## 3 Feature Engineering Based on Measurement of Dynamic Stability Index
### Feature Calculation
The calculation of the values \(\rho(\texttt{in},\mathcal{P})\) from a cell \(\texttt{in}\) to the fault \(\mathcal{P}\) was obtained using the Kolmogorov mean criterion with a negative index:  
\[\rho(\texttt{in},\ \mathcal{P})=\left\{\begin{array}{l}0,\!\!<\!/\!\!\! \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!  
Figure 4: Measure of dynamic activity index of relief, \(\mu\
abla_{Re}(w)\).  
Figure 5: Measure of dynamic activity index of proximity to tectonic faults, \(\mu^{\text{P}}(w\),\(\mathcal{P})\).  
The next MDAI referred to the stress-strain state. The indexes for stress tensor components \(\sigma_{xx}\), \(\sigma_{yy}\) and stress intensity \(\sigma_{int}\), which were obtained from the results of the numerical modeling in [30], were calculated. The indexes for deformation parameters of the Earth's crust, derived from GNSS measurements, were also calculated [19, 41]. The components of the strain tensor \(e_{xx}\), \(e_{yy}\) and the dilatation strain \(E_{Dil}\) were used as input data. The transformation of the stress-strain state parameters was carried out based on the conversion of these parameters to a gradient scale in the range 0 to 1. For this purpose, indicators \(a\), \(b\), \(c\), and \(d\) were determined. They correspond to the following measurements of the dynamic activity in Table 2: \(a\), maximum value of stresses/strains; \(b\), boundary value of stresses or strains on the positive part of the scale identified by expert judgment; \(c\), boundary value of stresses or strains on the negative part of the scale identified by expert judgment; \(d\), minimum value of stresses/strains. For each \(x_{i}\) interval, a transformation was performed according to Equation (14). Thus, each interval of stress and strain values \(x_{i}\) corresponds to a certain calculation formula and interval of the dynamic activity measure.  
\[x_{i}\ \in\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  
Figure 8: Measure of dynamic activity index of stress tensor component, \(\mu\sigma_{yy}(w)\).  
Figure 7: Measure of dynamic activity index of stress tensor component, \(\mu\sigma_{xx}(w)\).  
Figure 9: Measure of dynamic activity index of stress intensity, \(\mu\sigma_{int}(w)\).  
To determine the MDAI of the magnetic field, we used Equation (5) for magnetic field variability index \(L_{Mag}^{2}(w)\) and Equation (8) for magnetic field variation gradient \(\big{|}\
abla_{Mag}\big{|}(w)\).  
Figure 11: Measure of dynamic activity index of strain tensor component, \(\mu e_{yy}(w)\).  
Figure 12: Measure of dynamic activity index of dilatation strain, \(\mu E_{Dil}(w)\).  
Figure 10: Measure of dynamic activity index of strain tensor component, \(\mu e_{xx}(w)\).  
Figure 13 shows distributions of integral measures of geodynamic safety and graphs of the distribution of their values by intervals within selected groups: geomorphological variability \(S_{Re}(w)\), tectonic faults density \(S_{\rho}(w)\), stress-strain state \(S_{sss}(w)\), and magnetic field anomalies \(S_{Mag}(w)\):  
\[S_{Re}(w)=1-\frac{\mu L_{Re}^{1}(w)+\mu L_{Re}^{2}(w)+\mu\
abla_{Re}(w)}{3} \tag{16}\]  
\[S_{\rho}(w)=1-\frac{\mu\rho_{\rho}(w)+\mu\rho(n,\mathcal{P})}{2} \tag{17}\]  
\[S_{sss}(w)=\frac{1}{2}\times\left(\frac{\mu\sigma_{xx}(w)+\mu\sigma_{yy}(w)+ \mu\sigma_{int}(w)}{3}+\frac{\mu\sigma_{xx}(w)+\mu\sigma_{yy}(w)+\mu E_{Dil}( w)}{3}\right) \tag{18}\]  
\[S_{Mag}(w)=1-\frac{\mu L_{Mag}^{2}(w)+\mu\
abla_{Mag}(w)}{2} \tag{19}\]  
Figure 13: Integral measures geodynamic safety histograms values into groups: (**a**)—measure of safety by geomorphological variability, \(S_{Re}(w)\); (**b**)—measure of safety by tectonic fault density, \(S_{\rho}(w)\); (**c**)—measure of safety by stress-strain state, \(S_{sss}(w)\); (**d**)—measure of safety by magnetic field anomalies, \(S_{Mag}(w)\). The distributions of the integral measures within the groups differ significantly. The integral measure of geomorphological variability \(S_{Re}(w)\) is characterized by a uniform distribution of data in the measurement interval from 0.45 to 0.9 (Figure 13a).