Geodesic
Algorithms for solving direct and inverse problems of oblique radio-sounding ionosphere
Matematičeskoe modelirovanie, Tome 14 (2002) no. 11, pp. 23-32

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Layer model of ionosphere is considered, when electron density depends monotonically on height, i.e. the parts with lowered density (wave-guide or valley) are absent. The method of oblique radio-sounding is investigated under arbitrary direction of radio-ray to magnetic field of Earth. A special procedure of discretization (coordinated choice of grids) and computation algorithm are proposed to use Volterra type of the problem and to construct a solution in every layer step by step. For every step it is necessary to solve a system of two nonlinear equations with for functions of two variables. Represented results of numerical experiments show the effeciency of the proposed technique. 
@article{MM_2002_14_11_a2,
     author = {A. L. Ageev and T. V. Antonova and E. N. Bessonova and V. V. Vasin and V. M. Markushevich},
     title = {Algorithms for solving direct and inverse problems of oblique radio-sounding ionosphere},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {23--32},
     publisher = {mathdoc},
     volume = {14},
     number = {11},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2002_14_11_a2/}
}
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%A V. M. Markushevich
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A. L. Ageev; T. V. Antonova; E. N. Bessonova; V. V. Vasin; V. M. Markushevich. Algorithms for solving direct and inverse problems of oblique radio-sounding ionosphere. Matematičeskoe modelirovanie, Tome 14 (2002) no. 11, pp. 23-32. http://geodesic.mathdoc.fr/item/MM_2002_14_11_a2/