## 3 Results and Discussion
### The Geodynamic Model Examples
#### 3.2.2 Model of the Quasi-Plastic Deformation of Rocks  
The model shown in Figure 11 characterizes irreversible geodynamic processes in the layer pack as a result of quasi-plastic movement of the rock mass. It assumes that the geoelectric boundaries do not change in the layer unit. The layers themselves undergo changes in terms of the formation of micro-dislocations in the form of cleavage (see [100; 101]) in each layer. In a Cartesian coordinate system, a two-dimensional model is analogous to strata interlayering. Each layer, with a thickness of \(h_{i}\), is characterized by the anisotropy tensor of electric conductivity,  
\[\sigma_{i}= \begin{pmatrix}\sigma_{11}^{i}&0\\ 0&\sigma_{22}^{i}\end{pmatrix} ,\]  
with constant elements of this tensor. The macroscale anisotropy tensor of effective electric conductivity will then have the form  
\[\sigma^{eff}= \begin{pmatrix}\sigma_{11}&0\\ 0&\sigma_{22}\end{pmatrix} ,\]  
where for \(n\) layers  
\[\sigma_{11}=\frac{1}{\sum\limits_{i=1}^{n}h_{i}}{\sum\limits_{i=1}^{n}\sigma_ {11}^{i}h_{i}};\ \sigma_{22}=\frac{1}{\frac{1}{\sum\limits_{i=1}^{n}h_{i}}\frac{h_{i}}{\sigma_ {22}^{i}}}.\]  
Figure 11: Model of the quasi-plastic deformation of horizontally layered rocks with cleavage. (a) 1–9—random types of fractured anisotropic media with cleavage. Lines form tilted rock types with various directions of fractures. (**b**) Below surface cross section of layered rocks with cleavage, an example of the type of geologic formation for monoclinic layers is shown with undersurface perpendicular cut lines (effective parameters of electrical conductivity \(\hat{\sigma}_{1},\hat{\sigma}_{2},\hat{\sigma}_{3}\)), with the upper part showing calculated coefficients of macroscale anisotropy: \(\bullet\bullet\bullet k_{11}^{2}=\sqrt{\frac{\rho_{12}}{\rho_{11}}},-k_{11}^{2 2}=\sqrt{\frac{\rho_{22}}{\rho_{11}}}\). The anisotropy coefficient is equal to  
\[k_{22}^{11}=\sqrt{\frac{\sigma_{11}}{\sigma_{22}}}=\sqrt{\frac{1}{\sum\limits_{i=1 }^{n}\sum\limits_{i=1}^{n}\sigma_{11}^{i}h_{i}\frac{1}{\sum\limits_{i=1}^{n}h_{ i}}\sum\limits_{i=1}^{n}\frac{h_{i}}{\sigma_{22}^{i}}}}.\]  
Let us consider one important case observed experimentally that does not yet have a theoretical explanation. In some cases, during field and laboratory studies of geological objects, it is noted that the anisotropy coefficient is  
\[k_{22}^{11}=\sqrt{\frac{\rho_{22}}{\rho_{11}}}=\sqrt{\frac{\sigma_{11}}{\sigma_ {22}}},\]  
where \(\rho_{11}\) is the resistivity of the layered media along the strata and \(\rho_{22}\) is the resistivity of the layered media across the strata, which may be less than 1. To explain this fact, let us consider a two-dimensional model of a three-layer media, each layer of which has the following mesoanisotropy of electric conductivity: the first layer with electric conductivity and thickness, and the second with a thickness and electric conductivity tensor:  
\[\sigma_{2}= \begin{pmatrix}\sigma_{11}&0\\ 0&\sigma_{22}\end{pmatrix} ,\]  
where the third layer is isotropic with electric conductivity \(\sigma_{3}\) and thickness \(h_{3}\). The macroscale anisotropy tensor of the effective electric conductivity then takes the form  
\[\sigma^{eff}= \begin{pmatrix}\frac{\sigma_{1}h_{1}+\sigma_{11}h_{2}+\sigma_{3} h_{3}}{h_{1}+h_{2}+h_{3}}&0\\ 0&\frac{h_{1}+h_{2}+h_{3}}{h_{1}p_{1}+h_{2}p_{22}+h_{3}p_{3}}\end{pmatrix} \]  
where \(\rho_{1}=\frac{1}{\sigma_{1}},\rho_{22}=\frac{1}{\sigma_{22}}\), and \(\rho_{3}=\frac{1}{\sigma_{3}}\). For \(h_{1}=h_{2}=h_{3}\) and \(\sigma_{1}=\sigma_{3}=1/\rho=\sigma\), the anisotropy coefficient \(k_{22}^{11}\) takes the form  
\[k_{22}^{11}=\sqrt{\frac{5+2(\sigma\rho_{22}+\sigma_{11}\rho)}{9}}.\]  
Hence, it follows that the macroscale anisotropy coefficient \(k_{22}^{11}\) is greater than 1 at \(\sigma\rho_{22}+\sigma_{11}\rho>2\) and less than 1 at \(\sigma\rho_{22}+\sigma_{11}\rho<2\). Thus, the presence of an anisotropic layer in a stack of layers can lead to an anisotropy coefficient of less than 1.