# Volume Loss Assessment with MT-InSAR during Tunnel Construction in the City of Naples (Italy)
## 1 Introduction  
The need for new infrastructures in densely populated cities due to the increasing global population [1], as well as the increasing migration from rural to urban areas [2], must be satisfied. Intensive land use in the previous decades has saturated the space for the creation of new superficial infrastructures (i.e., roads, railways, and so on). Thus, the demand for mobility is directed towards the exploration of the still intact underground space, where it can be satisfied through the construction of underground infrastructures, including tunnels. Tunnel excavation in developed areas, while a delicate task to accomplish, may also pose a risk to the surrounding space, because the potential of causing damage to the nearby infrastructures and environment during the construction process. In fact, as urban tunnels are generally shallow, the field of displacements induced in the ground by the excavation propagates up to the ground level. This can be limited by implementing the appropriate engineering solutions, but not completely avoided. The prediction and monitoring of ground movements is thus a critical issue to assess potential damage and to undertake preventative measures [3, 4]. The excavation of a tunnel in urban areas can affect buildings in multiple ways, depending on the excavation technique, depth and length of excavation, ground conditions, as well as many other factors. Considering the relatively high number of buildings potentially affected by the excavation in urban areas, it is often impossible to monitor them all with traditional monitoring techniques, owing to the prohibitive cost. Therefore, often only those buildings or infrastructures that have cultural, historical, and public relevance aremonitored, or those that have been a priori identified as vulnerable according to the results of empirical or numerical methods. In the last decades, processing of data from synthetic aperture radar (SAR) satellites was used to obtain information on deformation processes of the Earth's surface, caused by various phenomena including, but not limited to, earthquakes [5; 6; 7], natural subsidence [8; 9], and volcanic movements [10; 11]. The recent development of high-resolution SAR satellites, such as the COSMO-SkyMed (CSK) (Constellation of Small Satellites for Mediterranean basin Observation) constellation or TerraSAR-X constellation, along with recent advancement in data processing techniques, such as the multi-temporal interferometric synthetic aperture radar (MT-InSAR), showed the capability to measure the field of displacements induced by tunnel excavations in urban areas [12; 13; 14; 15]. In [12], the authors used a single Master persistent scatters (PS) analysis carried out on CSK descending SAR images for the detection of surface settlements induced by Shanghai subway tunnels, in China. The velocity map of deformations clearly indicated the subway alignment. InSAR-monitored velocities were fitted with a standard Gaussian distribution along tunnel cross sections, and a comparison with published data in the same area confirmed the extension of the fitted settlement trough. A similar work was carried out by [16]. Here, MT-InSAR is applied to the excavation of Metro Line 6 in the city of Naples, using CSK SAR images in ascending direction. The authors projected InSAR-monitored data in the vertical direction first, and then compared their time series to the traditional surveying method (precise levelling points, PLP), showing a good agreement. Furthermore, in order to analyze the spatial distribution of the settlements, the researchers applied a standard Gaussian curve to fit the InSAR and PLP data. This analysis revealed a strong correlation between the two monitoring techniques, despite the fact that only a small number of scatterers was taken into account. A different approach was used in [13]. Here, the authors carried out an MT-InSAR analysis on CSK SAR images in both the ascending and descending direction.