## 6 Conclusions  
In this work, the analysis of the InSAR displacement time series during the Emilia 2012 seismic sequence allowed, for the first time, to observe the evolution over time of post-liquefaction consolidation subsidence over the San Carlo, Sant'Agostino, and Mirabello villages, which have been affected by widespread liquefaction evidence at the ground. We argued that the observed subsidence is associated with the slow pore pressure dissipation of a deep and almost spatially continuous sandy layer, which liquefied during the seismic sequence and whose consolidation is mainly governed by seepage flow across clayey upper layers to the top. Such a hypothesis is corroborated by the fact that the observed subsidence localizes in areas with liquefaction evidence at the ground and also spreads over areas where direct evidence of deep liquefaction has not been identified, as it is related to the consolidation of deeper and spatially continuous sandy strata. The observed ground displacements from the InSAR analysis confirm the proposed scheme, since the observed ground subsidence manifested independently at the location of liquefaction-related manifestations at the ground. Moreover, the amplitude of the observed displacements is compatible with the computed consolidation values, thus providing further confirmation about the origin of the post-liquefaction consolidation of the observed ground movements. **Supplementary Materials:** The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/rs16132364/s1](https://www.mdpi.com/article/10.3390/rs16132364/s1)]([https://www.mdpi.com/article/10.3390/rs16132364/s1](https://www.mdpi.com/article/10.3390/rs16132364/s1)), Figure S1. Spatial and temporal baseline distribution of the CSK data set. The data set begins 1 day before the 20 May 2012 main shock and includes \(\approx\)150 days of postseismic deformation. The lines between the different acquisitions define the interferometric pairs used for construction of the SBAS time series. Figure S2: **(a)** Spatial distribution of the available geotechnical investigations over the study area (from [PERSON] et al. [60]). **(b)** Boxplot of the computed maximum PGA over the study area (from [PERSON] et al. [42]). **(c)** Experimental shear modulus reduction curves from resonant column tests (from [PERSON] and [PERSON] [40]), together with the theoretical curve defined according to Equation (14) [66]. Figure S3. **(a)** Location of the available groundwater wells in the study area, classified according to their maximum depth (data available from: [[https://www.arpae.it/it/temi-ambientali/acqua/dati-acque/acque-sotterranee](https://www.arpae.it/it/temi-ambientali/acqua/dati-acque/acque-sotterranee)]([https://www.arpae.it/it/temi-ambientali/acqua/dati-acque/acque-sotterranee](https://www.arpae.it/it/temi-ambientali/acqua/dati-acque/acque-sotterranee)), accessed on 3 June 2024). **(b)** Measured groundwater depth from the ground at water wells in panel **(a)**. Figure S4. Mean InSAR displacement rate maps in the period 2003-2010 from ENVISAT SAR data, computed along the **(a)** ascending and (b) descending satellite orbit acquisitions. Panels c and d show the vertical and the east-west horizontal components of the displacement rate, obtained by combining the ascending **(a)** and descending (b) displacement rates. **Author Contributions:** Conceptualization, M.A. and A.C.; data curation, A.P. and G.S. ; formal analysis, M.A., A.P. and G.S. ; investigation, M.S. and M.M. ; methodology, M.A. and A.C.; software, M.A., A.P. and G.S. ; validation, A.C., M.S. and M.M. ; visualization, M.A. ; writing--original draft,M.A. ; writing--review and editing, A.C., M.S., M.M., A.P. and G.S. All authors have read and agreed to the published version of the manuscript. This research received no external funding. The raw data supporting the conclusions of this article will be made available by the authors upon request. We thank the Italian Space Agency for providing the CSK SAR data.