Calculating vertical deformation using a single InSAR pair based on singular value decomposition in mining areas

Vertical deformation estimation can be a significant tool in preventing geological hazards and managing environment impacts of underground mining. Common ground surface vertical deformation calculations are challenged by difficult data collection and dependence on prior knowledge. SVD (singular value decomposition) method was applied to estimate ground surface vertical deformation from single pair SAR (synthetic aperture radar) data in a mining region. During the study, LOS (line of sight) and azimuth displacement was obtained using two pass D-InSAR (differential interferometry synthetic aperture radar) and MAI (multi-aperture radar interferometry) technology, respectively. Two adjustment equations were composed using the imaging geometry of D-InSAR and MAI. The singular value decomposition theorem was used to acquire M-P (Moore-Penrose) generalized inverse of the rank deficiency coefficient matrix. From this, the optimal approximation solution of unknown parameters was calculated using weighted least squares. A working panel in the Datong mining area, Shanxi province, China, was selected to verify the SVD approach using the two ascending Sentinel-1A data. The accuracy of vertical deformation estimated by SVD approach is reliable. The RMSE (root mean square error) of vertical deformation is 2.64 mm (along upright profile) and 4.95 mm (along horizontal profile). These results suggest that the SVD approach will complement widely used vertical ground surface deformation calculations. Further study is needed to validate the method from other deformation scenarios from landslides, groundwater loss, earthquakes, underground mining, and glacier movement.