Separating coupled deformation modes: a case study of Hebi City, China, using time-series InSAR and blind source separation

Surface deformation in resource-based cities and agricultural plains is often attributed to residual mining, but the relative roles of groundwater fluctuation, irrigation, and urbanization remain poorly quantified. Here we focus on Hebi City, China, a typical coal-mining city where these stressors overlap, and use 48 Sentinel-1A SAR images (January 2021–December 2024) to derive a PS-InSAR approximate vertical deformation time series. A representative valid InSAR pixel near the HAHB GNSS station shows temporal evolution broadly consistent with the smoothed GNSS vertical observations (RMSE = 4.46 mm). PCA-FastICA separates statistical spatiotemporal modes, which are interpreted using land-use, precipitation, and groundwater-level data. Subsidence concentrates in Heshan District, parts of Shancheng District, and eastern Xun County, whereas uplift or recovery occurs mainly in Qibin District, the central-southern plain, and areas adjacent to water systems. Three statistical modes are retained: seasonal (IC1), long-term trend (IC2), and short-term anomaly (IC3), with dominant-point proportions of 7.76 %, 83.42 %, and 8.82 %, respectively. These proportions describe the locally dominant mode at sampled points, rather than the contributions of physical drivers. Cross-wavelet analysis shows enhanced precipitation-IC1 common power mainly at 9.5–13.5-month periods and common power between water-level and displacement increments at P3 mainly at 4.8–6.7-month periods. At P3, 23 monthly groundwater-level and displacement observations are moderately correlated ( r = 0.449), whereas their 22 monthly increments are weakly correlated ( r = −0.161). This single-site evidence does not establish groundwater as the primary regional control. The workflow provides an exploratory framework for separating deformation patterns and examining hydrological covariation in resource-based cities.