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High-resolution three-dimensional (3-D) displacements of mining areas are crucial to assess mining-related geohazards and understand the mining deformation mechanism. In 2018, we proposed a cost-effective and robust method for retrieving mining-induced 3-D displacements from a single SAR amplitude pair (SAP) using offset tracking (OT) procedures. Hereafter, we refer to this method as the “alternative OT-SAP” (AOT-SAP) method. A key step in the AOT-SAP method is solving the 3-D surface displacements from the AOT-SAP-constructed linear system using routine lower–upper (LU) factorization. However, if the AOT-SAP method is used to retrieve high-resolution 3-D displacements, the dimension of the linear system becomes very large (in the order millions), and a high-end supercomputer is often needed to perform the LU-based solving procedure. This significantly narrows the practical application of the AOT-SAP method, considering the limited availability of supercomputers. In this paper, owing to the banded nature of the AOT-SAP-constructed linear system, we introduce the SPIKE algorithm as an alternative to LU factorization to solve high-resolution mining-induced 3-D displacements. The SPIKE algorithm is a divide-and-conquer direct solver of a large banded system, which can parallelly or sequentially solve a large banded linear system, with a much smaller memory requirement and a shorter time cost than LU factorization. This allows us to retrieve the high-resolution 3-D mining-induced displacements with the AOT-SAP method on either a supercomputer or a standard personal computer. Finally, the accuracy of the retrieved 3-D displacements and the efficiency improvement of the SPIKE algorithm were tested using both simulation analysis and a real dataset. [ABSTRACT FROM AUTHOR]

Measuring 3-D mining-induced displacements is essential to understand mining deformation mechanisms and assess mining-related geohazards. In our previous work, we proposed a method for estimating 3-D mining-induced large displacements with the surface deformation along the radar line-of-sight (LOS) direction derived from a single amplitude pair (SAP) of synthetic aperture radar (SAR) using the offset tracking (OT) procedure (hereafter referred to as OT-SAP). The OT-SAP method effectively reduces the strict requirements on SAR data of the previous OT-based methods for 3-D mining-induced displacement retrieval. However, OT-SAP is not robust to errors in the LOS deformation, due to the lack of redundant observations. In this paper, we present an alternative approach (hereafter called AOT-SAP) to OT-SAP. The AOT-SAP method involves estimating the 3-D mining-induced large displacements with OT-derived 2-D deformation observations along the LOS and azimuth directions from an SAP of SAR, instead of just the LOS deformation in the OT-SAP method. Consequently, more redundant observations are incorporated in the AOT-SAP method compared with the previous OT-SAP method. The theoretical analysis and experiments based on both simulated and real data sets suggest that AOT-SAP can effectively improve the accuracies of the estimated 3-D displacements compared with the OT-SAP-estimated ones. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Underground extraction can be roughly classified into three types, i.e., subcritical, critical, and supercritical extraction, in accordance with the geological conditions in the overburden and the geometry of mined-out areas. In 2016, we proposed an approach based on the interferometric synthetic aperture radar (InSAR) technique and the probability integral method (PIM) for the cost-effective prediction of 3-D mining-induced displacements (abbreviated as InSAR-PIM). Due to the inherent assumption of critical extraction in the PIM, the InSAR-PIM method performs well in predicting the 3-D displacements caused by critical and/or supercritical extraction, but poorly for subcritical extraction. In this paper, we first propose a generalized PIM (GPIM) by modifying the traditional PIM with a simplified Boltzmann function. We then replace the PIM of the InSAR-PIM with the proposed GPIM to develop an extension of InSAR-PIM (referred as to InSAR-GPIM). The InSAR-GPIM was tested in the Qianyingzi coal mining area, China. The results show that the InSAR-GPIM-predicted horizontal and vertical displacements caused by subcritical, critical, and supercritical extraction agree well with the in situ observations, with average root-mean-square errors of about 0.032 and 0.050 m, respectively. These accuracies represent improvements of 60.9% and 59% when compared with the accuracies predicted by the InSAR-PIM in the horizontal and vertical directions. The results indicate that the InSAR-GPIM is capable of accurately predicting 3-D mining-induced displacements under different extraction conditions (i.e., subcritical, critical, and supercritical extraction), and it performs much better than the InSAR-PIM in the case of subcritical extraction. It is therefore believed that InSAR-GPIM will have a wider scope of applications than the previous InSAR-PIM. [ABSTRACT FROM PUBLISHER]