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

摘要

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 k/sub 2/, 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 /spl rho/, when |k/sub 2//k/sub 0/|<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 /spl rho/=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/sub 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/sub 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.