Reflection from and transmission through the ionosphere of VLF electromagnetic waves incident from the mid-latitude magnetosphere

Trans-ionospheric propagation of the VLF electromagnetic wave from an altitude of 800 km to the Earth's surface is considered using the model of stratified media. The numerical solution of the wave equations for the mid-latitude ionosphere model conditions is found. The wave field in the lower ionosphere is calculated using the full-wave approach. The wave field in the upper ionosphere is calculated using the matrix method of perturbations for a slightly inhomogeneous plasma. Energy reflection coefficient and the horizontal magnetic field amplitude of the wave on the ground surface are calculated. Peculiarities of the wave reflection and transmission at different times of the day are analyzed. The obtained results are important for studying the ELF/VLF emission phenomena observed both onboard the satellites and in ground-based observatories.