Analysis of experimentally validated trans‐ionospheric attenuation estimates of VLF signals

Abstract

Accurate models of trans‐ionospheric propagation are needed to assess the role of Earth‐originating very low frequency (VLF) electromagnetic waves in radiation belt dynamics. Recent studies have called the relatively crude early trans‐ionospheric models into question, finding that they underestimate the attenuation by 20–100 dB. A full wave model that includes all of the relevant physics has recently become available and experimentally verified to within a few decibels via comparison to more extensive satellite data. Using this model, we discuss the importance of wave polarization, incidence angle, bearing, ground conductivity, horizontal distance from the source, and the ionospheric profile, all of which are demonstrated to play a significant role in the trans‐ionospheric propagation. trans‐ionospheric attenuation estimates are provided both for the case of vertical incidence of a whistler‐mode wave and for the case of magnetospheric injection from a dipolar terrestrial VLF source. These estimates agree with observation to within ±6 dB. The remaining discrepancy may be attributable to ionospheric variation and/or factors not captured by our horizontally stratified model. On the basis of the full wave treatment presented herein, we find that the earlier work showing a >20 dB overestimation by traditional models results from the unrealistic simplifying assumption that the wave is vertically incident onto the ionosphere, exacerbated by the fact that most of the satellite data used for comparison came at large horizontal distances (hundreds of kilometers) from the source.