Combining InSAR and Time-Series Clustering to Reveal Deformation Patterns of the Heifangtai Loess Terrace

The Heifangtai Loess terrace in northwest China is frequently affected by landslides due to hydrological factors, establishing it as a significant research area for loess landslides. Advanced time-series InSAR technology facilitates the retrieval of surface deformation information, thereby aiding in the monitoring of landslide deformation status. However, existing methods that analyze deformation patterns do not fully exploit the displacement time series derived from InSAR, which hampers the exploration of potentially coexisting deformation patterns within the area. This study integrates InSAR with time-series clustering methods to reveal the surface deformation patterns and their spatial distribution characteristics in Heifangtai. Initially, utilizing the Sentinel-1 ascending and descending SAR data stack from January 2020 to June 2023, we optimize the interferometric phase based on distributed scatterer characteristics to reduce noise levels and obtain higher spatial density of measurement points. Subsequently, by combining the differential interferometric datasets from both ascending and descending orbits, the multidimensional small baseline subsets technique is employed to calculate the two-dimensional deformation time series. Finally, time-series clustering methods are utilized to extract the deformation patterns present and their spatial distribution from all measurement point time series. The results indicate that the deformation of the Heifangtai is primarily distributed around the surrounding area of the platform, with subsidence deformation being more intense than horizontal deformation. The entire terrace exhibits five deformation patterns: eastward subsidence, westward subsidence, vertical subsidence, westward movement, and eastward movement. The spatial distribution of these patterns suggests that the areas beneath the platform, namely Yanguoxia Town and Dangchuan Village, may be more susceptible to landslide threats in the future. Furthermore, wavelet analysis reveals the response relationship between rainfall and various deformation patterns, further enhancing the interpretability of these patterns. These findings hold significant implications for subsequent landslide monitoring, early warning, and risk prevention.