Finite difference frequency domain (FDFD) modeling of trans-ionospheric propagation of VLF signals over long sub-ionospheric paths

In this paper, we apply a recently developed Segmented-Long-Path (SLP) Finite Difference Frequency Domain (FDFD) model of VLF propagation over long (tens to hundreds of wavelengths) paths to determine the coupling of wave energy through the collisional (i.e., lossy) ionospheric D-region up to altitudes where collisions (and thus losses) are not significant, i.e., ~120 km or higher. In this context, the primary loss process is collisions of electrons with neutral molecules, and with the neutral density falling off with altitude with a scale height of ~6 km, most of the attenuation occurs in a narrow altitude range of ~80-100 km. However, in this same region, the electron density and thus the wave refractive index exhibit rapid variations over height ranges comparable to or smaller than the VLF wavelength, so that accurate modeling of the reflection from this stratified region and the absorption losses therein generally requires ´full-wave´ modeling.