Optimization of three-dimensional multi-level surface deformation in mining areas through integration of deformation fusion model and Lagrange multiplier method based on single high resolution OTD-InSAR pair

Underground longwall mining activities usually induce three-dimensional (3-D) multi-level surface deformation, which could lead to serious natural hazards. Offset-tracking (OT) and differential interferometric synthetic aperture radar (DInSAR) technology (referred to as OTD-InSAR) can be used to observe the large-level and smalllevel mining deformations based on single InSAR pair, but the measured deformation is only along the radar lineof-sight (LOS) or the azimuth directions rather than in the 3-D directions. The conventional InSAR-based methods to resolve 3-D mining deformation have the strict restrictions and low south-north accuracy. In this paper, a novel methodology is proposed to utilize a multi-level deformation fusion model and the Lagrange multiplier method based on single OTD-InSAR pair (hereafter called MAOTD-InSAR) to estimate and optimize the 3-D multi-level surface deformation. The Daliuta coal mining area of China was selected to verify the feasibility and precision of the proposed method using high resolution TerraSAR-X (TSX) SAR images with six pairs. Results show that the root mean square errors (RMSEs) of MAOTD-InSAR against in-situ measured data are less than 0.2214 m, 0.1612 m and 0.1880 m in the east, north and vertical directions, respectively. The minimum RMSE in the horizontal direction could reach 0.0361 m with an improvement of about 82.6%, which particularly improve the accuracy in the south-north direction for the TSX satellite since its direction of azimuth deformation is approximately north direction, and this is also adequate for the other satellites in the near-polar orbit. In addition, an empirical model was generated with respect to the gradients of ground fissures on horizontal deformation, and this model enabled us to remove large errors caused by ground fissures. The verification results show that the proposed method provides higher precision and reliability for the resolved 3-D multi-level surface deformation, which presents 3-D mining deformation with more details from the edge to the center of the subsidence basin and will show some possibilities for new findings and interpretations in the process of coal mining.