A 3-D inversion model for InSAR detected displacements based on ground subsidence symmetry induced by horizontal coal mining

When using synthetic aperture radar interferometry ( InSAR) technology to monitor coal mining sub-si- dence,the displacement of radar line of sight ( LOS) obtained is the vector superposition of three-dimensional displacement of surface points in vertical,north-south,east-west directions. Decomposing the LOS displacement into the surface subsidence and the horizontal displacement along the strike and incline of the working face is the basis for studying the law of mining subsidence and obtaining the parameters of surface movement. At present,the main method of inverting mining subsidence three-dimensional displacement based on InSAR LOS displacement is using three SAR images of different orbiting satellites to establish LOS displacement equations for solving three-dimensional displace- ment components. According to the prediction model of mining subsidence,the horizontal displacement of surface is re- garded as the correlation function of subsidence,and the subsidence and horizontal displacement are calculated from a single SAR image. The LOS displacement is projected into the sub-sidence component through directly ignoring the in- fluence of horizontal displacement. Based on the analysis of the limitations of the above methods and the basic charac- teristics of the surface subsidence and horizontal displacement of the near-horizontal coal seam mining on the main sec- tion of the mobile basin,the geometric equations of the multi-period InSAR LOS superposition displacement on the symmetry point of the surface moving basin was established. The equations are superimposed and differentially pro- cessed to derive the function model for LOS displacement inversion three-dimensional mining displacement. During the advancement of the working surface,because of the hysteresis of the surface movement,the center of the dynamic sub- sidence basin deviates to the side of the open hole. According to the characteristics of the central surface subsidence of the moving basin reaching the maximum and the horizontal displacement approaching zero,the dynamic center position of the surface moving basin is automatically searched based on the superposition and difference of the LOS displace- ment of adjacent pixels. Thereby,the decomposition of the dynamic three-dimensional displacement of the surface dur- ing the advancement of the working surface is realized. In this paper,the above three-dimensional displacement inver- sion model is implemented based on the platform of Matlab,and the model was validated by multi-phase InSAR data. The inversion results of subsidence and horizontal displacement are in a good agreement with the measured data,which is obviously superior to the method of directly decomposing surface subsidence without considering horizontal displace- ment. This model can be used to decompose the three-dimensional displacement monitored by InSAR in the process of surface movement stability and dynamic movement in near-horizontal coal seam mining.