## 3 Material and Methods
### GNSS Data  
We used the available raw observations provided by GNSS-RING network [81], managed by INGV [82], integrated by other active GNSS stations belonging to regional and national networks [83], in order to estimate the VLM rates at a set of stations located within 10 km from the coastlines of south-eastern Sicily (Figure 2). In our analysis, we considered all the data available from 1995 to 2020, but, specifically, the sites shown in Figure 2 span the 2006-2020 time-interval. The analysis was performed by the GAMIT/GLOBK software, following the three step procedures described in [PERSON] et al. [29]. The raw GPS observables have been analysed using the GAMIT/GLOBK software (V.10.70) [84; 85] adopting IGS standards [86]. In this step, the satellites orbit parameters are tightly constrained to the IGS final values. The GAMIT software estimates station positions, atmospheric delays, satellite orbits and Earth orientation parameters from ionosphere-free linear combination GPS phase observables using double differencing techniques in order to eliminate phase biases caused by drifts in the satellite and receiver clock oscillators. GPS pseudo-range observables are also used to constrain clock timing offsets and improving automated editing of phase data, helping in the resolution of integer phase ambiguities. GPS phase data are weighted adopting an elevation-angle-dependent error model [85]. The IGS absolute antenna phase centre model is used for both satellite and ground-based antennas, allowing us to improve the accuracy of vertical site positions by mitigating reference frame scale and atmospheric mapping function errors. While the first-order ionospheric delay is eliminated by the ionosphere-free linear combination, the second-order ionospheric corrections are applied using IONEX files from the Centre for Orbit Determination in Europe (CODE). The tropospheric delay is modelled as piecewise linear model and estimated using the Vienna Mapping Function 1 (VMF1). We use the Global Pressure and Temperature 2 (GPT2) model to provide a priori hydrostatic delays. The pole tide was also corrected in GAMIT adopting IERS standards. The Earth Orientation Parameters (EOP) are tightly constrained to priori values obtained from IERS Bulletin B. Ocean loading is corrected using the FES2004 model. The International Earth Rotation Service (IERS) 2003 model for diurnal and semi-diurnal solid Earth tides was set. Because of the large number of stations included in our Euro-Mediterranean GNSS data processing (\(\sim\)3000), the GAMIT analysis is performed for several sub-networks, each made by <50 stations, with each sub-network sharing a set of high-quality IGS stations that are later used as tie-stations in the combination step. The daily sub-nets, loosely constrained, solutions are combined using the GLOBK software, which adopts a Kalman filter estimation algorithm, simultaneously realizing a global reference frame by applying generalized constraints. Specifically, we define the reference frame by minimizing the velocities of the IGS core stations ([[http://igscb.jpl.nasa](http://igscb.jpl.nasa)]([http://igscb.jpl.nasa](http://igscb.jpl.nasa)). gov, accessed on 6 January 2021 [87]), while estimating a seven-parameter transformation with respect to the GPS realization of the ITRF2014 frame, i.e., the IGS14 reference frame. In the third step, we analyse the position time series in order to estimate the 3-components' (east, north and vertical) of linear velocities and uncertainties. Changes in stations positions are modelled using the following functional model:  
\[x(t)=x_{0}+bt+\alpha\sin(\omega t+\varphi)+\sum_{j=1}^{n}\Delta x_{j}H\big{(}t -t_{j}\big{)} \tag{1}\]  
where \(x\) is the position of a point, \(t\) is the time, \(x_{0}\) is the initial position bias, \(b\) is the secular rate, \(\alpha\) and \(\varphi\) are the amplitude and phase of the annual and semi-annual seasonal signals, respectively, and \(H\) is the Heaviside step function defining coordinate jumps (\(\Delta x\)) at a given time \(t_{j}\).