Derivation of the magnetic field on a metal cylinder excited by a longitudinal magnetic dipole transmitter: II. Cylinder in a two‐layer dissipative dielectric medium

摘要: We derive an exact convergent analytical solution for the complex frequency-dependent magnetic field on surface of infinitely long and perfectly conducting metal cylinder situated in a cylindrically layered dissipative medium. The inhomogeneous medium consists two exterior cylindrical layers that are concentric with cylinder. is excited by longitudinally oriented oscillating dipole transmitter surface. An to this problem has not been previously published theoretical as well practical importance, e.g., modeling responses electromagnetic wave propagation logging tools. It shown can be expressed real-axis integral; however, integrand oscillates rapidly diverges large values integration variable. integral replaced sum branch line integrals over residues poles integral. correspond physically waveguide modes propagate discrete numbers. A pole search algorithm developed locate positions compute their residues. Phase shifts attenuations between receivers 1.1 GHz tool computed elucidate spectra relative contributions cut different thicknesses innermost dielectric layer properties.