Radio-wave transmission over the surface of the Earth is a subject of enquiry going back to the beginning of the century. In this review, an attempt is made to describe the ground-wave mechanism that is omni-present. We first call attention to the early analytical contributions of Zenneck and Sommerfeld, based on a flat-Earth model. The subsequent controversies, particularly with regard to the role of the Zenneck surface wave, are outlined. Further developments by other pioneers, such as van der Pol, Fock, Bremmer, Norton, and Millington, are reviewed, and an attempt is made to put these in a modern context. We also show that the trapped surface wave can be a significant contribution to the total ground-wave field, when the Earth boundary is sufficiently inductive. Mixed-path theory and confirming model tests by Ray King are described briefly, along with calculated propagation curves for twoand three-section paths. The bibliography includes references to related topics, such as tropospheric refraction and topographic influences.

The ancient and modern history of EM ground-wave propagation

The first analytical model of Body Area Network channels is presented. The formulation includes the body morphology and the characteristics of the human tissues. The studied transmission paths are along curved parts like the waist or the head. The model is derived from the diffraction theory describing the attenuation of creeping waves along a circular path on a lossy dielectric surface. The model is validated by measurements performed with Planar Inverted-F Antennas on human subjects.

Analytical Propagation Modeling of BAN Channels Based on the Creeping-Wave Theory

Previous methods developed for computation of the attenuation function for a homogeneous spherical earth are generalized for an arbitrary surface impedance. The power series and small-curvature formula developed for short distances can be used for such surfaces without modification. Care must be taken, however, to include properly the trapped surface wave that may arise in the formulation. In general, it is found that the inductive type of boundary enhances the total field but, if the resistive part is small, rather strong interference takes place between the trapped surface wave and the usual ground wave. These effects are illustrated for a surface-based vertical electric dipole for frequencies from 1 to 30 MHz.

Ground wave attenuation function for a spherical earth with arbitrary surface impedance

This paper discusses the basic aspects of radio-wave propagation and antenna modeling at 150 to 1705 kHz The paper contains descriptions of both sky-wave and ground-wave propagation-prediction models, in addition to the methodology used to analyze antennas that operate in this band A method of calculating and normalizing antenna gain for system computations is also discussed The sky-wave models described in this paper are valid from 150 to 1705 kHz The ground-wave models described in this paper are valid from 10 kHz to 30 MHz The propagation of radio waves from 150 to 1705 kHz includes both a ground wave and a sky wave, and is quite different from propagation at any other frequency The methods used for antenna modeling and analysis in this band are also quite unlike those in other bands The AM broadcast band of 535 to 1605 kHz is planned to be used in the advanced traveler information systems (ATIS) of intelligent transportation systems (ITS), to provide information such as road conditions, road hazards, weather, and incident reporting for rural travelers The band of frequencies from 285 to 325 kHz is presently being used in another application of ITS, called the Differential Global Positioning System (DGPS), which will be used for precision location of vehicles The propagation-prediction models and antenna-analysis methods described here can be used for designing systems and making performance predictions for both of these ITS applications, or for any other systems that operate in this band of frequencies from 150 to 1705 kHz Some examples of comparisons of measured and predicted data are also presented A computer program that includes all of these propagation-prediction models and antenna-modeling techniques was used

Propagation prediction techniques and antenna modeling (150 to 1705 kHz) for intelligent transportation systems (ITS) broadcast applications

The classical Sommerfeld problem of electromagnetic wave propagation over a flat earth is reformulated by using the electromagnetic compensation theorem. The solution is carried through without recourse to the usual spectral representation of the potential function, and therefore complicated contour integrations are avoided in the subsequent evaluation. Using reciprocity and duality, the complete electromagnetic fields are calculated for elemental vertical or horizontal dipoles of both electric and magnetic types, which are elevated above an arbitrary but passive surface impedance such as that corresponding to homogeneous, horizontally stratified, or uniformly rough surfaces. The results are identical to the little known but more accurate work of Norton, and under certain approximations they reduce to the more well-known results of Norton, Hufford, Bremmer, and others. The restrictions on the impedance properties of the surface are given, and certain direction finding errors are discussed. It is shown that the index of refraction contrast between the upper and lower medium need not be large.

Electromagnetic Wave Propagation Over a Constant Impedance Plane

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.

H. Bremmer

Papers

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