## 4 Discussion and Conclusions  
In recent times the existence of a link between seismicity and ground tilt in the phenomena involved in volcanic/hydrothermal environments is well known [1; 4; 5; 6; 7; 8]. In our study we look at how and to what extent the two different physical observations could be interconnected in the case of Mt. Vesuvius earthquakes. Our work was mainly devoted to the research and calibration of an approach that could allow the comparison of two physical variables: the ground velocity recorded by seismometers and the ground inclination recorded by tiltmeters, during the occurrence of an earthquake. To the knowledge of the authors, this is the first of such an attempt at Mt. Vesuvius. The basic idea is to estimate the displacement field generated by each specific earthquake starting from the recorded seismograms. To do this we first estimate the seismic source spectra parameters, the seismic moment (M0), the corner frequency (fc), the fault dimensions and the net slip. In recent decades, several studies have been carried out to estimate the seismic source parameters at Mt. Vesuvius [13; 14; 21; 22]. In all those studies the quality of the data was fundamental. We concentrate our attention on the time interval 2018-2020 to ensure the simultaneous operation of the broadband digital stations and the tiltmeter network. During this period Mt. Vesuvius was characterized by a low-level seismicity, with maximum magnitude equal to 2.5. Moreover, the volcano is located inside the urban area of Naples district and is hence affected by a high level of anthropogenic noise. We selected 24 earthquakes which had the best signal-to noise ratio, considering those earthquakes with a magnitude \(\geq\) 2.0. In the considered period the seismicity of the volcano was also characterized by a predominance of shallow focal depths [1]. We found that the focal depths clustered in two depth ranges, with 14 earthquakes located above the sea level (depths less than 1 km), nine located in depths in 0-3 km b.s.l. and one below 4 km depth b.s.l.. This depth distribution is in contrast with the observation of [PERSON] et al. [11] who found the most focal depths to be in the deeper cluster for the period 1999-2012. This discrepancy could be due the decrement of the deep earthquake occurrence ascribed to the exhaustion of the effect of the 1999 seismic crisis [2]. Therefore, our dataset was significantly different from previous studies, in which the focal depth ranges in 1.5-4.2 km (and MD in 0.9-3.6) and for which a 1D-location algorithm and a layered velocity model are often suitable and preferred [14; 22]. In our case the earthquake foci could be inside the volcanic orifice above the sea level and, hence, the (location) algorithm must take into account the topography (and its velocity structure) to provide reliable locations. The estimated focal mechanisms show no clear patterns for fault geometries, in line with past studies [9; 10; 13; 14; 22]. With a particular reference to the study of [PERSON] et al. [11], we found thrust mechanisms to be predominant in the shallow cluster (50%), while the deeper earthquakes show prevailing normal mechanisms (40%), with a clear presence of strike components (see Table 1), in agreement with the observations of those authors. They attribute these patterns to the effect of a local stress field which is strongly constrained by the evolution of the Somma-Vesuvius complex. For the calculation of source spectra, we used two broadband seismic station of the mobile seismic network, since they do not present dramatic site effects [22]. In the estimation of the spectra, we did not account for propagation effects due to the short station-source distance value, in agreement with [PERSON] et al. [13]. Assuming the Haskell model for the source, we obtained a seismic moment in the range (0.2-6.1) \(\times\) 10\({}^{12}\) Nm and corner frequencies in the 5-17 Hz range, which are the values generally found for Mt.