A New Method for Extracting Three-Dimensional Surface Deformation in Underground Mining Areas Based on the Differentiability of D-InSAR Line-of-Sight Displacements

Monitoring three-dimensional (3D) deformation in underground mining areas is crucial for the prevention and control of mining-induced disasters. Differential interferometric synthetic aperture radar (D-InSAR) is limited to detecting one-dimensional (1D) deformation along the line of sight (LOS). This paper proposes a new method for extracting 3D mining-induced deformation based on the differentiability of D-InSAR LOS deformation fields. The method approximates the D-InSAR LOS deformation field in underground mining areas as a differentiable function and constructs a 3D deformation extraction model utilizing directional derivatives of this function. The least squares method is used for estimating and evaluating the 3D deformation. Simulation and real data experiments have been used to verify the feasibility of the method in extracting mining-induced 3D deformation. The simulation results show relative root mean square errors (RRMSES) of 1.24%, 6.05%, 0.97%, and 11.47% for vertical and horizontal displacements along the east-west and south-north directions, respectively. The real data experiments using Sentinel-1 images show that the root mean square errors (RMSES) of the up-down, south-north, and east-west directions are 14.06 mm, 7.37 mm, and 11.56 mm, respectively. Experimental results show that the method can provide a certain basis for 3D surface deformation monitoring of mining subsidence.