A New Dynamic Probability Integral Model for 3-D Deformation Monitoring of Loess Mining Subsidence Using InSAR

Mining-induced surface deformation is a spatiotemporal dynamic process. Relying solely on post-stabilization deformation patterns cannot effectively address monitoring demands during dynamic extraction phases. In loess mining areas, this complexity is further intensified by the coupling effect between dynamic mining processes and rugged terrain, resulting in deformation basins with more intricate geometries and distribution characteristics than in other mining areas. Traditional deformation monitoring methods that combine interferometric synthetic aperture radar (InSAR) and probability integral model (PIM) (InSAR-PIM) are unsuitable for such situations, leading to significant discrepancies between monitoring results and actual deformation. This study proposes a new dynamic PIM (NDPIM) suitable for loess mining areas, which introduces the mining width-to-depth ratio parameter and integrates a time function, thereby establishing a dynamic model applicable to the entire mining cycle. Meanwhile, slip correction is incorporated to account for slope slip effects. The InSAR-NDPIM method combines InSAR and NDPIM for deformation monitoring and we applied the method to monitor the surface deformation in the Yuanzigou mining area. Results show that the three-dimensional (3D) deformation derived from InSAR-NDPIM aligns more closely with the actual situation. The average root mean square error (RMSE) for subsidence and horizontal displacement are 13.2 mm and 15.8 mm, respectively, representing improvements of 68% and 30.2% compared to traditional InSAR-PIM. The overall surface deformation monitoring accuracy shows a 76.2% enhancement over conventional InSAR. These results demonstrate that InSAR-NDPIM can fulfill the demands for dynamic monitoring of surface deformation, offering higher accuracy and broader application prospects in loess mining areas.