fixed) \\ A (b/a) & 0.238 \(\pm\) 0.01 \\ AP/\(\mu\) & \(-\)0.18 \(\pm\) 0.03 \\ Dip Angle & 78 \(\pm\) 1\({}^{\circ}\) \\ Azimuth & 185 \(\pm\) 2\({}^{\circ}\) \\ Volume Change (M m\({}^{3}\)) & \(-\)6.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of the source modeled from SISTEM integrated deformation data. signals, confirming the decreasing energy and volumes emitted, as reported by [2]. By inverting the ground deformation data recorded during the first three events, the location of the modeled sources appears quite stable. Indeed, although the sources were estimated separately in each of the considered periods, the coherence in the retrieved positions suggests the presence of a single depletion volume; in fact considering the dispersion of the three solutions, all of them fall in a small volume located beneath the summit craters at a depth of about 5 km below the summit craters area. The involved volumes range from 0.9 to 1.4 \(\times\) 10\({}^{6}\) m\({}^{3}\). The total volume of the first three paroxysms, coming from the modeled sources by HR data, is about 3.3 \(\times\) 10\({}^{6}\) m\({}^{3}\). Even considering a hypothetical volume of the fourth one, that should not exceed that of the third, the total volume is lower than the volume erupted, as calculated by [2] for the entire sequence (around 7 \(\times\) 10\({}^{6}\) m\({}^{3}\)). This discrepancy could be related to the noisy data with respect to the low deformation signal and/or to the not completely elastic behavior of the medium close to the surface and around the summit craters and feeding system. We should also consider that the shallow single-shot source mainly represents a level where part of the magma, coming from depth, is temporarily stored for a few hours before each paroxysm. Thus, the deflation does not necessarily represent the total volume erupted from this source but only a partial variation of volume, the magma being mainly in transit there. The cumulated ground deformation revealed by more precise daily GNSS solution and 12-days Sentinel-1 SAR interferogram depicts an overall wide deflation and contraction of the entire edifice, suggesting a significant depletion of a deeper source, with respect to those resulting from HR data inversions. The integration of both datasets makes the ground deformation pattern even more evident and precise and allows a well-constrained inversion to search for the source feeding the eruptive sequence. The modeled source is a vertical and N-S oriented prolate spheroid, located at a higher depth of almost 6 km b.s.l., always beneath the summit craters area. The volume lost by this source is about 6 \(\times\) 10\({}^{6}\) m\({}^{3}\), much more similar to the 7.1 \(\times\) 10\({}^{6}\) m\({}^{3}\) calculated by [2] for the entire sequence, with respect to the single-shot sources. This seems to confirm the role of the shallower source as a local and temporary storage of magma in transit and coming, instead, from this middle-depth source at 6 km b.s.l.