Extremely Low Frequency (ELF) Propagation Along a Horizontal Wire Located Above or Buried in the Earth

The propagation constant of an electromagnetic wave on a long horizontal thin wire is determined from a modal equation for various situations: an elevated wire; a buried bare wire; a bare wire located in the air-earth interface; and a buried insulated wire. Analytical expressions are derived under the assumption that the height or depth of the wire is much less than the skin depth of the conducting earth and that the angular variation around the wire can be ignored. Although not restrictive in frequency, these conditions are satisfied for extremely low frequency (ELF) and very low frequency (VLF) applications except possibly for deeply buried wires when the effect of the interface is negligible anyway. We show that the propagation constant of a buried bare wire is significantly different from an elevated one for almost all heights of practical interest. When the bare wire is in the interface or buried in close proximity of the earth surface, we find that the square of the wave propagation constant is the average of the squares of the propagation constants in the two media. Of particular interest is the fact that a buried insulated wire has a much smaller propagation constant than a bare wire at the same location. Thus, a horizontal ELF radiating structure, such as the Sanguine antenna, could behave in much the same manner whether it is elevated or located in a buried cylindrical insulating cavity. This conclusion is strictly valid when the length of the structure is small compared with the wavelength of the propagating current in either case, and when adequate grounding of the structure can be achieved.