# InSAR-CTPIM-Based 3D Deformation Prediction in Coal Mining Areas of the Baisha Reservoir, China
## 6 Discussion and Analysis
### Effect of Phase Error on Deformation Prediction Results  
Although a number of operations such as filtering, multi-viewing, deleveling, etc., have been performed on the SAR images, there is still unavoidable residual noise when the observed phase values are obtained by using the InSAR technique. In order to verify the influence of the differential interferometric phase error on the prediction results of the settlement deformation of the mining area, and to further analyze the error transfer characteristics of the method in this paper, two groups of error transfer simulation experiments were respectively carried out: (1) Using Equation (18) introduced in Section 2.3, noise phases with 0.1-0.6 rad intervals of 0.1 rad are added to the differential interferometric phases on the left side of the equal sign, and the GA-SM algorithm is used to solve for each set of model parameters with different errors added to the differential interferometric phases, and the corresponding vertical displacements are generated according to Equation (4) and analyzed; (2) Using the differential interference phases with different horizontal noise phases added to generate the corresponding time series deformation by using the SBAS method to generate the corresponding time series deformation results, and using the requested time series deformation results to solve the unknown parameters of the static PIM, and analyzing the corresponding generated vertical deformation prediction result errors. From the results of the parameter sensitivity analysis in Section 6.2, it can be seen that the subsidence coefficient \(q\), the tangent of the main influence angle \(\tan\beta\) and the mining influence propagation angle \(\theta_{0}\) are the parameters that have a greater influence on the vertical displacement. Therefore, the experiments were conducted to explore the effects of the initial errors of deformation on the deformation prediction results by adding different levels of noise phases. Figure 16a,b show the RMSE of the vertically oriented predicted deformations caused by \(q\), \(\tan\beta\), and \(\theta_{0}\) errors obtained from the InSAR-3D-CTPIM model and static-PIM, respectively, under the influence of the noise phases at different levels. As can be seen from Figure 16, the deformation errors due to the parameters \(q\), \(\tan\beta\), and \(\theta_{0}\) all increase gradually with the increase in the noise phase, where the total vertical prediction deformation errors of the InSAR-3D-CTPIM model are smaller than those of the static probability integral model. At the added noise phase of 0.6 rad, the RMSEs of the real and predicted deformations of the InSAR-3D-CTPIM model due to the errors of the unknown parameters are less than 4.2 mm, while the static-PIM leads to a maximum RMSE of 3.9 mm in the predicted deformation results with a small change (0.4 rad phase noise level), and a maximum RMSE error of 6.1 mm in the deformation prediction results with the effect of a 0.6 rad noise level, and all three parameter errors lead to a larger RMSE errors of deformation prediction than the InSAR-3D-CTPIM.  
The experimental results show that compared with the traditional static PIM prediction method, the method in this paper directly uses the InSAR temporal differential interferometric phase to estimate the prediction model parameters, and then calculates the three-direction temporal deformation prediction results, which can effectively avoid the sec  
Figure 16: Root-mean-square error of deformation prediction results for different noise levels.  
ondary transmission of error under the influence of the same phase error, and significantly improve the prediction accuracy of the deformation prediction.