A Variance-Covariance method to estimating the errors of 3-D ground displacement time-series using small baseline InSAR algorithms and multi-platform SAR data

The joint exploitation of complementary information from independent satellite and ground-based SAR observations can allow reconstructing the three-dimensional (up-down, east–west, north–south) ground displacement profile. Some attempts have recently been made to complement satellite and ground-based SAR (GB-SAR) data. However, a method for generating the 3-D ground displacement time-series and evaluating the quality of these estimates is still lacking. Our research aims to develop a statistical framework that is beneficial to evaluate the quality of the reconstructed 3-D ground deformation measurements achieved by jointly using space-borne and GB-SAR systems. To this purpose, the quality of multi-platform Line-of-Sight (LOS)-projected ground displacement time series is first assessed by deriving the variance–covariance matrices of noise sources (i.e., time-inconsistent phase unwrapping mistakes, decorrelation effects, and atmospheric phase screen). Subsequently, the precision of the retrieved 3-D ground displacement products is derived. Some experiments have been performed considering the zone of Gorgoglione in southern Italy, for which three sets of SAR images are available. The first set is composed of radar images collected through a GB-SAR measurement campaign performed with the IBIS-L instrument from September 2016 to July 2017. In contrast, the spaceborne sets consist of two groups of images gathered during the same observation period by the European Copernicus Sentinel-1A/B sensors over complementary ascending (Path 146) and descending orbits (Path 124). The experimental results for the selected case-study area showed that the error bounds for the 3-D ground deformation time-series are about 3.6 mm, 3.7 mm, and 0.6 mm for the up-down, east–west, and north–south profiles, respectively.