Refined inversion of 3D surface subsidence in mining areas by integrating SBAS-InSAR and Log-logistic function

To address the poor convergence of the traditional Probability Integral Method (PIM) in predicting the boundaries of mining-induced subsidence – which often leads to substantial errors in three-dimensional (3D) displacement decomposition – this study proposes a refined 3D dynamic deformation monitoring method by integrating an improved PIM with Small Baseline Subset Interferometric Synthetic Aperture Radar (SBAS-InSAR). First, Global Navigation Satellite System (GNSS) and SBAS-InSAR observations are jointly used to invert the parameters of the DPIM model, resulting in a more realistic GDPIM model that better reflects actual geological and mining conditions. Then, a Log-logistic temporal function is introduced to construct the GDPIM-Log model, enhancing the capacity to model the temporal evolution of subsidence. On this basis, leveraging the large-scale and high spatial resolution characteristics of InSAR data, a weighting strategy based on coherence, pixel distribution, and deformation gradient is applied to build a fused model – GDL-InSAR – for high-resolution 3D reconstruction of both vertical and horizontal displacements. The proposed method is validated using the Dahaize coal mine as a case study, with InSAR imagery and GNSS data acquired from July 2022 to June 2023. Results show that the average Root Mean Square Error (RMSE) along GNSS observation lines are 32.1 mm (vertical), 22.9 mm (east–west), and 34.2 mm (north–south), significantly outperforming the results of single-model inversion. The findings demonstrate that the proposed fusion method offers notable advantages in improving the accuracy of 3D subsidence monitoring in mining areas, enhancing model adaptability, and supporting practical engineering applications.