Penetration and reflection of VLF waves through the ionosphere: Full wave calculations with ground effect

Abstract

Numerical calculations of the full-wave treatment are made for VLF electromagnetic waves that are incident on to the plane-stratified ionosphere both from below and above. For the both cases, special attention is paid to the variation of penetration and reflection coefficients with wave frequency, angle of incidence, magnetic dip angle and various model of the ionospheric structure. The effect of conductive ground is taken into account in the calculation of the penetration and reflection coefficients of the waves incident from above. The modifications due to the presence of ground reflection are 1. (1) both penetration and reflection coefficients vary considerably with angle of incidence as a result of the interference between the upward and the downward propagating waves. 2. (2) reflection coefficient in the nighttime ionosphere is large enough to account for common type of repeated whistler echo trains. A new reciprocity relation is established which is related to the reflection coefficients of the waves incident onto the ionosphere from above.