## 2 Materials and Methods
### Calculations of the Effective Electric Conductivity of Rocks  
Transition from the local electromagnetic characteristics of geological media to integral parameters is of great practical importance. Due to the large linear dimensions of the electromagnetic field sources and/or receivers, as well as the complex structure and vast volumes of the geological media, obtaining information about the local distribution of electromagnetic parameters within the rock is fundamentally impossible. Figure 4: Micrographs of thin sections of Ortosuu mantle and crustal xenoliths. (**A**–**F**) Spinel (Sp) Iberzolites; (**G**,**H**) mafic granulites; OI, olivine; Opx, orthopyroxene; Cpx, clinopyroxene; PI, plagioclase; Kph, kelphite aggregate that replaces primary garnet. Tool: Camebax electron microprobe manufactured by Cameca with automated stages down to \(<\)3-micrometer precision. Analysis down to a weight of several hundred ppm for selected elements. The field of width of each micrograph is 8 mm [65]. The problem of transitioning from local to integral parameters in electrical prospecting is analogous to the transition from microfields to macrofields in electrodynamics. Homogenization (averaging) of physically infinitesimal volumes transforms the Lorentz equations for microfields (describing the electromagnetic field under vacuum) into [PERSON]'s equations, which describe the electromagnetic field in continuous media. The nature of charge location, movement, and interaction is not considered in [PERSON]'s equations; instead, these phenomena are characterized through the relative dielectric and magnetic permeability and electric conductivity (\(\epsilon\), \(\mu\), \(\sigma\)) media parameters. Spatial and temporal averaging of microscale fields simplifies the solution of electromagnetic problems. However, solving [PERSON]'s equations introduces the challenge of dealing with boundary conditions, which are absent in the Lorentz equations [66]. In geoelectrics during prospecting, a similar problem arises where each grain of rock-forming minerals has its own electromagnetic parameters, such as relative permittivity, magnetic permeability, and specific electrical resistivity. The complex relationship of electromagnetic parameters across spatial coordinates within rock samples poses significant challenges in solving [PERSON]'s equations for such media. To overcome these difficulties, an additional stage of Maxwell homogenization is proposed. During this stage, [PERSON]'s equations for a continuous media are averaged while considering the boundary conditions. Spatial averaging is performed over a small, physically finite volume, leading to the consideration of macroscale anisotropy in the effective resistivity and electric conductivity (\(\sigma^{\textit{eff}}\)). We show this procedure in Appendix A. There are different approximations of two-phase geological media that are still under investigation, and we introduce some of them here. The effective electric conductivity for spherical inclusions and layered media has been a subject of research since [PERSON]'s work to obtain the effective resistivity of two-phase media [67; 68]. Subsequently, many researchers have tackled this problem. An up-to-date view is supported by [PERSON] [69; 70]. According to [PERSON] [69], we know that, \"a homogeneous anisotropic conductive media with a set of anisotropic heterogeneities and its' numerical solution, using Gaussian approximating functions around isolated anisotropic spherical and cylindrical inclusions in an anisotropic homogeneous host media was studied by numerous researchers\" [71; 72]. These approaches share a common model that describes the relationship between electric and elastic properties through effective properties by following [PERSON]'s methodology [68]. Understanding the effective conductivity of bianisotropic media in terms of composites with anisotropic components is an up-to-date view proven by [PERSON] [69].