Analytical method for determining the location of ionospheric and atmospheric layers from radio occultation data

We generalize the fundamental principle of the radio-occultation method for studying the atmospheres and ionospheres of planets and the Earth. The criterion containing the necessary and sufficient condition under which the tangential point, at which the refractive-index gradient is normal to the ray trajectory coincides with the radio-ray perigee, is obtained. The method for determining the location and parameters of ionospheric and ionospheric layers, which is based on the relationship between the amplitudes and phases of the analytic functions determined from variations in the phase path (eikonal) and intensity of the radio-occultation signal, is proposed. This method yields qualitative and quantitative estimations of the value of the spatial displacement of the ionospheric or ionospheric layer with respect to the radio-ray perigee and allows one to determine the altitude and inclination of the ionospheric layer. The developed method is, in particular, required for determining the location and inclination of the wind-shear region and the direction of propagation of internal waves in the ionosphere and the atmosphere. This method is simpler and more accurate than the back-propagation, radio-holographic method which was previously used for determining the location of the ionospheric irregularities.