The seasonal variation of land cover and the large deformation gradients in coal mining areas often give rise to severe temporal and geometrical decorrelation in interferometric synthetic aperture radar (InSAR) interferograms. Consequently, it is common that the available InSAR pairs do not cover the entire time period of SAR acquisitions, i.e., temporal gaps exist in the multi-temporal InSAR observations. In this case, it is very difficult to accurately estimate mining-induced dynamic subsidence using the traditional time-series InSAR techniques. In this investigation, we employ a logistic model which has been widely applied to describe mining-related dynamic subsidence, to bridge the temporal gaps in multi-temporal InSAR observations. More specifically, we first construct a functional relationship between the InSAR observations and the logistic model, and we then develop a method to estimate the model parameters of the logistic model from the InSAR observations with temporal gaps. Having obtained these model parameters, the dynamic subsidence can be estimated with the logistic model. Simulated and real data experiments in the Datong coal mining area, China, were carried out in this study, in order to test the proposed method. The results show that the maximum subsidence in the Datong coal mining area reached about 1.26 m between 1 July 2007 and 28 February 2009, and the accuracy of the estimated dynamic subsidence is about 0.017 m. Compared with the linear and cubic polynomial models of the traditional time-series InSAR techniques, the accuracy of dynamic subsidence derived by the logistic model is increased by about 50.0% and 45.2%, respectively.

This paper presents a novel method for estimating the model parameters of the probability integral method (PIM) based on the line-of-sight deformation derived from the interferometric synthetic aperture radar. Then, it applies the settled PIM to forward predict the horizontal and vertical displacements induced by the extraction of a new working panel. The proposed method first constructed the functional relationship between the InSAR-derived LOS deformation and the model parameters of PIM. Subsequently, an improved genetic algorithm (GA), in which gross error elimination was imposed, was proposed, and used to estimate the model parameters of PIM with a large number of LOS deformation measurements. The estimated model parameters and PIM were then employed to forward predict the horizontal and vertical displacements induced by the extraction of a working panel. Simulated experiments show that the rmses of the predicted displacements along the up-down, west-east, and north-south directions are 1.5, 0.9, and 2.5 mm, respectively. Real data experiments over the Qianyingzi coal mining area of China indicate that the predicted displacements are highly consistent with those by field surveys, with rmses of 4.1 and 3 cm for the vertical and horizontal directions, respectively. These imply that the proposed approach can be a very promising tool for predicting the mining-induced displacements and will potentially contribute to the assessing and forecasting of possible geological hazards in the mining area.

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.