The effects of tool eccentricity and formation anisotropy on resistivity logs: forward modeling

The theory of resistivity logging (RL) originally stems from the Fock–Stefãnescu forward problem solution for the stationary electric field E in a piecewise homogeneous isotropic medium, with a single boundary corresponding to the surface of a cylinder unlimited by height. The cylinder simulates a borehole filled with drilling mud of resistivity ρ = ρb, which penetrates a formation with resistivity of rocks ρ = ρr. The primary field E is produced by the charge of a current electrode A placed on the cylinder axis. In this paper the forward problem for the field E is investigated for the electrode A at an arbitrary point off the axis of a borehole embedded in a transversely isotropic formation, with an anisotropy axis parallel to the borehole axis. The solution of forvard problem is used in algorithms and respective software for processing resistivity logs affected by electrode eccentricity and formation anisotropy. The changes caused to apparent resistivity by the two effects are estimated in percent for axial and lateral electrode dispositions.