3D Surface Displacement Reconstruction of Mountainous Coalfields Considering Topographic Effects Using DS-InSAR

To address the challenges of severe surface undulation in mountainous mining areas, significant InSAR geometric distortion, and the inability to directly calculate three-dimensional (3D) displacement from single-track Line-of-Sight (LOS) data, this paper proposes a 3D deformation reconstruction method that integrates Distributed Scatterer Interferometric Synthetic Aperture Radar (DS-InSAR) with an improved Probability Integral Model (PIM) considering topographic sliding effects. The traditional Probability Integral Method (PIM) ignores the additional sliding caused by topographic slope, leading to significant deviations when applied in mountainous areas. This study introduces a nonlinear sliding influence function and constructs a topographic correction model incorporating sliding intensity, position offset, and morphological attenuation parameters to quantitatively describe surface movement patterns under the coupling effect of mining and topography. Based on this, a model parameter-driven single-track InSAR observation equation is established, and the Adaptive Genetic Algorithm (AGA) is employed to invert the complete set of model parameters using high-density LOS deformation obtained from DS-InSAR as constraints, thereby resolving the full-basin 3D displacement field. Experimental results from a typical mountainous coal mine in the Taihang Mountain area of China demonstrate that this method effectively overcomes the ill-posedness of 3D displacement inversion from single-track InSAR data. The maximum vertical subsidence is 1050 mm, and the maximum horizontal displacement was 370 mm, consistent with leveling measurements (vertical RMSE: 75.1 mm; horizontal RMSE: 27.2 mm). Compared with traditional PIM methods without topographic correction, the proposed model reduces 3D displacement RMSE by approximately 35%, significantly improving calculation accuracy in mountainous areas with topographic undulation. Validation against leveling measurement points distributed along strike and dip directions confirms the reliability of reconstructed 3D displacement fields. This method not only restores the physical characteristics of topographic sliding but also provides a low-cost, high-precision solution for mining damage monitoring in complex terrain.