Comparison of the up-over-down approximation with the quasi-electrostatic approximation for ELF fields in layered media

Two approximate methods are presented that quantify low frequency field effects of a horizontal electric dipole in a layered environment. The first is a far-field approximation (relative to water) that is interpreted as the up-over-down effect. In this situation, wave processes are characterized using classical ray optics arguments and equations. The second method focuses on the quasi-static nature of the fields to arrive at an infinite image representation of the field. Both yield good results when compared to the exact solution, albeit the quasi-electrostatic solution does better at extremely low frequencies (e.g. 30 Hz) and the up-over-down solution does better at ultra-low frequencies (e.g. 1,000 Hz).