## 4 Discussion  
Correlation matrices and correlation strength thresholds were calculated for dynamic indexes \(D_{f}\) and their MDAI \(\mu D_{f}\). [PERSON]'s correlation coefficient is presented in the matrix:  
\[r=\frac{\sum((x_{i}-\overline{x})\times(y_{i}-\overline{y}))}{\sqrt{\sum\left( (x_{i}-\overline{x})^{2}\times\sum(y_{i}-\overline{y})^{2}\right)}} \tag{20}\]  
The lower threshold for the presence of correlation was determined using Student's \(t\)-test Equation (21) and the intervals for the strength of the correlation according to Equation (22):  
\[r_{0}=\frac{t}{\sqrt{t^{2}+n-2}} \tag{21}\]  
\[r_{int}=\frac{1-r_{0}}{3} \tag{22}\]  
Correlation strength intervals were determined for the dataset used (27,495 rows in each of the indicators and a significance level of 0.95): weak correlation in the 0.012-0.341 interval, medium correlation in the 0.341-0.671 interval, and strong correlation in the 0.671-1 interval. The strength of the correlation was represented as a discrete color scale. Figure 14 shows the correlation matrix of MDAI \(\mu D_{f}\). As shown in the figure, 65 out of 78 correlation values of MDAI \(\mu D_{f}\) have a weak correlation relationship. This is a good indicator in terms of data analysis as the features must be noncollinear, otherwise, the aggregation ability of the integral measure of geodynamic safety is reduced due to the high dispersion of the data \(S_{F}(w)\). Medium and strong correlations are found within index group \(\mu D_{f}\). In the relief group, indexes of geomorphological variability \(\mu L_{Re}^{1}(w)\) and \(\mu L_{Re}^{2}(w)\) have a strong correlation with the index of relief gradient \(\mu\
abla_{Re}(w)\). MDAIs \(\mu L_{Re}^{1}(w)\) and \(\mu L_{Re}^{2}(w)\) have a medium correlation. The measures of proximity to tectonic faults index \(\mu\boldsymbol{\rho}(w,\boldsymbol{\mathcal{P}})\) and fault density \(\mu\boldsymbol{\rho}(w)\) have a strong correlation, as the indices show high spatial correspondence [42,45] (Figures 5 and 6). The fault group measurements have an average correlation strength with the stress measurements \(\mu\sigma_{yy}(w)\) and \(\mu\sigma_{int}(w)\). This is primarily due to the mathematical model for calculating the stress state [43], which considers the fault tectonics of the area. In the stress group, \(\mu\sigma_{yy}(w)\) and \(\mu\sigma_{int}(w)\) have a strong correlation relationship, as the stress \(\sigma_{yy}\) has the greatest contribution to the stress intensity \(\sigma_{int}\)[44]. The MDAIs of the strain tensor components \(\mu e_{xx}(w)\) and \(\mu\sigma_{yy}(w)\), determined from GNSS observations [19], have a weak correlation. The MDAI of dilatation strain \(\mu E_{Dil}(w)\) has a strong correlation with the measure \(\mu e_{xx}(w)\) and a medium correlation with the measure \(\mu e_{yy}(w)\); therefore, their spatial relationship can be seen (Figures 7-9). This is explained by the formula for calculating strain dilatation, which includes the components of the  
strain tensor \(e_{xx}\) and \(e_{yy}\)[41]. The average correlation strength was found between the measure of magnetic field anomaly variability \(\mu L_{Mag}^{2}(w)\) and the gradient of magnetic field anomaly variability \(\mu\
abla_{Mag}(w)\). Internal correlation of feature groups was due to either interdependent formulas for deriving the initial properties of the dynamic indicators \(D_{f}\), or the same set of initial feature data F (as in the case of topography or magnetic field anomalies). Table 3 shows the correlation of the integral geodynamic safety groups: safety measure of geomorphological variability, \(S_{Re}(w)\); safety measure of tectonic faults density, \(S_{\mathbf{\rho}}(w)\); safety measure of a stress-strain state, \(S_{sss}(w)\); and safety measure of magnetic field anomalies, \(S_{Mag}(w)\). Their correlation everywhere indicates a weak correlation or no correlation at all. This characterizes these indexes as reflecting different properties of the geological environment and as independent datasets.