Long-term deformation prediction and quantitative brine estimation are of great significance for safety precautions and environmental protection in salt mining areas. Traditional Interferometric Synthetic Aperture Radar (InSAR) combined with Probability Integral Method (PIM) has the following limitations: mathematical empirical models are mostly used in InSAR deformation modelling, which ignore the mechanisms of underground mining thus may limit the accuracy of deformation observations; InSAR deformation models have theoretical contradictions and inconsistencies with the future prediction models; PIM is not applicable to the deformation induced by salt solution mining. In this study, a novel Water-Solution Kinetic (WSK) InSAR model was proposed to replace the traditional InSAR models. It considers the principles of substance diffusion and mass transfer of salt, thus can be used directly for the quantitative prediction of both the deformations and extracted brine. Least Squares with Inequality Constraints (LSIC) was introduced to solve the unknown WSK parameters based on the InSAR phases to improve the computational efficiency. Two salt mines in China were selected for the experiments. The results show that the maximum predicted deformation was 296 mm in XR and 155 mm in HR, and the brine composition was estimated to be 0.406 and 1.477 million tons per year, respectively. Compared to traditional Static-PIM, the accuracy was improved by 48.3% and 54.5%, respectively. The results indicated that WSK is more precise and reasonable for predicting the deformation in salt mining areas, which can provide data reference for the management of salt mines.

Time series dynamic prediction of surface deformation in mining areas can provide reference data for coal mine safety and production, which has important impacts. The combination of interferometric synthetic aperture radar (InSAR) technology and the probability integral method (PIM) is commonly used for predicting deformation. However, most surface subsidence prediction in mining areas is based on the static PIM parameters, failing to achieve the three-dimensional (3D) dynamic deformation prediction. This paper proposed a 3D deformation dynamic prediction model (InSAR-3D-CTPIM) between InSAR deformation observations and dynamic coordinate-time PIM (CTPIM) parameters, which can realize the prediction of east–west, north–south, and vertical series deformation caused by mining. The method has been validated by simulation experiments and real experiments in the mining area of Jiansheng Coal Mine in Baisha Reservoir, Henan Province, China. The results showed that the modeling accuracy was improved by 34.3% compared to the traditional multi-rate model, and the accuracy was improved by 28.5% compared to the vertical deformation obtained by the traditional static PIM method. The InSAR-3D-CTPIM model can be used to predict the evolutionary history of basin-wide surface deformation dynamics in coal mining areas, and provide a reference for the early warning and prediction of geological hazards in coal mining areas.