Determining the geographic location and spatial distribution of underground goaf is of great significance for the prevention of mining subsidence hazards and the detection of illegal mining. However, traditional goaf detection techniques mainly focus on geophysical methods that are labor intensive, have low efficiency, and are expensive. Due to the large range and off-site monitoring capability of interferometric synthetic aperture radar (InSAR) techniques, research on goaf location detection based on InSAR measurements has been increasing. This paper proposes a new method for locating underground goaf based on cross-iteration and InSAR measurements. Firstly, the functional relationship between the geometric parameters of the goaf and the line of sight (LOS) deformation retrieved by InSAR techniques is constructed. Then, the three initial model parameters of the probability integration method (PIM) are determined by mining geological conditions. Finally, the cross-iteration method is used to determine the parameters to characterize the spatial location of underground goaf. The experimental results show that the average relative errors of the simulated experiment and the real experiment are 1.5% and 5.1%, respectively, and the inverted goaf parameters are in good agreement with the real values. Moreover, the proposed method only requires the main lithology of the overlying rock in the goaf and does not depend on the accuracy of PIM model parameters. Therefore, this method has engineering application value for the detection of goaf lacking actual measurement data or that caused by illegal mining.

Phase unwrapping (PU) is a key step in InSAR surface monitoring, which is directly related to the accuracy of the LOS displacement observations. Underground coal mining generally results in large gradient displacements, producing dense and aliasing fringes in interferograms. In this case it is challenging to accurately unwrap interferometric phases using traditional methods. This letter proposes an iterative algorithm to unwrap interferometric phases over underground coal mining areas. Firstly, differential interferogram is unwrapped by the minimum cost flow (MCF) method to obtain unwrapped phases at the edge of the mining subsidence basin. Then, a 2D elliptical Gaussian function, which could approximately describe the spatial shape of mining subsidence basin, is used to iteratively reduce the phase gradients of interferograms, so that residual wrapped phases at more pixel in subsidence basin can be unwrapped. The presented method was tested over Datong coal mine, China, based on 16 TerraSAR-X acquisitions. The result suggests that the accuracy of time-series displacements along the line-of-sight direction solved from the unwrapped phases using the new PU method is 1.1cm, indicating an improvement of 73.2% compared with that of using the traditional MCF method.

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.