Remarks on “The electromagnetic field of a vertical electric dipole over the Earth or sea” [and reply]

The author comments on the solution given by King and Sandler (see vol.42, p.382-89, 1994) of the electromagnetic field of a vertical electric dipole (VED) over Earth or sea and in the presence of a three layered region. For a homogeneous half-space with complex bulk wavenumber k₂, King and Sandler present expressions for the E and B field components which are claimed to be accurate in all ranges of the radial distance ρ, when |k₂/k₀|>3-k0 being the wavenumber in air. Wait (see ibid., vol.44, p.271-2, 1996) has questioned the completeness and generality of King´s and Sandler´s formulas. In particular, two of Wait´s comments have attracted this author attention. The first one is related to the usefulness of King´s and Sandler´s formulas directly above the VED axis (at ρ=0). The second is the usefulness of their formulas in deriving the input impedance of the VED. The authors investigate these two comments by comparing King´s and Sandler´s formulas to exact numerical results for E _z on the VED axis and for the input impedance as affected by the lower half-space. King and Sandler reply that the questions raised in the remarks of Mahmoud (see ibid., vol.46, no.12, p.1745-6, 1998) are based on a comparison of their formulas with the “exact numerical results for E_z, on the VED axis and for the input impedance as affected by the lower half-space”. Evidently, Mahmoud did not review the derivation of the King-Sandler formulas