Transmission and total reflection of subhertz electromagnetic waves at the earth-atmosphere interface

For the purpose of providing for a theoretical background for the study of electromagnetic fields generated by precursory effects of earthquakes, the problem of transmission and total reflection at the earth-atmosphere interface is investigated in detail for a subhertz plane electromagnetic wave incident from the earth’s crust. The term “subhertz” means “below 1 Hz.” First, for the special case of normal incidence, the overall power transmission coefficient at the earth–atmosphere interface is found to take a maximum value at a definite frequency f₀ which is inversely proportional to the square of the depth of a virtual hypocenter. A typical value of f₀ falls around 0.01 Hz. For oblique incidence as well, this feature of the overall power transmission coefficient is retained except in the vicinity of the critical angle of incidence for the H-wave. At the critical angle of incidence, the power flow carried by a surface wave along the interface becomes anomalously large for the H-wave. However, over a wide range of angles of incidence greater than the critical angle, the power flow carried by the E-wave exceeds that carried by the H-wave by orders of magnitude. Finally, the energy conservation relations for the incident, reflected, and transmitted waves at the earth-atmosphere interface are discussed. For an incident wave coming from the earth’s crust, the interactive power between the incident and reflected waves plays a crucial role for the conservation of energy at the interface.