An Extraction Method for Large Gradient Three-Dimensional Displacements of Mining Areas Using Single-Track InSAR, Boltzmann Function, and Subsidence Characteristics

This paper presents an extraction method for large gradient three-dimensional (3-D) displacements of mining areas using single-track interferometric synthetic aperture radar (InSAR), Boltzmann function, and subsidence characteristics. This is mainly aimed at overcoming the limitations of surface deformation monitoring in mining areas by using single-track InSAR technology. One is that the rapid and large gradient deformation of the mine surface usually leads to image decoherence, which makes it difficult to obtain correct deformation information. Second, the surface deformation monitored by InSAR is only one-dimensional line of sight (LOS) displacement, and thus it is difficult to reflect the real 3-D displacements of the surface. Firstly, the Boltzmann function prediction model (BPM) is introduced to assist InSAR phase unwrapping; thus the missing large gradient deformation phase of InSAR is recovered. Then, the subsidence characteristics in mining horizontal (or near-horizontal) coal seams are used as prior knowledge for theoretical derivation, and a 3-D displacement extraction model of coal seam mining with single-track InSAR is constructed. The feasibility of the method is verified by simulating LOS displacements with random noise and underestimation phenomenon caused by the large gradient deformation as InSAR observations. The results show that the root mean square error (RMSE) of 3-D displacements on the observation line calculated by the proposed method is 21.5 mm, 19.0 mm, and 32.9 mm, respectively. Based on the single-track Sentinel-1 images, the method in this paper was applied to the extraction of surface 3-D displacements in the Huaibei coal mine, and the experimental results show that the extracted 3-D displacements are in good agreement with that of measurement by the surface observation station. The proposed method can adapt to limited InSAR acquisitions and complex monitoring environments.