Numerical modeling of anisotropy paradoxes in direct current resistivity and time-domain induced polarization methods

Based on an analytical solution for the current point source in an anisotropic half-space, we study the apparent resistivity and apparent chargeability of a transversely isotropic medium with vertical and horizontal axes symmetry, respectively. We then provide a simple derivation of the anisotropy paradoxes in direct current resistivity and time-domain induced polarization methods. Analogous to the mean resistivity, we propose a formulation for deriving the mean polarizability. We also present a three-dimensional finite element algorithm for modeling the direct current resistivity and time-domain induced polarization using an unstructured tetrahedral grid. Finally, we provide the apparent resistivity and apparent chargeability curves of a tilted, transversely isotropic medium with different angles, respectively. The subsequent results illustrate the anisotropy paradoxes of direct current resistivity and time-domain induced polarization.