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We present a robust algorithm for the computation of electromagnetic fieldsradiated by point sources (Hertzian dipoles) in cylindrically stratified mediawhere each layer may exhibit material properties (permittivity, permeability,and conductivity) with uniaxial anisotropy. Analytical expressions are obtainedbased on the spectral representation of the tensor Green's function based oncylindrical Bessel and Hankel eigenfunctions, and extended for layered uniaxialmedia. Due to the poor scaling of these eigenfunctions for extreme argumentsand/or orders, direct numerical evaluation of such expressions can producenumerical instability, i.e., underflow, overflow, and/or round-off errors underfinite precision arithmetics. To circumvent these problems, we develop anumerically stable formulation through suitable rescaling of variousexpressions involved in the computational chain, to yield a robust algorithmfor all parameter ranges. Numerical results are presented to illustrate therobustness of the formulation including cases of practical interest togeophysical exploration.

Stable evaluation of Green's functions in cylindrically stratified regions with uniaxial anisotropic layers