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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 380, Pages 31–44 (Mi znsl3844)  
Exact solution of a model problem of subsurface sensing

F. D. Edemskiia, A. V. Popova, S. A. Zapunidia, B. R. Pavlovskiib

a Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Troitsk, Moscow reg., Russia
b Institute of Physical Diagnostic and Modelling, Moscow, Russia
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Abstract: 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.
Key words and phrases: subsurface sounding, migration, ground penetrating radar, inverse radiation problem.
Received: 30.08.2009
English version:
Journal of Mathematical Sciences (New York), 2011, Volume 175, Issue 6, Pages 637–645
DOI: https://doi.org/10.1007/s10958-011-0379-6
Bibliographic databases:
Document Type: Article
UDC: 537.8
Language: Russian
Citation: F. D. Edemskii, A. V. Popov, S. A. Zapunidi, B. R. Pavlovskii, “Exact solution of a model problem of subsurface sensing”, Mathematical problems in the theory of wave propagation. Part 40, Zap. Nauchn. Sem. POMI, 380, POMI, St. Petersburg, 2010, 31–44; J. Math. Sci. (N. Y.), 175:6 (2011), 637–645
Citation in format AMSBIB
\Bibitem{EdePopZap10}
\by F.~D.~Edemskii, A.~V.~Popov, S.~A.~Zapunidi, B.~R.~Pavlovskii
\paper Exact solution of a~model problem of subsurface sensing
\inbook Mathematical problems in the theory of wave propagation. Part~40
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 380
\pages 31--44
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3844}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 175
\issue 6
\pages 637--645
\crossref{https://doi.org/10.1007/s10958-011-0379-6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80955180066}
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