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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]

Surface deformations caused by underground mining are time-dependent and highly nonlinear, and can result in progressive damage to surface structures during underground extraction. However, the previous methods based on the interferometric synthetic aperture radar (InSAR) technique are generally incapable of accurately predicting the mining-induced dynamic deformations occurring during the entire period of underground extraction, due to the inaccurate model parameters inverted under the condition of ignoring the horizontal motions of the InSAR-derived measurements and the model errors for predicting dynamic deformations. Consequently, the risk of mining-related structural damage cannot be reliably assessed based on the deformations predicted by the previous InSAR-based methods. To overcome this limitation, we propose a novel method that combines InSAR with a new mining deformation model: the temporal probability integral method (TPIM). Theoretically, the integration of InSAR and TPIM allows the InSAR-TPIM to accurately predict mining-induced dynamic deformations occurring in the entire period of underground extraction. Furthermore, InSAR-TPIM can reliably assess mining-related progressive structural damage based on the predicted dynamic deformations. However, these advantages cannot be achieved by the previous InSAR-based methods. The Qianyingzi coal mining area of China is selected to test the proposed method. The results demonstrate that the accuracies of the predicted dynamic deformations are about 0.030 and 0.041 m in the horizontal and vertical directions, respectively, which can meet the accuracy requirements of mining-induced dynamic deformation prediction. Furthermore, the comparison between the potential structural damage predicted by the proposed method and the previous InSAR-based methods indicates that the damage risks of around 131 buildings (43.9% of the 298 buildings) are underestimated by the previous InSAR-based method. [ABSTRACT FROM PUBLISHER]

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]