Spatiotemporal prediction of mining-induced surface subsidence using integrated D-InSAR and boltzmann time function models

With the expansion of underground coal mining, accurate prediction of surface subsidence dynamics has become increasingly critical. This study proposes a hybrid prediction framework integrating Differential Interferometric Synthetic Aperture Radar (D-InSAR) and the Boltzmann time function to address this challenge. In low-gradient deformation zones at the edges of subsidence basins, D-InSAR time-series deformation data are directly coupled with the Boltzmann function to achieve spatiotemporal subsidence prediction. In contrast, for high-gradient central zones where InSAR measurements are affected by decorrelation, edge deformation constraints derived from D-InSAR are combined with leveling observations to invert parameters of the Probability Integral Method (PIM), which are subsequently fused with Boltzmann model parameters to construct a spatiotemporal coupling model. Parameter inversion analysis reveals quantitative relationships between the Boltzmann parameters and key influencing factors, including maximum subsidence, mining rate, and overburden lithology. Validation at the 2301 working face demonstrates that the proposed framework achieves stable dynamic prediction performance, with relative errors ranging from 2.1% to 7.0%, in good agreement with field measurements. The proposed framework enables continuous subsidence prediction across the entire mining basin and provides effective technical support for mining-induced subsidence management and ecological restoration. Overall, the paradigm integrating remote sensing observations, time-dependent functions, and spatial modeling offers a scalable and adaptable solution for dynamic subsidence prediction in similar mining regions.