The theory of VLF Doppler signatures and their relation to magnetospheric density structure

The published spectrograms of signals from ground-based VLF transmitters observed aboard satellites show a wide variation from sample to sample. In general, the observed signals are Doppler shifted by the motion of the satellite, but in some published samples there is no observed Doppler shift. A ray tracing study of differing VLF Doppler signatures observed by the Ogo 4, FR 1, and Isis 2 VLF experiments has shown that each signature can be reproduced by a distinct class of electron density gradient models. Large positive and negative Doppler shifts (∼100 Hz) are reproduced by a strong decreasing electron density gradient which interacts with the magnetic field curvature gradient between L ∼ 2 and L ∼ 3. Presence of a strong signal with no Doppler shift is shown to be a result of trapping of upgoing rays by steep density drop-offs. Merging of the spectral components in the Doppler shifted signals is interpreted in terms of scattering by small-scale field-aligned density irregularities. These results allow VLF Doppler observations to be used as a new diagnostic tool in determining magnetospheric density structure below L ∼ 3 and in estimating the effective coverage of the lower ionosphere by the ground-based VLF transmitter in the excitation hemisphere.