## 2 Materials and Methods
### Satellite Data  
It is necessary to underline that the satellite data used are subjected to different levels of preliminary treatments to obtain SAR standard products and higher-level products, such as the interferometric ones [22; 23]. Afterward, these are additionally processed according to the SBAS-DinSAR algorithm [20; 21]. The processing methods could cause new difficulties in the further treatment of data, e.g., the improper elimination of useful points, or the preservation of non-structural points, increasing the uncertainty of the results [16]. In addition, it has to be considered that the LOS data do not refer to the point on the ground, but to the point measured by the sensor (e.g., the roof of a building). Thus, to exploit them in the assessment of subsidence, the simplifying assumption of having structures undergoing a uniform subsidence phenomenon is introduced. Finally, a further limitation in the use of satellite data is due to the presence of a large dataset, in which points with incorrect measurements due to preliminary processing or insignificant ones (i.e., those that do not fall within the built area) are also included. As mentioned in reference [16], this presence contributes to increasing the analysis' uncertainty, so these measures should be removed. However, this study considers an average, approximate behavior of the urbanized area and not the individual building. Therefore, this issue is neglected. For the evaluation of the case study, SAR images were extrapolated only for the area related to the T3 section of the Line C subway in Rome (Figure 1). This route connects the station of San Giovanni to the Colosseum, with an intermediate station (Amba Aradam/Ipponio). The area has great importance because it includes many structures of architectural and monumental value, such as the Colosseum itself, the Basilica of Santo Stefano Rotondo, the Basilica of Maxentius, the Aurelian Walls, the Colonnades of the Forum of Nerva and the Church of Santa Maria in Domnica. Although construction operations started in 2013, the project required various preparatory works and was subjected to delays. Therefore, tunnel excavation only began in 2018, after the inter-tract shafts realization in 2017 [24] (see Figure 1 for reference). This information is relevant for the identification of the area affected by the subsidence phenomenon induced by the excavations. Regarding the soil characteristics, starting from the ground level, the stratigraphic succession shows the first layer of recent deposits, whose thickness reaches values of 13-16 m. It follows a layer of recent alluvial deposits lying on Pleistocene deposits, characterized in the upper portion by clayey salts and silty clays, locally sandy, and in the lower portion by sands and gravels. The water table level is placed at about 8-10 m from ground level. The depth of the tunnels is approximately 30 m between the San Giovanni and Amba Aradam stations, then increasing up to 57 m at shaft 3.2 and subsequently decreasing to 32 m at the Fori Imperiali station. For each of the measured points, the employed dataset contains the geographic coordinates, the topographic elevation, the velocity and the LOS displacement at each time interval with respect to the initial one. The displacement and velocity values are given along the line of sight of the satellite sensor. Therefore, information on their overall deformation process can only be derived by processing the data obtained from both orbits (ascending and descending). However, a single dataset can still be used to obtain some preliminary information. In the case of subsidence phenomena, it can be assumed that the main direction of deformation is vertical. Thus, it is possible to derive the intensity of the displacement or the velocity along this direction, starting from the projection measured along the LOS of the satellite [18].