## 3 Feature Engineering Based on Measurement of Dynamic Stability Index
### Feature Calculation  
For the realization of the methodology, software modules based on the calculation of morphometric indicators and normalization of geological and geophysical parameters were developed. These parameters reflect patterns of relief \(L^{1}_{Re}(w)\), \(L^{2}_{Re}(w)\), and \(|\
abla_{Re}|(w)\); fault densities \(\rho(w\),\(\mathcal{P})\) and \(\rho(w\), \(\rho)\); stress-strain states \(\sigma_{xx}(w)\), \(\sigma_{yy}(w)\), \(\sigma_{int}(w)\), \(E_{xx}(w)\)\(E_{yy}(w)\), and \(dil(w)\); and magnetic field anomalies \(L^{2}_{Mag}(w)\), \(|\
abla_{Mag}|(w)\). The first two indicators, \(L^{1}_{Re}\) and \(L^{2}_{Re}\), characterize the geomorphological variability landform sections at node \(w\), and the third, \(|\
abla_{Re}|\), is the gradient of relief:  
\[L^{1}_{Re}(w)=\frac{\sum_{\overline{w}\in C(w)}|Re(\overline{w})-Re(w)|}{4} \tag{4}\]  
\[L^{2}_{Re}(w)=\frac{2+cos\theta_{\Gamma}+cos\theta_{\mathrm{B}}}{2} \tag{5}\]  
\[cos\theta_{\Gamma}=\frac{-1+\left(Re(w_{4})-Re(w)\right)\times\left(Re(w_{6}) -Re(w)\right)}{\sqrt{1+\left(Re(w_{4})-Re(w)\right)^{2}}\times\sqrt{1+\left(Re (w_{6})-Re(w)\right)^{2}}} \tag{6}\]  
\[cos\theta_{\mathrm{B}}=\frac{-1+\left(Re(w_{2})-Re(w)\right)\times\left(Re(w_{ 8})-Re(w)\right)}{\sqrt{1+\left(Re(w_{2})-Re(w)\right)^{2}}\times\sqrt{1+\left( Re(w_{8})-Re(w)\right)^{2}}} \tag{7}\]  
The third relief gradient index is the gradient modulus \(|\
abla_{Re}(w)|\); it is responsible for the maximum change in relief at a node \(w\) and calculated by the Sobel operator:  
\[|\
abla_{Re}(w)|=\left|\
abla^{\Gamma}_{Re}(w)\right|+\left|\
abla^{\mathrm{ B}}_{Re}(w)\right| \tag{8}\]  
\[\
abla^{\Gamma}_{Re}(w)=\left(Re(w_{7})+2 Re(w_{8})+Re(w_{9})\right)-\left(Re( w_{1})+2 Re(w_{2})+Re(w_{3})\right) \tag{9}\]  
\[\
abla^{\mathrm{B}}_{Re}(w)=\left(Re(w_{3})+2 Re(w_{6})+Re(w_{9})\right)-\left( Re(w_{1})+2 Re(w_{4})+Re(w_{7})\right) \tag{10}\]  
The MDAI for \(L^{1}_{Re}\), \(L^{2}_{Re}\), and \(|\
abla_{Re}|\) are calculated as:  
\[ \begin{array}{l}\mu L^{1}_{Re}(w)=\frac{L^{1}_{Re}(w)}{1^{k}_{Re}(w)+L^{1}_ {Re}}\\ \mu L^{2}_{Re}(w)=\frac{L^{2}_{Re}(w)}{1^{2}_{Re}(w)+L^{2}_{Re}}\\ \mu\
abla_{Re}(w)=\frac{\
abla_{Re}(w)}{\
abla_{Re}(w)+\
abla_{Re}}\end{array}  \tag{11}\]  
In studying the stability of a structural-rectonic block, the key issue is the macroscopic manifestation of the geodynamic process. In the Earth's crust, this macroscopic manifestation is most often represented by the relative displacement of parts of a massif concerning each other. Analysis of the processes occurring at the boundaries between structural-tectonic blocks is a necessary step for the creation of modern analytical and numerical geodynamic models [44]. For this, we added the indicators \(\rho(w)\), which characterizes fault density, and \(\rho(n\),\(\mathcal{P})\), which characterizes proximity to tectonic faults. The MDAI of fault density was determined using the linear density, which was obtained in a circular vicinity within each cell of the grid. The length of the segment of each line crossed by the circular neighborhood was multiplied by the line weight factor. Then all the length values were summed up and divided by the area of the circle. This process was repeated for all cells in the grid.