## Appendix A Solution for the Calculation of Effective Electromagnetic Parameters
Obviously, in a real situation, the volume of natural homogenization due to the huge volumes of the studied media, large linear dimensions of sources, and receivers of the electromagnetic field can be much larger than the homogenization volume used to obtain mesoscale anisotropy. Indeed, it is possible to observe the strata interlayering in geological rocks, which individually have a clear-cut anisotropic characteristic. Macroscale anisotropy will characterize such a pack of layers as a single unit, where each layer has its own mesoanisotropy of electric conductivity. The mathematical model of such a geologic pack can be represented, in general form, by the diagonal tensor of electric conductivity of the second rank:  
\[\sigma= \begin{pmatrix}\sigma_{11}&0&0\\ 0&\sigma_{22}&0\\ 0&0&\sigma_{33}\end{pmatrix} , \tag{13}\]where each diagonal element of the symmetric electric conductivity tensor depends on the coordinates in the form  
\[\sigma_{ii}=X_{ii}(x)Y_{ii}(y)Z_{ii}(z),\ i=(1,3). \tag{104}\]  
In this case, the interfaces of the anisotropic layers will be parallel to the coordinate planes. This model of the local electric conductivity of rocks, which generalizes case (102), characterizes the strata interlayering with different anisotropic electrical parameters. Moreover, each layer has different electric conductivity along and across the strata. After averaging the constitutive equation (Equation (101)) with the local electric conductivity given in the form (104), we obtain  
\[\sigma^{eff}=\left( \begin{array}{cccc}\left\langle Y_{11}\right\rangle_{x} \left\langle Z_{11}\right\rangle_{z}&0&0\\ 0&\frac{\left\langle X_{22}\right\rangle_{x}\left\langle Z\right\rangle_{22} }{\left\langle\frac{1}{\tau_{22}^{2}}\right\rangle_{y}}&0\\ 0&0&\frac{\left\langle X_{33}\right\rangle_{x}\left\langle Y_{33}\right\rangle _{y}}{\left\langle\frac{1}{23}\right\rangle_{z}}\end{array} \right). \tag{105}\]  
The next model of local electric conductivity for which the use of the mean value theorem is valid, and the model of greatest interest, is the model where the electric conductivity tensor is given in the form  
\[\sigma=\left( \begin{array}{cccc}\sigma_{11}&\sigma_{12}&\sigma_{13}\\ \sigma_{21}&\sigma_{22}&\sigma_{23}\\ \sigma_{31}&\sigma_{32}&\sigma_{33}\end{array} \right), \tag{106}\]  
where each element of the conductivity anisotropy tensor depends only on one spatial coordinate, such as  
\[\sigma_{ii}=X_{ii}(x),\ i=(1,3). \tag{107}\]  
This model can be interpreted as a layered anisotropic model of the geological media. The ideology of the Maxwell homogenization method in this case could be expressed as the following representation. We need to go from the general form of relationship between the electric current density (**J**) and the electric intensity (**E**), using homogenization over one of the \(x,y,z\) coordinates, to the representation where the discontinuous **J** and **E** components of the vectors depend on the continuous **J** and **E** components:  
\[\begin{array}{l}J_{x}=\sigma_{11}E_{x}+\sigma_{12}E_{y}+\sigma_{13}E_{z},\\ J_  
After one-axis mean value theorem application over the coordinate \(x\) (A11) equations and transforming them to the form (1.10), we obtain  
\[ \begin{array}{l}\widetilde{J}_{x}=\sigma_{11}<E_{x}>_{x}+\sigma_{12}\widetilde{ E}_{y}+\sigma_{13}\widetilde{E}_{z},\\ <J_{y}>_{x}=\sigma_{21}<E_{x}>_{x}+\sigma_{22}\widetilde{E}_{y}+\sigma_{23} \widetilde{E}_{z},\\ <J_{z}>_{x}=\sigma_{31}<E_{x}>_{x}+\sigma_{32}\widetilde{E}_{y}+\sigma_{33} \widetilde{E}_{z},\end{array} \] (A12)  
where  
\[