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Accurate monitoring of mining-induced three-dimensional surface deformation is critical for safety and environmental protection. Conventional InSAR often loses coherence in high-deformation areas and provides only one-dimensional measurements, while the Probability Integral Model (PIM) suffers from low accuracy at subsidence edges, caused by premature numerical convergence of its error-function-based mathematical formulation—the model prediction rapidly drops to zero and fails to capture subtle real-world deformations in marginal zones. This study developed a fusion method integrating multi-source InSAR (Sentinel-1A and SAOCOM), PIM, and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Applied in the Yinying Mining Area, Shanxi Province, the approach combined ascending and descending SAR data processed via SBAS-InSAR, used CMA-ES to optimize PIM parameter inversion, and employed a zonal fusion strategy to reconstruct complete deformation fields. The method demonstrated substantial improvement in monitoring accuracy, with mean absolute errors in the vertical, north–south, and east–west directions reduced by more than 86% compared with the standalone PIM model in edge zones. The fusion approach effectively captured both large-magnitude center deformations and subtle edge displacements. Multi-source data fusion with intelligent optimization algorithms significantly enhances the accuracy of 3D deformation monitoring in mining areas, providing reliable technical support for safety management and environmental protection.
Ma et al. (Thu,) studied this question.