## Appendix A Solution for the Calculation of Effective Electromagnetic Parameters
\begin{array}{l}\sigma_{11}=\frac{1}{<\frac{1}{\chi_{11}>_{x}}};\,\sigma_{12 }=\frac{<\frac{\chi_{12}>_{x}}{\chi_{11}>_{x}}}{<\frac{\chi_{11}}{\chi_{11}>_{ x}}};\,\sigma_{13}=\frac{<\frac{\chi_{12}>_{x}}{\chi_{11}^{2}>_{x}}}{<\frac{ \chi_{11}}{\chi_{1}^{2}>_{x}}};\\ \sigma_{21}=\frac{<\frac{\chi_{21}>_{x}}{\chi_{11}^{2}>_{x}}}{<\frac{\chi_{21 }^{2}>_{x}}{<\frac{\chi_{21}^{2}>_{x}}{\chi_{11}^{2}>_{x}}}}<<X_{22}>_{x}-<< \frac{\chi_{21}X_{22}}{\chi_{11}}>_{x};\\ \sigma_{23}=\frac{<\frac{\chi_{21}^{2}>_{x}}{\chi_{11}^{2}>_{x}}}{<\frac{\chi _{21}^{2}>_{x}}{\chi_{11}^{2}>_{x}}}+<X_{23}>_{x}-<\frac{\chi_{21}X_{31}}{\chi _{11}}>_{x};\,\sigma_{31}=\frac{<\frac{\chi_{31}>_{x}}{\chi_{11}^{2}>_{x}}}{< \frac{\chi_{31}}{\chi_{11}^{2}>_{x}}};\\ \sigma_{32}=\frac{<\frac{\chi_{31}^{2}>_{x}}{\chi_{11}^{2}>_{x}}}{<\frac{\chi _{31}}{\chi_{11}^{2}>_{x}}}+<X_{32}>_{x}-<<\frac{\chi_{31}X_{12}}{\chi_{11}}> _{x};\\ \sigma_{33}=\frac{\left<\frac{\chi_{31}}{\chi_{11}}\right>_{x}}{\left<\frac{ \chi_{31}}{\chi_{11}^{2}}\right>_{x}}+\left<X_{33}\right>_{y}-\left<\frac{ \chi_{31}X_{13}}{\chi_{11}}\right>_{x}.\end{array} \]  
As a result, we finally obtain the macroscale anisotropy tensor of electric conductivity:  
\[\sigma^{eff}= \begin{pmatrix}\sigma_{11}&\sigma_{12}&\sigma_{13}\\ \sigma_{21}&\sigma_{22}&\sigma_{23}\\ \sigma_{31}&\sigma_{32}&\sigma_{33}\end{pmatrix} .\] (A13)  
Thus, we obtain the effective electric conductivity tensor for a gradient anisotropic medium, which is related to the spatial coordinates in the presented form in Equation (A9). Comment. Obviously, the volume of the mean homogenization value is associated with the geometric divergence of the electromagnetic field: the closer the front of the electromagnetic wave is to the plane, the more accurate the result of homogenization is. It is difficult to provide any precise quantitative estimate of the homogenization volume. [PERSON] showed [73] that if the electric current density \(\mathbf{J}\) and the electric intensity \(\mathbf{E}\) in each homogeneous element of the Maxwell homogenization volume are constant vectors, and if the continuous components of these vectors vary weakly within the Maxwell homogenization volume, then the homogenization method (physical meaning of mean value averaging) provides practically exact dependences of the effective parameters from the local physicoelectric characteristics of rocks. Macroscale anisotropy of electric conductivity is associated with the observation system and the scale of the study of geological media, which contrasts with true anisotropy that is associated with the structure of the crystal lattice substance. It is known that electromagnetic microscale fields obey the [PERSON] equations [66]. There are dielectric vacuum permittivity and vacuum magnetic permeability and there is no electric conductivity. The latter appears as a result of space-time mean value averaging, and transformation to [PERSON]'s equations for macroscale fields is thus carried out. Consequently, relative electric conductivity and relative dielectric and magnetic permeabilities appear. Obviously, the scale of geophysical research is associated with the observation system. Hence, we conclude that the effective electromagnetic parameters present the effect of the observation system. It is necessary to consider inhomogeneous media with one observation system in relation to another in order to ascertain the macro anisotropic parameters of the geoelectric media.