Pseudo-Analytical Modeling of Tilted-Coil Antennas in Anisotropic Geophysical Formations

In this paper we present an efficient mode-matching technique to analyze tilted-coil antennas in anisotropic geophysical formations. In this problem, a number of coil antennas with arbitrary relative tilt angle with respect to the symmetry axis are used to radiate electromagnetic fields in a cylindrically layered medium comprised of a metallic mandrel, a borehole, and a surrounding layered Earth formation. This configuration corresponds to that of directional well-logging tools used in oil and gas exploration. Our technique combines closed-form solutions for the Maxwell's Equations in uniaxially anisotropic and radially-stratified cylindrical coordinates with the generalized scattering matrix (GSM) at each axial discontinuity based on the mode-matching technique. The field from the transmitter tilted-coil source is represented by a set of modal coefficients which, after computation using GSM matrices, are used to compute the transimpedances. We present validation results which show that our technique can efficiently model directional well-logging tools used for oil and gas exploration.