Applications of operational calculus to ground-wave propagation, particularly for long waves

Abstract

All results of the approximative diffraction theory dealing with the propagation of radio waves around a smooth spherical earth (surrounded by a homogeneous atmosphere) can be derived from a one-dimensional integral equation originally discussed by Hufford. This equation can be solved in terms of operational calculus which leads, first of all, to the well-known residue series. In this treatment the Sommerfeld theory for a fiat earth appears at once as a limiting case; moreover, analytic expressions for correction terms accounting for the finite value of the earth's radius are easily determined. Finally, the equation in question can also be used for the extension to inhomogeneous soil conditions, without neglecting the earth's curvature.