Geodesic
Exact solution of a model problem of subsurface sensing
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 40, Tome 380 (2010), pp. 31-44 
F. D. Edemskii; A. V. Popov; S. A. Zapunidi; B. R. Pavlovskii. Exact solution of a model problem of subsurface sensing. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 40, Tome 380 (2010), pp. 31-44. http://geodesic.mathdoc.fr/item/ZNSL_2010_380_a2/
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     title = {Exact solution of a~model problem of subsurface sensing},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {31--44},
     year = {2010},
     volume = {380},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_380_a2/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

An inverse electromagnetic wave radiation problem simulating subsurface radio sensing is considered. We assume synchronous external currents emerging in the subsurface medium with unknown spatial density. As shown, its distribution can be found from the pulsed radiation waveformes measured along the border of the examined half-space. In a model formulation, the problem is reduced to the reconstruction of a 2D function from its integrals over a set of semicircles. An explicit solution of that tomographic problem is found by means of Darboux equation. Numerical examples are given. Bibl. 13 titles.

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