Characterization of bimodal facies distributions using effective anisotropic complex resistivity: A 2D numerical study based on Cole-Cole models
Subsurface heterogeneity characteristics are of major importance in hydrologic modeling, and likely result in anisotropic electrical properties. We computed the anisotropic effective complex resistivity of 2D bimodal facies distributions numerically. Complex resistivities of individual facies are described in terms of the Cole-Cole relaxation model. First, we determined that effective DC resistivities of the distributions can be reasonably well described by power averaging the properties of individual facies. We found a clear relationship between the mixing parameter and correlation lengths of the facies distributions with respect to horizontal and vertical directions. Then, we used the power-law mixing model to invert for individual Cole-Cole model parameters by fitting predicted electrical responses to simulated spectral effective complex-resistivity data for the two perpendicular directions. Thus, it is possible to derive the electrical properties of individual facies as well as structural parameters describing bimodal facies distribution by means of a noninvasive measurement approach. In particular, anisotropy of the spectral complex-resistivity response provides information on correlation lengths of the distribution. This finding is relevant for all applications of electrical-impedance spectroscopy where anisotropy might be encountered.