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It is a common method to resolve three-dimensional (3-D) deformation components associated with underground mining by incorporating Single-track interferometric synthetic aperture radar (InSAR) with a prior deformation model termed linear proportion model (LPM) (hereinafter referred to as Sin-LPM). Nevertheless, the Sin-LPM method relies on three model parameters that are needed to be in situ collected, and it neglects their dynamic changes during the period of underground extraction, narrowing the practical applications of the Sin-LPM method, and degrading the accuracy of the estimated 3-D displacements. In this article we propose a new method to resolve 3-D mining displacements from multi-track InSAR observations by incorporating with the LPM. In which, the model parameters are first considered as dynamic and further adaptively estimated from the multi-track InSAR observations using a robust solver. Following that, 3-D mining displacements are resolved from the multi-track InSAR using the conjugate gradient method (CGM). The proposed method was tested in Datong coalfield, China. The results suggest that the proposed method can well estimate 3-D mining displacements with a mean error of about 1.8 cm. Compared with the previous Sin-LPM, the proposed method can effectively improve the accuracy of the estimated 3-D displacements (e.g., 69% in this study), and can work well even over a large area where the model parameters are unknown. The proposed method offers a new insight to improve the InSAR-based retrieval of 3-D displacements induced by other anthropologic or geophysical activities. [ABSTRACT FROM AUTHOR]

The time-varying baseline error (TVBE) caused by the residual motion errors is one of the most significant error sources in the airborne interferometric synthetic aperture radar (InSAR). Although global digital elevation model (DEM) products can be used to extract the TVBE for areas without high-precision DEMs, they cause remarkable height differences (HDs) relative to the actual InSAR-measured topography. In addition, due to the low flight height of airborne SAR platforms, the range-dependent phases resulted from the HDs have significant impacts on the TVBE estimation. Through the mutual restraint of multibaseline observations, this research establishes a multibaseline parameterized model jointly considering HDs and TVBEs in each range direction for the absolute phase calibration. A weighted truncated singular value decomposition (TSVD) algorithm is used to solve the ill-posed problem in joint parameter estimation. Note that, to improve the TVBE extraction, a two-step strategy is adopted. In step one, TVBEs and HDs are preliminarily estimated by the multibaseline parameterized model. After that, bare areas with flat topography, where the truths of HDs can be assumed to be 0, are selected to correct the bias of the estimated HDs. If the flat and bare areas are absent, global ecosystem dynamics investigation (GEDI) or Ice, Cloud, and land Elevation Satellite (ICESAT) points can be used instead. In step two, the multibaseline parameterized model is updated by the calibrated DEM and then used to reestimate the TVBEs. The proposed method was validated by using a simulated data set and two real data sets (i.e., the P- and L-band data sets acquired by the airborne E-SAR system during the BioSAR2008 campaign). The results show that, with respect to the reference values, the root-mean-square error (RMSE) of the calibrated DEMs is 0.48 m for the simulated data set, 2.6 m for the P-band data set, and 3.6 m for the L-band data set, suggesting that the high-precision DEMs are well reconstructed and the TVBE-induced phases can be precisely extracted. After correcting the TVBE-induced phases, the accuracy of the DEMs generated by every linked phase (LP) is improved by at least 38.2% for P-band and by at least 51.0% for L-band. To assess the effectiveness and practicability of the proposed model, we further investigated the influence of the limited multibaseline number, and the baseline combination, and the precision of external DEMs on the TVBE correction. In conclusion, without high-precision DEMs, the multibaseline parameterized method can work well in accurately extracting the TVBE, even for the limited airborne InSAR data set. [ABSTRACT FROM AUTHOR]

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]

The previous multi-track InSAR (MTI) method can be used to retrieve mining-induced three-dimensional (3D) surface displacements with high spatial–temporal resolution by incorporating multi-track interferometric synthetic aperture radar (InSAR) observations with a prior model. However, due to the track-by-track strategy used in the previous MTI method, no redundant observations are provided to estimate 3D displacements, causing poor robustness and further degrading the accuracy of the 3D displacement estimation. This study presents an improved MTI method to significantly improve the robustness of the 3D mining displacements derived by the previous MTI method. In this new method, a fused-track strategy, instead of the previous track-by-track one, is proposed to process the multi-track InSAR measurements by introducing a logistic model. In doing so, redundant observations are generated and further incorporated into the prior model to solve 3D displacements. The improved MTI method was tested on the Datong coal mining area, China, with Sentinel-1 InSAR datasets from three tracks. The results show that the 3D mining displacements estimated by the improved MTI method had the same spatial–temporal resolution as those estimated by the previous MTI method and about 33.5% better accuracy. The more accurate 3D displacements retrieved from the improved MTI method can offer better data for scientifically understanding the mechanism of mining deformation and assessing mining-related geohazards. [ABSTRACT FROM AUTHOR]