Analysis of standing wave patterns in VLF transmitter signals: Effects of sporadic E layers and in situ measurements of low electron density

An analysis of standing waver patterns formed by the reflection of VLFtransmitter signals incident upon a sporadi E layer is presented. The patterns were detected by electric field sensors on a sounding rocket designed to study the upward propagation of lightning-induced electric fields. To model the measured standing wave patterns it was necessary to have an accurate electron density profile. However, it has always been difficult to make accurate measurements of the low electron densities in the nighttime D and E regions. They devise a unique method to determine the electron concentration from the measured vertical wavelength of the standing wave patterns. The data from this analysis are then used to calibrate Langmuir probe measurements which, in turn, give a reasonable (but not perfect) electron density profile to use for full-wave modeling of the transmitter signals. This analysis yields several interesting characteristics, including the possibility that some energy is trapped in the sporadic E layer. The amplitude-versus-frequency characteristics of upgoing electromagnetic waves are also modeled. It is discovered that a sporadic E layer can act as a half-wave window at appropriate frequencies. A method for using VLF signals to measure electron densities without the existence of a standing wave pattern is also derived. Such a method is ideally suited for measuring the low electron densities in the nighttime D and E regions