## 5 Results
The smallest troughs formed after seismic events of 8 April 2017, and 7 February 2020 (550 m \(\times\) 600 m and 500 m \(\times\) 750 m respectively). The largest troughs, with spatial extents of 1900 m \(\times\) 2350 m and 1850 m \(\times\) 2700 m were caused by tremors on 26 December 2017, and 29 January 2019, respectively. The individual vertical displacement maps obtained from both ascending and descending orbits were combined into a single vertical displacement map for each seismic event. The resulting maps represent the probable shape of the deformation area. For this purpose map algebra raster functions were used where average values of spatially congruent pixels representing vertical displacements were calculated. The resulting maps of terrain deformations have been presented in Figure 5.  
In order to examine more precisely the shape of deformations of the ground surface, the generalized horizontal extent of troughs that developed after each event were superimposed with their centroids as the joint center (Figure 6). The value of \(-\)10 mm was assumed as the limit of the deformation area. Generally, the resulting deformation areas have oval shapes (five cases), slightly elongated in the N-S direction that differs in extent depending on the energy of the seismic event that caused it. Two events produced almost circular deformation areas. Slight rotation of several deformation areas, greatest in the case of the event from 7 December 2017, can be noticed. The S-W elongation of the 26 December 2017, trough, may have been caused by the influence of the earlier shock that occurred in close vicinity on the 7 December 2017. This will beyond the scope of this paper and will be investigated in a separate study. Figure 5: Raster maps of vertical displacements for the 8 analyzed induced shocks. Figure 6: Superimposed spatial extents of the analyzed eight deformation areas. The vertical profiles of individual deformation areas in approximately W-E and N-S directions are shown in Figure 7a,b, respectively. The analyzed vertical profile lines show similar subsidence properties. The troughs, which were caused by shocks: 29 November 2016, 16 December 2016, 8 April 2017, 7 December 2017, 26 December, 2017, and 7 February 2020, have generally smooth and similar shapes that differ in size. In contrast, the profiles for the troughs of 15 September 2018, and 29 January 2019, are characterized by disturbances (local peaks in profile lines). This may be caused by noise in the obtained interferograms. In the case of the troughs of 15 September 2018, there is no visible disturbance of the geometry in the N-S direction as opposed to the W-E direction. The trough of 29 January 2019, shows numerous peaks, the course of the trough profile is not rectilinear which results from low coherence. In the next stage of analysis, the potential relationships between the energy of tremors induced by underground mining activity and maximum vertical displacements, as well as energy and their spatial ranges in W-E and N-S directions were assessed. For this purpose Pearson statistical correlation coefficient (r) was calculated for three cases, energy vs. maximum mean vertical displacement, energy and W-E extent and energy and N-S extent of deformation areas. These relationships have been shown graphically in Figure 8a-c, respectively. Figure 7: Profiles of troughs formed by eight induced shocks (mean value of spatial extent vs. mean value vertical displacements). (**a**) Profiles towards the W-E. (**b**) Profiles towards the N–S. Figure 8: Graphs and Pearson coefficient (\(r\)): (**a**) energy vs. max value of vertical displacements, (**b**) energy vs. mean value of W–E extent, (**c**) energy vs. mean value of N–S extent. The strongest relationship between the analyzed variables was determined for the pair of energy vs. W-E extent and N-S extent variables (\(r\) = 0.79). The relationship of energy vs. vertical displacements is the weakest of all three analyzed pairs but still with strong positive correlation of \(r\) = 0.74.