## 3 Data and Methods
### SAR Data and Processing  
We analyzed the ground displacements caused by the 2012 earthquake seismic sequence. To this aim, we considered the same set of synthetic aperture radar (SAR) data exploited in [PERSON] et al. [30], consisting of a collection of 18 SAR images taken along the descending orbit of the COSMO-SkyMed (CSK) constellation satellites at a side-looking angle of approximately 32\({}^{\circ}\) (the SAR data footprint corresponds to the dashed purple line in Figure 1). This SAR dataset covers the period from 19 May 2012 to 10 May 2013, enabling us to assess the co-seismic and the post-seismic displacement fields for one year. The first post-seismic SAR image was obtained on 23 May 2012, thus capturing the co-seismic and post-seismic displacements of the earliest three days after the May 20 mainshock. A total of 55 interferograms were generated from the available SAR data (Figure S1) using the well-known small baseline subset (SBAS) algorithm [43]. It is worth remarking that the investigated area is mostly located rurally, where multi-temporal InSAR methods based on the small baseline-oriented paradigm have demonstrated their superiority with respect to large-baseline approaches (e.g., the PS method [44]) in detecting and monitoring the evolution of ground displacements associated with coherent distributed targets (DTs) on the ground. Moreover, as further clarified in the following, the observed ground displacements, at least in the Sant'Agostino-Mirabello area, can be assumed to be mostly vertical. Thus, SAR data gathered from one single track (i.e., the used descending orbits data) are sufficient to recover the vertical components of the ground deformation, making the processing of both ascending and descending orbits less relevant for the purpose of the presented analyses. The application of SBAS yielded a comprehensive spatial map showcasing the average displacement velocity within the surveyed area and the displacement time series for each detected coherent DT in the scene. The InSAR interferograms were flattened using the one-arcsec (30 m of spatial sampling) Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) of the area. To mitigate the decorrelation noise of the generated interferograms, a complex multi-look (ML) operation [45] was performed considering 10 looks in both the azimuth and range directions, accompanied by the Goldstein noise-filtering operation [46] on each interferogram. Subsequently, the interferograms were unwrapped using the 2D (space) plus 2D (time) phase unwrapping method proposed by [PERSON] and [PERSON] [47] and further inverted using the SBAS strategy. The SBAS processing chain and its relevant codes were designed and developed at the CNR-IREA lab [37]. Over the years, these codes have been updated and massively applied to investigate several ground displacement phenomena (e.g., see [18; 48; 49; 50]). The processing chain includes steps for the identification and correction of orbital and residual topography artifacts (e.g., see [51]), the filtering of time-inconsistent phase decorrelation noise affecting generated multi-look interferograms [52], and the correction of atmospheric phase screen (APS) artifacts [44]. In particular, the APS was estimated and removed for each analyzed SAR pixel, relying on the assumption that it exhibited a relevant spatial correlation but a limited temporal correlation [44]. Interested readers can find additional details on SBAS processing in [PERSON] [53] and [PERSON] et al. [54]. As a result, the SBAS processing returned 97,902 DT measurement points over an area of approximately 1270 km\({}^{2}\) (density of roughly 80 DT/km\({}^{2}\)). The spatial resolution of the DT points was further enhanced by exploiting the spatial correlation among the obtained displacements with Kriging interpolation techniques [55]. The latter includes a variety of least-squares methods that provide predictions with the minimum variance of the investigated variable [56; 57; 58].