EXTRA LOW-FREQUENCY TERRESTRIAL RADIO-WAVE FIELD CALCULATIONS WITH ZONAL HARMONICS SERIES

Use of the zonal harmonics series for calculating the terrestrial wave guide fields directly is described. The analysis is extended to include radio waves propagating into seawater or below the earth's surface. A sample calculation of ELF radio waves is analyzed into a direct wave and a wave that has traveled the circumference of the earth. The location of the ripples in the standing wave pattern is compared with the locations predicted by less exact but simpler mathematical models. Approximate formulas check within a few percent of the exact analysis when used to estimate positions of maxima and minima near the antipode.