A multivariate time series analysis of ground deformation using Persistent Scatterer Interferometry
Authors: Rigamonti Serena , Colombo Francesca , Crosta Giovanni Battista , Dattola Giuseppe , Frattini Paolo , Presta Asciutto Alberto , Previati Alberto 
Published: February 2023

Usually, ground deformations are the result of complex interactions of multiple triggering factors due to natural processes and anthropogenic causes. For this reason, areas affected by ground deformations require appropriate monitoring systems, analyses, and methodologies to implement the necessary risk mitigation strategies. In this context, Synthetic Aperture Radar (SAR) sensors enable the monitoring of displacements of the Earth's surface, providing time series with high spatial resolution and wide temporal coverage.In this contribution, we present a new multi-method approach for analysing main trends and seasonal signals in the time series of ground displacements in order to correlate ground deformation phenomena with triggering factors (e.g. rainfall, snow, temperature, piezometric level, pumping/injection) and to recognize specific footprints and patterns of the different phenomena.We analysed large datasets of ground displacement data in different areas of Italy, spanning in total the period from 1992 to 2021, acquired from C-band radar sensors on board ERS-1/2 and ENVISAT platforms of the European Space Agency (ESA), as well as from X-band sensors of COSMO-SkyMed (CSK) constellation, TerraSAR-X (TSX) and Sentinel-1 satellites processed with the PSInSAR (Permanent Scatterer Interferometric Synthetic Aperture Radar) technique by TRE Altamira.In the first step, we applied and optimized T-mode PCA, ICA and MSSA to perform a spatial-temporal separation of the data into a set of components/functions. Then, hierarchical clustering (HC) approach was implemented to group the PSInSAR time series of characteristic deformation patterns and, finally, wavelet transforms were applied to analyse the time series in the time-frequency domain, detecting localised non-stationary periodicities and identifying possible causal relationships in time-frequency space.The approach has been validated on different surface phenomena at local and regional scale, including subsidence, uplift and sinkholes in urban areas, landslides, rock glaciers and slope creep movements, which differ in dynamics, exposure, land cover, triggers, and evolutionary behaviour. As result, we were able to recognize and separate a limited number of main components/functions that occur systematically in the time series, describing, in particular, the long-term displacement, the seasonal periodicity, and changes in the displacement rate. The weight and ranking of these components may provide a footprint for the different phenomena (e.g., seasonal periodicity for rock glaciers, change of displacements for active landslides, etc.), potentially allowing to recognize the phenomena based on the time series analysis. Finally, the application of the wavelet transforms to the components/functions separated from the times series seems to optimize the analysis of the correlation between the displacements and the natural/anthropogenic triggers.In conclusion, interpreting the results obtained from the multi-method approach, considering geological geotechnical, hydrogeological and environmental factors, allows a deeper understanding and characterisation of the phenomena and their triggers, overcoming the limitations due to the application of single techniques.