Abstract
This paper studies the mathematical foundation of time dependent three-dimensional (3-D) computerized ionospheric tomography (CIT) for reconstructing ionospheric electron density,N e, from ground-based GPS beacon observations. After simplifying the relation betweenN e and time, the time-dependent 3-D inversion in consideration is reduced to a 3-D tomography with incomplete projections. To see clearly the effects of the incompleteness on the quality of reconstruction under 3-D condition, the formula of 3-D parallelbeam tomography is deduced theoretically. After establishing the mathematical foundation, simulations based on actual GPS ray paths with the help of the IRI-90 model are performed, and reasonable time-dependent 3-D distribution images ofN e are obtained when taking proper layout of the netowrk and allowing variable resolutions. The quality of the reconstruction is rather good when compared with the images from the IRI-90 model directly. Therefore, results in this paper demonstrate that imaging of the ionospheric electron density distribution from GPS beacon observations is reasonable in theory and feasible in practice.
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