Objectives  Differential interferometric synthetic aperture radar (D-InSAR) has its own unique monitoring methods in acquiring surface deformation. In view of the difficulties in the application of D-InSAR technology in three-dimensional (3D) deformation monitoring of coal mine surface, this paper proposes a dynamic monitoring method based on fusion of single sight D-InSAR and Boltzmann-Knothe (BK) model.

  Methods  First, taking into account the characteristics of D-InSAR that it is difficult to obtain large gradient deformations, the Boltzmann function model with good boundary fit was selected, and BK model was constructed by the fusion of the Knothe time function. Second, due to the decoherence of the time-space baseline and the limitation of D-InSAR principle, it can often only obtain the short-term, one-dimensional deformation of the surface in line of sight (LOS). Therefore, based on the projection relationship between the 3D deformation and the LOS deformation, combined with the geological mining conditions of the target area, the fitness function with non-cumulative deformation was constructed. Finally, a dynamic monitoring method of surface 3D deformation of coal mine based on fusion of single sight D-InSAR and BK model was proposed by introducing the fireworks algorithm (FWA).

  Results and Conclusions  Simulation experiments show that the proposed method can reliably and accurately inverted all dynamic prediction parameters of mining subsidence, and the relative error of the solved parameters was between 0.11% and 7.51%. The subsidence and horizontal movement monitored by this proposed method were consistent with the real values, and the monitoring effect of the PIM-Knothe method was distorted. The results of the anti-error experiment show that under the influence of observation error or model parameter error, the overall effect of the solved parameters by the method in this paper was better, and the ability to resist errors was shown to a certain extent. The proposed method was applied to the 13121 working face of Gubei Mine in Huainan, and the surface 3D deformation of the coal mine from 2019-10-25 to 2019-12-12 was obtained. The conversion of short-term D-InSAR observation to 3D deformation dynamic monitoring based on the proposed method was realized, and the monitoring results were more consistent with the surface movement and deformation measured by the observation station. The reliability and scientificity of the dynamic prediction method for solving the surface 3D deformation of coal seam based on D-InSAR technology has been verified.