## 2 Materials and Methods
### DInSAR Technique  
DInSAR is one of the most used remote sensing techniques. It is based on the processing of high-resolution radar image pairs acquired through the Synthetic Aperture Radar (SAR) system [26] over an area of interest and allows to derive the magnitude of the displacement component projected along the sensor line of sight (LOS). The effects of additional phase components (e.g., related to changes in the electromagnetic characteristics of the targets on the ground in the time interval of observation, to geometric distortions, to the orbital information inaccuracy, or to changes in atmospheric conditions between the acquisitions) are minimized by taking advantage from the use of the Multi-Temporal DInSAR techniques, such as the Small BASeline Subset (SBAS) approach [27] that, starting from the appropriate processing of a large number of interferometric SAR data pairs, allows to generate mean deformation velocity maps extended over several hundred thousand of km\({}^{2}\) and, for each coherent point [28], provides the temporal evolution of the displacements occurred in the period of interest by means of the deformation time series. The SBAS technique is able to perform deformation analyses at different spatial resolution scales, producing displacement time series and velocity maps at both regional and local resolution scales [28; 29; 30]. In particular, when operating at local scale, e.g., for the monitoring of buildings and infrastructures, full resolution differential interferograms generated from the single-look SAR data (characterized by a spatial resolution of the SAR sensor ranging from 3 to 10 m), are employed. Generally, the SBAS-DInSAR products have an accuracy of 1-2 mm/year on the measurement of the mean displacement velocity, and of 5-10 mm on the single measurement of displacement [31; 32; 33; 34]. The full resolution SBAS-DInSAR technique provides a large set of measuring points for the investigated area, called Persistent Scatterers (PSs), each of which representative of a portion of surface. The interferometric measurements are always calculated with respect to a defined reference point, whose displacement value directly impacts all the points of the dataset. For each PS, a set of information is provided, made of geographical coordinates (latitude and longitude), height with respect to a global reference system, LOS directional cosines, LOS mean deformation velocity in the overall acquisition period, and LOS displacement measures in each acquisition time. Moreover, the quality of the results from an interferometric point of view is estimated through the temporal coherence value ([28; 35]). The accuracy in the planimetric geolocation of the PSs is related to the estimation of residual topography compared to the Digital Elevation Model (DEM) used in the interferometric processing. For the same area, ascending (\(ASC\)) and descending (\(DES\)) measurements may be generally available, with the satellite moving along the acquisition orbits from South to North, or from North to South, respectively. The two datasets can be combined to obtain the deformation components along global directions, commonly East-West (\(EW\)) and vertical (\(z\)) [36]. It is worth specifying that the deformation along the North-South (\(NS\)) direction can be overlooked, accepting a limited error, since the sensor is not quite sensitive to the measurement of the components along this direction. This is because of the lateral view and of the near polar orbit trajectories of the satellite system. Indicating the mean yearly deformation velocity with \(V\), the following system can be written:  
\[\left\{ \begin{array}{l}V_{ASC}\cong V_{EW}\cdot n_{EW,ASC}+V_{V}\cdot n_{z,ASC }\\ V_{DES}\cong V_{EW}\cdot n_{EW,DES}+V_{V}\cdot n_{z,DES}\end{array} \right., \tag{1}\]  
where \(n_{EW,ASC/DES}\) and \(n_{z,ASC/DES}\) are the directional cosines of the sensor LOS.