Abstract. This paper presents a model-independent algorithm for tomography of the ionosphere. Prior knowledge consists of the following pieces of information: electron density cannot be negative, the ionosphere is basically smooth and stratified, and electron density is low at high (•>700 km) and low (•<100 km) altitudes. Tests based on simulated measurements show that the method recovers the latitudinal structure well, whereas the vertical structure is recovered with moderate success: the estimated height of the layer of maximum electron density may be as much as 90 km in error. Because of the imposed smoothness the method tends to underestimate the peak in electron density by as much as one third in unfavorable cases.
IntroductionSince its conception in 1986 [Austen et al., 1986], radiotomography of the ionosphere has grown into a relatively inexpensive technique to image the electron density distribution in vertical cross sections of the ionosphere. In general, tomography is a method to reconstruct a distribution from its line integrals. In ionospheric tomography the line integrals of electron density (called total electron content (TEC)) are measured by the differential Doppler technique, where a receiver registers the differential Doppler shift of an orbiting beacon satellite [Leitinger et al., 1984]. An array of receivers placed parallel to the satellite's ground path should yield enough data to make the tomographic inversion from the measurements into an image of electron density. The surface of reconstruction is defined by the lines of sight (or rather phase paths) between satellite and receivers (see Figure 1).The first studies in ionospheric tomography were based on simulated TEC measurements using model ionospheres. Later, real experimental data were used on the basis of phase shift measurements from either the U.S. Navy Navigation Satellite System (NNSS) or A literature study reveals that every research group has its own reconstruction algorithm. Why should this paper add one more to the stack? Here we argue why our algorithm is a valuable contribution to the field.The main problem in ionospheric tomography is the absence of (near-)horizontal line integrals in the data set [Yeh and Raymund, 1991]. This absence is the result of a geometry where the lines of integration correspond to lines of sight between an orbiting satellite and ground-based receivers (Figure 1). Consequently, there are no lines of sight that remain at an approximately constant altitude. A set of such lines would contain the vertical profile of ionospheric electron density. This information is virtually missing from the data set, and tomography cannot be expected to provide a reconstruction where the vertical profile is rendered truthfully. A mathematician would say that the inverse problem is ill posed. In this jargon the inverse problem is the reconstruction of the "cause" from the "effect," the cause being the ionospheric electron density distribution and the effect being the result of the experiment (the TEC data). The problem ...