Electrical conductivity model for transversely isotropic rocks with interconnected cracks

The electrical conductivity of subsurface rocks is generally anisotropic. The anisotropy of the subsurface electrical conductivity provides important information on the stress-strain state and geodynamics. To quantitatively interpret anisotropic conductivity structures revealed by electromagnetic surveys, it is essential to use a mixing model considering the anisotropy. Although there exists a mixing model for transversely isotropic rocks with crack-shaped pores, the previous model seems inappropriate in interpreting conductive anomalies revealed by electromagnetic exploration because cracks are assumed to be isolated in the model. Therefore, this study develops a theoretical mixing model for transversely isotropic rocks with mutually interconnected cracks by a statistical approach. The derived mixing model considers the macroscopic tortuosity of a collection of cracks as well as the tortuosity of each crack. The derived model can represent general transverse isotropy and includes the isotropic and parallel models as special cases. I compare the developed model to previously proposed mixing models, showing that the developed model can reproduce a much wider range of anisotropy than the already-existing anisotropic mixing model. By applying the developed model to an example of the anisotropic conductivity in the oceanic upper crust inferred by electromagnetic exploration, I demonstrate that the developed mixing model enables us to quantitatively infer the crack orientation and fluid volume fraction that reproduce significant anisotropic conductivity found by field observations. Furthermore, I compare the developed model to the anisotropic seismic velocity model for fluid-filled cracks.