Response to remarks by J.R. Wait on the comments and reply to “The electromagnetic field of a vertical electric dipole over the Earth or sea”

In his remarks on the comments by Yokoyama (see ibid., vol.43, no.5, p.541-42, 1995) and the reply by King and Sandler (see ibid., vol.43, no.5, p.542-44, 1995) regarding our paper (see ibid., vol.42, no.3, p.382-9, 1994) J. R. Wait (see ibid., vol.44, no.2, p.271-72, 1996) makes a number of statements that require correction. These are considered in turn, but since they all center about the definition of the Sommerfeld numerical distance, this is introduced first. In a paper by Norton (1937), which is later quoted and applied by Wait, a formula is given for the generalized numerical distance for the height z and radial distance ρ due to a vertical dipole at the height d in the air (region 2, real wave number k_z) over a conducting or dielectric region 1 (complex wave number k₁). It is important to emphasize that the purpose of this response is not to belittle the important pioneer work of Norton, Wait, and others. Interest a half century ago was in communication over the surface of the Earth and sea with (z+d)²≪ρ². In this range, their formulas are accurate. However, recent progress which eliminates the restriction (z+d)²≪ρ² or k₂ρ≫1 should not be ignored by blindly using restricted formulas where they do not apply