# InSAR-CTPIM-Based 3D Deformation Prediction in Coal Mining Areas of the Baisha Reservoir, China
###### Abstract  
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. InSAR; coal mining area; coordinate-time function; land subsidence; 3D deformation prediction +
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time series resolution, making it difficult to use these techniques to obtain sparse point measurements to characterize the dynamic evolution of the entire subsidence cone. It is difficult to use these techniques to obtain sparse point measurements to describe the dynamic evolution of the whole sedimentation funnel, and they require significant manpower, material and financial resources [6]. The interferometric synthetic aperture radar (InSAR) technique can be used to obtain a large amount of surface deformation observation data in mining areas under all-weather, non-contact conditions [7; 8], so it has been widely used to monitor surface deformation in coal mining areas [9; 10; 11; 12; 13]. The basic idea is to use the radar line-of-sight (LOS) time series deformation obtained by InSAR as the input value of the time series prediction model, estimate the prediction model parameters, and then realize the prediction of surface deformation in the mining subsidence area. For example, [PERSON] et al. [14] and [PERSON] et al. [15] projected the LOS deformation generated by InSAR in the vertical direction and then used the resulting vertical displacement as an input value to estimate the parameters of the probability integral method (PIM) to predict the vertical deformation of the surface caused by mining. However, the PIM method is a static model that cannot predict the dynamic changes in mine subsidence over time. If the SAR image is missing, the deformation results for the time period outside the image cannot be obtained. Therefore, [PERSON] et al. [16] proposed the InSAR deformation model based on the coordinate-time PIM (CT-PIM) [17] and realized the prediction of the vertical deformation of a mine caused by drilling and water-soluble mining in Xinhua, Hunan Province, China. However, the above study neglected the effect of horizontal movement and could only provide a one-dimensional prediction of mine subsidence, but could not realize the prediction of 3D surface displacement caused by mining activities. To address this problem, [PERSON] et al. comprehensively considered the influence of horizontal displacement and proposed combining the probabilistic integral method (PIM) with the Knothe time function to realize the prediction of three-dimensional displacement induced by full-scale mining in the vertical, east-west, and north-south directions [18; 19].