Advancing InSAR analysis: TimeSAPS for linear and nonlinear displacement modeling

The Synthetic Aperture Radar Interferometry (InSAR) technique enables precise monitoring of ground displacements over extensive areas based on radar data. While several open-source software packages have been developed for SAR data processing, most retrieve the average velocity of Persistent Scatterers (PS) clusters under the assumption of linear behavior, limiting their application in complex scenarios. To enable more advanced and detailed analysis of InSAR time series, the TimeSAPS software package has been developed. This tool addresses the limitations of existing open-source packages, which primarily focus on linear approximations of displacement time series, by introducing advanced capabilities for analyzing both linear trends and nonlinear components. TimeSAPS performs a comprehensive analysis of PS derived from InSAR processing, characterizing time series in terms of linear trends, periodic signals, and nonlinear movements. Nonlinear components are modeled as a combination of sinusoids, each defined by its phase, amplitude, and frequency power spectrum. TimeSAPS overcomes the limitations of existing tools by providing advanced methods to recognize and model nonlinear surface movements, even when they are not known a priori. This paper presents the theoretical foundations of TimeSAPS and demonstrates its capabilities through two case studies based on real InSAR data. These examples showcase the software's effectiveness in reconstructing nonlinear displacement patterns and identifying periodic trends. The results underline TimeSAPS's potential to analyze complex ground displacement scenarios, making it a valuable resource for the scientific and engineering communities.