Time-Series 3-D Mining-Induced Large Displacement Modeling and Robust Estimation From a Single-Geometry SAR Amplitude Data Set

This paper presents a novel method for modeling and robustly estimating the time-series 3-D mining-induced large displacements from a single imaging geometry (SIG) synthetic aperture radar (SAR) amplitude data set using the offset-tracking (OT) technique (hereafter referred to as the OT-SIG). It first generates multitemporal observations of 3-D mining-induced displacements from the single-geometry SAR amplitude data set with the assistance of a prior model. Then, a functional relationship between mining-induced time-series 3-D displacements and the multitemporal 3-D deformation observations generated is constructed. Finally, the time-series 3-D displacements are robustly estimated based on the constructed function model using the M-estimator. The proposed OT-SIG provides a robust and cost-effective tool for retrieving time-series 3-D mining-induced large displacements, relaxing the basic requirement of the traditional method that at least two different viewing geometries' SAR data are needed. Finally, we tested the proposed OT-SIG with descending TerraSAR-X SAR amplitude data set over the Daliuta coal mining area in China. The results show that the root-mean-square errors (RMSEs) of OT-SIG-estimated time-series displacements are about 0.22 and 0.11 m in the vertical and horizontal directions, respectively. These RMSEs are around 5.7% and 10.9% of the maximum in situ deformation measurements in the corresponding directions, which can meet the accuracy requirements of practical applications.