Reconstruction formula of time-dependent 3-D computerized ionospheric tomography

This paper illuminates the mathematical foundation of time-dependent three-dimensional computerized ionospheric tomography (CIT) for reconstructing ionospheric electron density (Ne) from ground-based GPS beacon measurements. After simplifying the relation between Ne and time, the formula of 3-D parallel-beam tomography is theoretically deduced and proved to be the same as the 2-D CIT inversion formula derived by K. C. Yeh when it is applied to 2-D cases. Furthermore, this paper investigates the effects of limited view angle and finite receiver aperture on recovered images. Specifically, the response to an impulse source function with the established 3-D parallel-beam reconstruction formula under these non-idealized conditions is numerically computed. The results indicate the feasibility of time-dependent three-dimensional CIT to reconstruct (Ne) from ground-based GPS beacon measurements.