A Robust Mode-Matching Algorithm for the Analysis of Triaxial Well-Logging Tools in Anisotropic Geophysical Formations

In this paper, a new pseudoanalytical axial mode-matching formulation is introduced to provide a flexible technique for analyzing direction well-logging tools in anisotropic formations. The presented technique does not rely on spatial discretization as former well-known methods. 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 with both axial and radial stratifications, composed of a metallic mandrel, a borehole, and a surrounding layered earth formation. This configuration corresponds to that of triaxial well-logging tools used for oil and gas exploration. Our approach combines closed-form solutions of Maxwell's equations for uniaxially anisotropic media in cylindrical coordinates with the generalized scattering matrix (GSM) at each axial discontinuity based on the mode-matching technique. The electromagnetic field from the tilted-coil source is represented by a set of modal coefficients that, after computation using GSM matrices, are used to extract the transimpedances of the well-logging tool.