Stage-Adapted InSAR–Probability Integral Method Fusion for Monitoring and Spatially Continuous Reconstruction of Repeated-Mining Subsidence

Repeated-mining subsidence in low-hilly terrain causes InSAR decorrelation and incomplete deformation fields. At the 2301 working face in Shanxi Province, China, this study combines InSAR observations near basin margins with central estimates from the probability integral method (PIM). D-InSAR and SBAS-InSAR were applied to the initial-mining and repeated-mining stages, with operational retrieval limits of 149 and 194 mm. PIM was fitted to three late field campaigns per stage, with development factors constrained by the complete observation sequences. Fusion weights varied with PIM-predicted subsidence magnitude. Full-data fusion RMSEs of 28.58–134.78 mm (R2 = 0.956–0.990) describe internal agreement. Same-site spatial-block fusion RMSEs were 62.16 and 166.79 mm for the two stages, respectively: 1.25% higher and 3.62% lower than PIM, and 81.3% and 76.6% lower than InSAR alone, largely reflecting its underestimation of much larger central subsidence. The same folds informed model selection, so these are not external validation results. Symmetric power-ratio weighting removed theoretical threshold jumps and reduced local transition gradients relative to hard-threshold and fixed-weight fusion. Sparse transition observations limited assessment of predictive accuracy. The supported benefit is retention of margin observations and model-based completion of central gaps with a continuous threshold transition, rather than consistent accuracy improvement over PIM.