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An inversion method is proposed to estimate the wave energy distribution of magnetospheric VLF radio waves (VLF/ELF emissions and whistlers) at the ionospheric base by using the simultaneously observed two horizontal magnetic and a vertical electric field components. The simulation experiments are extensively carried out to examine the effectiveness of the method. Two models for the wave source (a single source and two simultaneous sources) have been used, in which the observed signal is simulated to be composed of a number of elementary plane waves whose arriving directions are distributed around a specific direction in the case of a single source (two specific directions for the case of two simultaneous sources) and whose polarizations are distributed around right-handed circular. The distributions how the wave energy density is distributed at the ionospheric base have been obtained as an inversion problem in which the entropy of the wave distribution function is made maximum for the spectral matrix composed of the auto-and cross-power spectra of the three field components. It is then found that the present new method is very promising especially for the situation when a few wave sources (ducts) are present or when the ionospheric exit region is widely spread for which the previous direction finding systems are ineffective. Finally, the present method is applied to the actual data of whistlers observed at a low latitude, and it is found that the method is very effective in locating the wave source distribution, being in good agreement with the results by the previous direction finding methods. Further useful information on the mechanism of magnetospheric duct propagation and the ionospheric transmission is obtainable from the present method.

journal of geomagnetism and geoelectricity

On the Estimation of Wave Energy Distribution of Magnetospheric VLF Waves at the Ionospheric Base with Ground-Based Multiple Electromagnetic Field Components.