## Appendix A Solution for the Calculation of Effective Electromagnetic Parameters  
In order to study the assessment of the sensitivity of anisotropic parameters of the media to the dynamics of geological processes during geophysical monitoring, we investigate the problem of obtaining effective electromagnetic parameters of a rock based on the mean value theorem [106]. A detailed explanation with a proof demonstration can be found in a PhD thesis [17]. According to this theorem, if the functions \(f(x)\) and \(g(x)\) are integrable at the \([a,b]\) segment while \(g(x)\geq 0\) or \(g(x)\leq 0\), and if \(f(x)\) is continuous, then the number \(\zeta\) in the interval \([a,b]\)\(a<\zeta<b\) exists, and \(\int\limits_{a}^{b}f(x)g(x)dx=f(\zeta)\int\limits_{a}^{b}g(x)dx\). This allows us to go to mean values:  
\[\frac{1}{b-a}\int\limits_{a}^{b}f(x)g(x)dx=f(\zeta)\frac{1}{b-a}\int\limits_{a }^{b}g(x)dx=f(\zeta)\widetilde{g}.\]  
We subsequently introduce the homogenization (averaging) operator:  
\[<\bullet>_{\zeta}=\frac{1}{\Delta_{\zeta}^{\zeta}}\int\limits_{0}^{\Delta_{ \zeta}^{\zeta}}\bullet d\widetilde{g},\]  
where \(\zeta\) represents any of the \(x\), \(y\), or \(z\) spatial coordinates in a Cartesian coordinate system. Let us carry out the averaging of [PERSON]'s law written in differential form:  
\[\mathbf{J}=\sigma\mathbf{E}. \tag{1}\]Connecting the current density of conductivity **J** and the electric intensity **E** through the electric conductivity \(\sigma\) is given as a product of isolated functions of spatial coordinates:  
\[\sigma=X(x)Y(y)Z(z). \tag{10}\]  
In this case, the possible interfaces between the media will coincide with the coordinate planes. Taking this circumstance and the mean value theorem into account, we will average the \(x\)-th component of the constituent equation (Equation (10)) in projection onto this axis. To do this, we find the average density of the electric current flowing in the direction of the \(X\) axis:  
\[\frac{1}{\Delta y\Delta z}\int\limits_{0}^{\Delta y}\int\limits_{0}^{\Delta z }J_{x}dydz=\frac{1}{\Delta y\Delta z}\int\limits_{0}^{\Delta y}\int\limits_{0} ^{\Delta z}\sigma F_{x}dydz=\frac{1}{\Delta y\Delta z}\int\limits_{0}^{\Delta y }\int\limits_{0}^{\Delta z}\sigma dydz\widetilde{\widetilde{E}}_{x}, \tag{11}\]  
where \(\widetilde{\widetilde{E}}_{x}=E_{x}(x,\lambda_{2},\lambda_{3})\), \(\lambda_{2}\in[0,\Delta y]\), \(\lambda_{3}\in[0,\Delta z]\). For averaging over the \(x\) coordinate, we rewrite (11) in the following form:  
\[\frac{1}{\frac{1}{\Delta y\Delta z}\int\limits_{0}^{\Delta y}\int\limits_{0}^{ \Delta z}\sigma dydz}<<l_{x}>_{y}>_{z}=\widetilde{\widetilde{E}}_{x}.\]  
Averaging the last equation over \(x\), we obtain:  
\[\frac{1}{\Delta x}\int\limits_{0}^{\Delta x}\frac{dx}{\frac{1}{\Delta y\Delta z }\int\limits_{0}^{\Delta y}\int\limits_{0}^{\Delta z}\sigma dydz}<<\widetilde{ l}_{x}>_{y}>_{z}=\frac{1}{\Delta x}\int\limits_{0}^{\Delta x}E_{x}(x,\lambda_{2}, \lambda_{3})dx=<\widetilde{\widetilde{E}}_{x}>_{x},\]  
where \(<<l_{x}>_{y}>_{z}=<<l_{x}(\lambda_{1},y,z)>_{y}>_{z}\), \(\lambda_{1}\in[0,\Delta x]\), or  
\[<<\widetilde{l}_{x}>_{y}>_{z}=\frac{<Y>_{y}<Z>_{z}}{<\frac{1}{\widetilde{X}}> _{x}}<\widetilde{\widetilde{E}}_{x}>_{x}.\]  
Making similar transformations for the remaining components of the constituent equation (Equation (10)), we obtain the anisotropy tensor of effective electric conductivity \(\sigma^{eff}\):  
\[\sigma^{eff}= \begin{pmatrix}\frac{\langle Y\rangle_{y}\langle Z\rangle_{z}}{ \langle\frac{1}{\widetilde{X}}\rangle_{x}}&0&0\\ 0&\frac{\langle X\rangle_{x}\langle Z\rangle_{z}}{\langle\frac{1}{\widetilde{ Y}}\rangle_{y}}&0\\ 0&0&\frac{\langle X\rangle_{x}\langle Y\rangle_{y}}{\langle\frac{1}{2}\rangle_{z}} \end{pmatrix}  \tag{12}\]  
We will characterize this type of anisotropy with the auxiliary term mesoanisotropy.