Identification and analysis of nonlinear trends in InSAR displacement time series

Multi-temporal SAR interferometry (MTInSAR), by providing both mean displacement maps and displacement time series over coherent objects on the Earth, allows analysing wide areas, identifying critical ground instabilities, and studying the phenomenon evolution in a long time-scale. Nowadays satellite SAR constellations provide datasets covering time periods of several years with short revisit times (up to 6 days for Sentinel-1), which allow investigating ground displacements showing non-linear kinematics. These are particularly interesting since they include warning signals related to pre-failure of natural and artificial structures. Recently, approaches have been proposed for recognising and analysing nonlinear displacements, which use different strategies. The authors have introduced two innovative indexes for characterising MTInSAR time series: one relies on the fuzzy entropy and measures the disorder in a time series, the other performs a statistical test based on the Fisher distribution for selecting the polynomial model that more reliably approximate the displacement trend. This work reviews the theoretical formulation of these indexes and evaluate their performances by simulating time series with different characteristics in terms of kinematic (stepwise linear with different breakpoints and velocities), level of noise, signal length and temporal sampling. Finally, the proposed procedures are used for analysing displacement time series derived by processing real datasets acquired by both Sentinel-1 and COSMO-SkyMed constellations. In particular the hilly villages of Pomarico and Montescaglioso have been investigated, which are located in Southern Italian Apennine (Basilicata region), in an area where several landslides occurred in the recent past, causing damages to houses, commercial buildings, and infrastructures. The MTInSAR displacement time series have been analysed by using the proposed methods, searching for nonlinear trends that are possibly related to relevant ground instabilities and, in particular, to potential early warning signals for the landslide events affecting Mtescaglioso in 2013 and Pomarico in 2019.