Axial mode-matching technique for analysis of directional well-logging sensor tools

We present an new axial mode-matching technique to analyze directional well-logging tools used for oil and gas exploration. The geometry of this problem consists of a number of coil antennas (each with arbitrary relative tilt with the respect to the axis of symmetry) in a cylindrically layered medium comprised of a metallic mandrel, a borehole, an invasion zone, and a surrouding layered Earth formation. The proposed technique is based on a judicious eigenfunction expansion for the fields in cylindrical coordinates followed by a derivation the generalized scattering matrix (GSM) at each axial discontinuity based on the mode matching technique. Particular tilted coil excitations are represented by a set of modal coefficients, combined with the GSM matrices, and integrated over the receiver coils to compute the transimpedances. We present a series of validation results which show that our technique can efficiently and accurately model directional logging tools.