Hertzian dipole radiating over a lossy earth or sea: some early and late 20th-century controversies

This paper presents a contemporary solution to the problem of radiation from a vertical Hertzian dipole over a lossy earth. Sommerfeld´s 1909 solution to the problem is re-examined. It is demonstrated that a change in sign in the square root of the numerical distance is mathematically not allowed. Thus, the sign error that has been claimed in the technical literature for more than 65 years is a myth. Recent work by King and Sandier is also examined. It is found that due to an incorrect asymptotic expansion of the complementary error function for the problem of a lossy earth or sea covered with a thin dielectric layer, a trapped surface wave was missed in their solution.