# Mining Deformation Life Cycle in the Light of InSAR and Deformation Models
## 4 Results
### Verification with Levelling  
The reliability of the achieved results is validated with the data from two cycles of in-situ geodetic levelling carried out in the area of the coal seam 503 (Figure 7). The surface subsidence along six levelling lines was compared with the analogous DInSAR and predicted subsidence for the period between the levelling measurements in 2017, namely between April and October (Figure 20a-f). Figure 20 shows that the model overestimates the subsidence for most of the levelling lines (see Figure 7 for lines locations)--for example, line 2\({}^{\prime}\)2\({}^{\prime\prime}\) (Figure 20b), line 3\({}^{\prime}\)3\({}^{\prime\prime}\) (Figure 20c), line 4\({}^{\prime}\)4\({}^{\prime\prime}\) (Figure 20d), and line 6\({}^{\prime}\)6\({}^{\prime\prime}\) (Figure 20f). Surprisingly, line number 1\({}^{\prime}\)1\({}^{\prime\prime}\) (Figure 20a) traces through longwall No. 5, and the prediction of the subsidence does not represent the actual deformation, as the location of the subsidence trough was different. It is also interesting to note that line 5\({}^{\prime}\)5\({}^{\prime\prime}\) (Figure 20e) stretching across longwall No. 6 shows mediocre deformation similar to that obtained  
Figure 19: Velocity (**left**) and acceleration (**right**) of the subsidence for the extremal points by months. Figure 20: Comparison of the subsidence [in meter] along the levelling lines from Figure 7 between DInSAR results, levelling and predicted by the model data: (**a**) profile along levelling line 1\({}^{\prime}\)1\({}^{\prime\prime}\), (**b**) profile along levelling line 2\({}^{\prime}\)2\({}^{\prime\prime}\), (**c**) profile along levelling line 3\({}^{\prime}\)3\({}^{\prime\prime}\), (**d**) profile along levelling line 4\({}^{\prime}\)4\({}^{\prime\prime}\), (**e**) profile along levelling line 5\({}^{\prime}\)5\({}^{\prime\prime}\), (**f**) profile along levelling line 6\({}^{\prime}\)6\({}^{\prime\prime}\)from the DInSAR, whereas the model did not predict deformation in this area. The DInSAR is not in full agreement with levelling; however, it shows deformation trends similar to the levelling in all investigated lines. The deviations between DInSAR and levelling depends mostly on complex interconnections between subsidence and image acquisition (ascending and descending viewing angles) geometries. The correlations of the subsidence between the validation set of benchmarks and the remotely measured radar values and prediction model data, respectively, are presented by \(R\) in Table 2.  
The statistical study of the differences between the radar measured and modelled data compared to the levelling data for a set of 122 benchmarks within the investigated area in the Miechowice district is presented in Table 2. It shows a significant averaged difference (Equation (8)) corresponding to an off-set of about 20 cm in the modelling set, while, for the radar measurements, the error is about 4 cm. The graphical representation of the correlation in Figure 21a shows a better fit with fewer outliers and a stronger correlation between the levelling and DInSAR-derived subsidence. \begin{table}
\begin{tabular}{c c c c} \hline  & \(R\) & \(\overline{dw}\), \(\mathbf{m}\) & \(\sigma_{\overline{dw}^{\prime}}\), \(\mathbf{m}\) \\ \hline L-D & 0.89 & -0.04 & 0.183 \\ L-M & 0.85 & 0.20 & 0.388 \\ \hline \end{tabular}
\end{table} 
Table 2: Statistical assessment of the DInSAR (D) and model (M) data compared to the verification data from levelling (L). Figure 21: (**a**) Correlation between subsidence from the levelling (vertical axis) and DInSAR (blue) and model (red) along the horizontal axis; (**b**) histogram of the distribution of errors between subsidence derived from levelling (L), DInSAR (D), and modelling (M); and fields of errors for (**c**) L-D and (**d**) L-M. When the histograms (Figure 21b) for the two series are observed, the wider deviation of modelling subsidence and the skewness of its distribution can be noticed.