Evaluation of Eccentered Electrode-Type Resistivity Logging in Anisotropic Geological Formations With a Matrix Method

Abstract

A robust and succinct matrix-based method is developed to simulate the response of eccentered resistivity logging tools in anisotropic geological formations. This is done by first deriving the solution of the state vector describing the potential and the current component along the radial direction in a cylindrical system. Rescaled cylindrical eigenfunctions are employed to overcome the poor scaling inherent to the canonical cylindrical functions for very small or very large arguments. A Levin-type method for approximating integrals with rapidly oscillatory functions is introduced to effectively perform the numerical integrals. The influence of both the translational and rotational eccentricities of the logging tool within the borehole surrounded by an anisotropic formation is studied based on numerical results provided by the present matrix method. We found that neither translational nor rotational eccentricity can be neglected, especially in low-resistive or anisotropic geological formations.