# Mining Deformation Life Cycle in the Light of InSAR and Deformation Models
## 5 Discussion  
Coal mining deformations using InSAR have been intensively studied by several research groups in China and Australia. The results show the deformations in the area of interest due to nonlinearity (three phases of deformation). The rapid progress of deformation (5-20 mm/day) and large yearly deformations (exceeding 1.40 m/year) exceeds the capabilities of the PSI or SBAS methods. Hence, as in several other studies [14; 17; 19; 21] related to the coal mine extraction, DInSAR was applied. The most important lesson learned from high frequency (six days) DInSAR observation processing is that the quality of the observation varies over time (Figure 4) with a low percentage of overlay in the beginning of 2017 and uncertainties in deformations (Figures 10a and 12). In general, when there are two consecutive interferograms with low quality, it may be considered that the common image has high perturbations due to atmospheric effects. To reduce the signal delay, different approaches may be performed, but the most preferable approach is by applying a weather model based on the information from global atmospheric models [40], models generated from GNSS observations [41], models that integrate both the weather forecast and GNSS tropospheric delay estimations [42], or spectrometer observations by systems like the Medium Resolution Imaging Spectrometer (MERIS) on-board the Envisat satellite or the Moderate Resolution Imaging Spectroradiometer (MODIS) on-board the Terra and Aqua satellites [43]. The aggregation to lower frequency observations, in line with the mining extraction plan, results in removing some of the lower coherence data, but highly tropospheric varying conditions still affect DInSAR deformations. Further studies using, for example, a generic atmospheric correction model [53; 54], are required to quantify the effect of the troposphere on the obtained deformation. One of the reasons to aggregate the solution to one month was to reduce the impact of the troposphere. The DInSAR-based extent of the subsidence received for the investigated case is reasonable. In the case of longwalls No. 5 and 6 from coal seam 503 of the Bytom-III mining area, the coal layer is 2.00 m in the area of the building of the Holy Cross Church; it is 2.30 m in the rest of the zone, which may produce a subsidence of 1.40-1.60 m to 1.61-1.84 m. It agrees well with the literature [55]. In the simplest situation, the theoretical expected subsidence due to the roof falling in longwall mining is 70% to 80% in the volume of the coal seam thickness. The amount of monthly vertical movement (Figure 18) correlates to the averaged material extraction. However, it must be noted also that the modelling assumptions must also consider the reactivation of old exploitations. It is surprising to note that the subsidence model overestimates the maximum subsidence by 50% for the maximum subsidence point; however, we understand that safety precautions state that the model should present the worst-case scenario. There are two other significant discrepancies. The first is that the model of the maximum subsidence almost follows the current extraction panel, whereas in the DInSAR (Figures 12-17) data, there is a substantial gap between Phase I and Phase II deformation. The shift between the two phases (see Figures 14, 16 and 18) covers approximately eight months, which corresponds to the phase of the main subsidence described in [17; 18]. The second is the size and location of the subsidence trough. In the case of DInSAR deformations, these parameters are clearly under the influence of: Coal extraction parameters and 3D decomposition mis-modelling as described by several authors [14; 56; 57] that result in different impacts of horizontal deformation on vertical subsidence for data from ascending and descending orbits. The overestimated prediction values and locations of vertical displacements are in a relation with the time coefficients.