Localized three-dimensional ionospheric tomography with GPS ground receiver measurements

This paper describes a technique for 3-D tomographic imaging of the ionosphere with high spatial resolution (75 to 95 km in latitude/longitude and 30 km in altitude). The total electron content (TEC) values are derived from dual-frequency measurements obtained from GPS satellites by ground-based receivers. When available, ionosonde data are used to construct a priori vertical profiles modeled using Chapman functions. Two regularization algorithms are investigated for tomographic image reconstruction: Tikhonov and Total Variation (TV), corresponding to quadratic and l(1) norm minimizations of the penalty constraint, respectively. The TV method is used because it generally preserves discontinuities in the image effectively and is more resistant to noise. By contrast, Tikhonov, or quadratic, regularization tends to oversmooth image structures and discontinuities. However, a closed-form solution of the TV method does not exist and so performance depends heavily on numerical optimization techniques, which are nontrivial to implement because the inverse problem is both ill-posed and ill-conditioned. We also apply regularization parameter-selection methods to demonstrate their applicability in our study. The algorithms are demonstrated using real GPS TEC measurements from an observation geometry centered in southern California. We demonstrate the performance of these techniques under quiet, midlatitude conditions. The resulting reconstructions reasonably determine the shape of the ionospheric profile. Artifacts can potentially appear near voxels with no raypath information, which is directly related to the sparseness and nonuniform distribution of the GPS raypaths. We discuss some methods to constrain the solution to realistic bounds.