Prediction of Mining-Induced 3-D Deformation by Integrating Single-Orbit SBAS-InSAR, GNSS, and Log-Logistic Model (LL-SIG)

Accurately predicting large-scale surface displacements is a vital task in the prevention and control of geological hazards in mining areas. Small baseline subset interferometric synthetic aperture radar (SBAS-InSAR) faces challenges in capturing significant deformations, and implementing extensive global navigation satellite system (GNSS) monitoring can only obtain a single point of deformation. To combine the strengths of both techniques, we proposed a novel approach named the LL-SIG (integrating single SBAS-InSAR pair, GNSS, and log-logistic model), which leverages the understanding of mining subsidence patterns and integrates single-orbit InSAR data with limited GNSS data to achieve overall and high-gradient 3-D deformation monitoring and prediction in mining areas. First, we employed empirical Bayesian kriging (EBK) interpolation to integrate GNSS and SBAS-InSAR data at a consistent time interval. This allowed us to obtain an overall large-gradient deformation pattern of the mining area based on its subsidence characteristics. Subsequently, we combined the log-logistic model with the SIP (single InSAR pair) model to calculate the 3-D deformation resulting from mining activities at any moment. The proposed method was tested in the Fenxi Ruitai mine. The root-mean-square error (RMSE) of the fit deformation in the line-of-sight (LOS) direction was within 10% of the maximum deformation. Compared to the logistic model and Gompertz model, the log-logistic model shows superior accuracy and efficiency in mine deformation prediction under the same testing conditions. The RMSE of deformation for this method was 3.20, 5.85, and 3.73 cm in the vertical, northward, and eastward directions, respectively.