This paper describes a sensitivity analysis for a prototype induction logging instrument designed for three dimensional imaging of the region surrounding a wellbore. This prototype tool consists of three mutually orthogonal magnetic solenoidal transmitters and multiple three-component magnetic field receivers offset at different distances from the source. The sensitivity functions are derived by taking the Born approximation to the integral equation for dipole magnetic fields within an inhomogeneous medium. The analysis shows that the standard axial configuration, where the magnetic moments of both the source and the receiver are aligned with the well-bore axis, offers superior sensitivity away from the borehole as compared to any other configuration. It also offers the best signal-to-noise characteristics. However, due to the cylindrically symmetric configuration of the instrument and the borehole, coaxial data can be interpreted only with a two-dimensional cylindrical model; three-dimensional (3-D) interpretation requires the measurements of the two orthogonal transverse field components in conjunction with the axial component. Coil configurations where both the source and receiver are perpendicular to the instrument axis can increase resolution and provide some directional information, but they offer no true 3D information and are sensitive to borehole effects. 3D imaging is possible at offsets up to 50m from the wellbore, if larger-than-normal source-receiver offsets are employed, although the resolution decreases rapidly away from the borehole. An inversion algorithm is employed to demonstrate the plausibility of 3-D imaging using three component magnetic field data. The model employed simulates a horizontal well drilled through a faulted dipping oil sandwater sandshale sequence. Synthetic data were generated using a 3-D finite difference code, noise added, and a 3-D inversion applied. In general, the inversion recovers the main features of the model including the location of the fault and the dip of the structure. When mutually orthogonal sources are employed, in addition to a single axial transmitter, the resolution of the image is markedly improved. The use of longer transmitter-receiver offsets results in greater depth of imaging away from the borehole.

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