Deriving Mining-Induced 3-D Deformations at Any Moment and Assessing Building Damage by Integrating Single InSAR Interferogram and Gompertz Probability Integral Model (SII-GPIM).

It is necessary to timely and accurately estimate the surface deformations in mining areas, especially the 3-D deformations during surface movement. At present, nearly all mining-induced 3-D deformations retrieved by interferometric synthetic aperture radar (InSAR) pertain to the SAR imaging interval. Research on progressive 3-D deformations during surface movement is limited, and the existing approaches are unsatisfactory in practical engineering. Aiming at these challenges, we proposed a novel method for deriving mining-induced 3-D surface deformations at any moment by integrating single InSAR interferogram (SII), the Gompertz time function, and the probability integral model (PIM), named the SII-GPIM method. We established an inversion approach for GPIM parameters and derived the mining-induced 3-D surface deformations at any moment. Subsequently, we conducted experiments considering two ALOS PALSAR images in the Huaibei mining area. The accuracy of the proposed method was evaluated in subsidence, tilt, curvature, horizontal displacement, and horizontal strain. Compared with existing methods, the SII-GPIM method is the state of the art. Additionally, we assessed the building damage, performance of parameter inversion, and method generality. The results demonstrated that the proposed method can accurately determine the mining-induced 3-D surface deformations and deformation level at any moment under different geological mining conditions. Moreover, accurate GPIM parameters can be acquired with only two SAR images and traditional measurement is nearly not required. Consequently, the SII-GPIM method owns great value for improving economic efficiency, assessing building damage, and restoring the ecological environment in the mining area.