## 3 Materials and Methods  
### InSAR Data  
The ground displacement induced by UGS activity can be detected using both ground-based and remotely sensed data. The latter involves non-contact techniques that receive and record signals interacting with the surface or objects above the reservoir area. Over the last decade, InSAR has become a widely recognised tool for monitoring storage activities, taking advantage of the emission/reception sensors mounted on satellites. Its popularity can be largely attributed to the advent of differential interferometry (DInSAR) techniques. The working principle of InSAR is rooted in the measurement of the phase difference of the return signal at each pixel between two radar images. DInSAR revolves around the analysis of a pair of radar images acquired by a Synthetic Aperture Radar (SAR) sensor [25]. Specifically, InSAR methods rely on the phase delay of a reflected microwave (radar wave) to gauge variations in distance along the Line-of-Sight (LoS) direction of the satellite [12]. The final result of the DInSAR approach is the interferogram, expressing the phase difference for each pixel of the images acquired from two satellites passing over the same area. In operational terms, an interferogram is produced by summing the complex values of one SAR image with the complex conjugate of another image once they are adequately resampled (co-registered) on the same grid (for more detail see [12; 25; 26; 27; 28]). The variation in phase components for each pixel can be represented by the equation:  
\[\varphi\mathrm{i}=\varphi\mathrm{d}+\varphi\mathrm{a}+\varphi\mathrm{t}+\
u\]  
where \(\varphi\mathrm{d}\) represents the phase shift caused by target displacement between the two acquisitions; \(\varphi\mathrm{a}\) denotes the phase contribution resulting from differing atmospheric conditions during the acquisitions; \(\varphi\mathrm{t}\) is a component related to changes in the acquisition geometry, which is highly influenced by local topography; and \(\
u\) accounts for the noise, which encompasses thermal, temporal, and geometrical decorrelation phenomena affecting the phase value of the pixel [26]. The analysis of multiple SAR images (Advanced Differential InSAR, A-DInSAR) and derived interferograms allows the temporal evolution of ground deformations to be recovered. The displacement time series are extracted from ground features with reflective capabilities (e.g., buildings, roads, and rock outcrops) that maintain an optimal level of coherence during the monitoring period. The literature on InSAR techniques and applications is extensive. Pixel selection can be performed using different algorithms [27]. These algorithms usually fall under two main approaches: permanent (or persistent) scatterers interferometry (PSI [28]) and distributed scatterers interferometry (DSI [29]). The first group creates a dominant scattering point centre within the resolution cell and results from a combination of all the signal backscattered by the elements inside, limiting phase decorrelation effects due to different acquisition geometries (characterised by high reflectivity values and stable phase values), whereas the second group consists of ground features that, when considered individually, do not exhibit strong amplitude or a stable phase. However, when integrated by averaging, their spatial and electromagnetic homogeneity enables specific algorithms to enhance their radar response (DS are much more common in natural environments). The result of multi-temporal A-DInSAR analyses is a deformation map composed of multiple points. Each point is defined by an annual velocity value and a displacement time series. This product boasts millimetre-level accuracy and delivers both high temporal and spatial resolutions [11]. The InSAR data used in this study were extracted from the European Ground Motion Service (EGMS) under the responsibility of the CLMS (Copernicus Land Monitoring System) [30] using the EGMSstream application [31].