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

Abstract

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.

An InSAR Deformation Phase Retrieval Method Combined with Reference Phase in Mining Areas

“…When comparing the leveling data with the subsidence values obtained by combining the reference phase retrieval method and the displacement vector depression model in Figure 15, we find that the maximum difference is 0.14 m, with a root mean square error (RMSE) of 0.05 m, accounting for 3.3% of the maximum subsidence. In contrast, Jiang et al [48] calculated three-dimensional deformation based on the Boltzmann function and subsidence characteristics, achieving an RMSE of subsidence compared to the measurement data, accounting for 9.4% of the maximum subsidence. This represents a 23.1% improvement in monitoring accuracy compared to the corresponding PIM prediction accuracy of 0.065 m. Errors in the edge areas of the basin are minimal, all within 0.01 m, while larger errors primarily occur in the central area of the basin.…”

“…The comparison results are shown in Figure 21. In contrast, Jiang et al [48] measured three-dimensional deformation based on the retrieved phase, with the RMSE in relation to measurement data comprising 9.4% of the maximum subsidence. Employing the DPIM phase unwrapping technique and the three-dimensional deformation monitoring approach in mining territories, Jiang et al [44] gleaned surface subsidence, and the RMSE, as validated against measured data, stood at 3.5% of the maximum subsidence.…”

“…Consequently, some scholars have explored prior models, establishing the theoretical constraint relationship that exists between the actual LOS deformation phase and the predicted LOS deformation phase. They have formulated an InSAR phase unwrapping model, thereby deriving the recovered deformation phase, including the entire basin [41][42][43][44][45][46][47][48]. Shi et al [47] posited a novel PU algorithm, reinforced by the 2D elliptical Gaussian function, with the aim of heightening the accuracy of time-series LOS displacements over coal mining areas featuring pronounced displacement gradients.…”

“…Shi et al [47] posited a novel PU algorithm, reinforced by the 2D elliptical Gaussian function, with the aim of heightening the accuracy of time-series LOS displacements over coal mining areas featuring pronounced displacement gradients. Jiang et al [48] harnessed the Boltzmann function prediction model (BPM) as an ancillary condition to facilitate interferometric phase unwrapping within mining areas. These research efforts have borne practical applications within specified mining areas employing C-band SAR data.…”

LOS Deformation Correction Method for DInSAR in Mining Areas by Fusing Ground Data without Control Points

“…Despite the efforts of some scholars to incorporate subsidence prediction models that better align with mining mechanisms, single-measurement data still struggle to overcome their inherent limitations and improve the accuracy of deformation determination. Recently, Yan et al [24] proposed a "space-sky-ground" integrated collaborative monitoring framework in mining areas, and Jiang et al [25] discussed the possibility of integrating other source measurement data with space data. These scholars have attempted to fuse other source measurement data in order to obtain high-precision deformation information, providing innovative research directions for deformation monitoring in mining areas [24][25][26].…”