IONOSPHERIC STRUCTURES INVISIBLE IN SATELLITE RADIOTOMOGRAPHY

In satellite ray tomography the measurements are samples of Radon tran sform of the ionospheric electron density. Regardless of the practical numerical method applied, the goal of tomographic inversion is to cal culate the inverse of the Radon transform. From mathematical point of view it is clear that provided a function satisfies certain mathematic al conditions, it has a unique Radon transform, which also has a uniqu e inverse. In satellite radiotomography, however, the sampling of the Radon transform is seriously restricted by the small number of receive rs. No unique inverse can be calculated from such an incomplete set of samples. It turns out that an infinite number of electron density fun ctions can be defined which are completely invisible for a given exper imental setup, not only in practice but also in a strict mathematical sense. These functions are not necessarily horizontally stratified, bu t they may contain strong horizontal gradients, in which case their in visibility is not associated with the lack of horizontal rays. In this paper a method of constructing such functions is presented and exampl es of them are shown, some of which could be reasonable in a realistic ionosphere. An experimental result and a simulation is also presented , which indicates how a wave-like traveling ionospheric disturbance ma y be partly invisible to transmitters on the ground.