A Numerical Feasibility Study of Three-Component Induction Logging for Three Dimensional Imaging About a Single Borehole

A theoretical analysis has been completed for a proposed induction logging tool designed to yield data which are used to generate three dimensional images of the region surrounding a well bore. The proposed tool consists of three mutually orthogonal magnetic dipole sources and multiple 3 component magnetic field receivers offset at different distances from the source. The initial study employs sensitivity functions which are derived by applying the Born Approximation to the integral equation that governs the magnetic fields generated by a magnetic dipole source located within an inhomogeneous medium. The analysis has shown that the standard coaxial configuration, where the magnetic moments of both the source and the receiver are aligned with the axis of the well bore, offers the greatest depth of sensitivity away from the borehole compared to any other source-receiver combination. In addition this configuration offers the best signal-to-noise characteristics. Due to the cylindrically symmetric nature of the tool sensitivity about the borehole, the data generated by this configuration can only be interpreted in terms of a two-dimensional cylindrical model. For a fill 3D interpretation the two radial components of the magnetic field that are orthogonal to each other must be measured. Coil configurations where both the source and receiver are perpendicular to the tool axis can also be employed to increase resolution and provide some directional information, but they offer no true 3D information