A Variational Data Assimilation Framework for Mining Subsidence Reconstruction from Heterogeneous D-InSAR and TLS Observations

Accurate characterization of mining-induced surface subsidence is essential for safety assessment in mining areas; however, single monitoring techniques have inherent limitations. Spaceborne interferometric synthetic aperture radar (InSAR) provides large-area coverage but suffers from low signal-to-noise ratio in the subsidence center, whereas terrestrial laser scanning offers high accuracy but limited spatial coverage. To achieve physically consistent quantitative fusion, a multi-source subsidence fusion framework based on variational data assimilation is proposed. By constructing an objective function that incorporates a background prior, D-InSAR-derived boundary constraints, TLS observations, spatial smoothness constraints, and gradient penalty terms, multi-source data are integrated into a unified optimization framework. The results show that, compared with RTK observations, the fused subsidence field achieves an RMSE of 0.12 m and an RRMSE of 2.4% approximately. Parameter sensitivity analysis indicates that the smoothing strength has the greatest influence on fusion accuracy, whereas the observation weight and gradient penalty coefficient exhibit relatively wide stable intervals, and the background constraint has a minor effect on the results. Parameter interaction analysis further demonstrates that the coupling between smoothing strength and observation weight is the most significant. The proposed method provides a physically consistent and parameter-controllable framework for multi-source deformation data fusion in mining subsidence monitoring.