The Theory of Loran-C Ground Wave Propagation-A Review

The essential portion of a received Loran-C signal of 100 kHz consists of groundwave only. The phase velocity of the groundwave which is related to TOA (time of arrival) and TD (time difference) values depends on various parameters, such as ground conductivity (or surface impedance), terrain variation, and the refractive index profile of the atmosphere. In order to calculate exactly the phase velocity, signal strength, etc., it is necessary to solve the electromagnetic wave equation, rigorously incorporating all of the above mentioned parameters. Since this is an impossible mathematical task, several approximate methods with various degrees of complexities had been sought by various authors in the past. Among these approximate methods or propagation models, the following are notable: (1) homogeneous flat earth model of Sommerfeld and Norton, (2) homogeneous spherical earth model of Watson, Van der Pol and Bremmer (the last two authors included also the effect of inhomogeneous atmosphere), (3) Millington's empirical model for an earth with mixed surface conductivities for computing signal strength, (4) Pressey and his associates' empirical model for earth with mixed surface conductivities for computing phase, (5) Wait's multisection spherical earth model, (6) Hufford's integral equation approach to the propagation over an irregular surface, and (7) Jollier's integral equation approach which is a generalization of Hufford's method with the aid of a computer. This paper presents a general overview of these methods and their limitations with a special emphasis directed towards Loran-C.