Simplified formulas for ELF propagation at shorter distances
Abstract
It is the purpose of this article to present new formulas for ELF electric and magnetic dipole propagation in the earthionosphere waveguide. These new formulas extend the results of Wait and Galejs, which are valid for measurement distances greater than approximately three ionospheric reflecting heights, to the quasinear field range, which is defined as the range where the measurement distance is greater than an earth wavelength, but much less than freespace wavelength. These new formulas will be particularly applicable in the range of approximately 20 to 300 km from the source. We will also present plots of the VED and HED (or HMD) radial wave impedance versus distance for both daytime and nighttime propagation conditions. These plots show a substantial variation in the radial wave impedances for distances less than 1,000 kilometers. We will also show that there is a unique distance where the minimum value of the VED radial wave impedance occurs.
 Publication:

Radio Science
 Pub Date:
 June 1986
 DOI:
 10.1029/RS021i003p00529
 Bibcode:
 1986RaSc...21..529B
 Keywords:

 Electric Dipoles;
 Extremely Low Frequencies;
 Ionospheric Propagation;
 Magnetic Dipoles;
 Distance;
 Diurnal Variations;
 Communications and Radar;
 Electromagnetics: Electromagnetic theory;
 Electromagnetics: Guided waves;
 Electromagnetics: Wave propagation;
 Ionosphere: Wave propagation