A Numerical Mode-Matching Method Based on Multiple-Knot Cubic B-Splines Applied to the Analysis of Well-Logging Tools

Abstract The numerical mode-matching (NMM) technique is a very efficient approach to analyze well-logging tools used for hydrocarbon exploration. This problem is typically modeled as a cylindrically layered medium (subterranean formation) including both horizontal and vertical stratifications. In this paper, we present a new NMM formulation based on the use of B-splines expansion functions with variable knot multiplicity to represent the dependency of fields on the vertical direction, and cylindrical Bessel functions to represent the fields along the radial (horizontal) direction. We show that this type of expansion allows to better capture the spatial variation of the electromagnetic field near vertical layer interfaces. Illustrative examples elucidate the advantage of knot multiplicity in the modeling of earth formations with anisotropic and lossy layers. A case study on compensated dual resistivity (CDR) well-logging tool sensors is also presented based on the proposed method.