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
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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. 
@article{ZNSL_2010_380_a2,
     author = {F. D. Edemskii and A. V. Popov and S. A. Zapunidi and B. R. Pavlovskii},
     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/}
}
TY  - JOUR
AU  - F. D. Edemskii
AU  - A. V. Popov
AU  - S. A. Zapunidi
AU  - B. R. Pavlovskii
TI  - Exact solution of a model problem of subsurface sensing
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2010
SP  - 31
EP  - 44
VL  - 380
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2010_380_a2/
LA  - ru
ID  - ZNSL_2010_380_a2
ER  - 
%0 Journal Article
%A F. D. Edemskii
%A A. V. Popov
%A S. A. Zapunidi
%A B. R. Pavlovskii
%T Exact solution of a model problem of subsurface sensing
%J Zapiski Nauchnykh Seminarov POMI
%D 2010
%P 31-44
%V 380
%U http://geodesic.mathdoc.fr/item/ZNSL_2010_380_a2/
%G ru
%F ZNSL_2010_380_a2
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/

[1] A. Yu. Grinev, Voprosy podpoverkhnostnoi radiolokatsii, Radiotekhnika, M., 2005

[2] J. G. Hagedoorn, “A process of seismic reflection interpretation”, Geophys. Prospect., 2:1 (1954), 85–127 | DOI

[3] G. I. Petrashen, S. A. Nakhamkin, Prodolzhenie volnovykh polei v zadachakh seismorazvedki, Nauka, L., 1973

[4] J. F. Claerbout, “Toward a unified theory of reflector mapping”, Geophysics, 36:3 (1971), 467–481 | DOI

[5] J. F. Claerbout, S. M. Doherty, “Downward continuation of moveout-corrected seismograms”, Geophysics, 37:5 (1972), 741–768 | DOI

[6] J. F. Claerbout, Imaging the Earth's Interior, Stanford University, Stanford, 1984

[7] J. Gazdag, “Wave-equation migration with the phase-shift method”, Geophysics, 43:12 (1978), 1342–1351 | DOI

[8] R. H. Stolt, “Migration by Fourier transform”, Geophysics, 43:1 (1978), 23–48 | DOI

[9] W. S. Schneider, “Integral formulation for migration in two or three dimensions”, Geophysics, 43:1 (1978), 49–76 | DOI

[10] J. F. Claerbout, Fundamentals of Geophysical Data Processing, McGraw Hill, 1976

[11] L. D. Landau, E. M. Lifshits, Elektrodinamika sploshnykh sred, Nauka, M., 1982 | MR

[12] R. Kurant, Uravneniya s chastnymi proizvodnymi, Mir, M., 1964 | MR

[13] E. T. Uitteker, Dzh. N. Vatson, Kurs sovremennogo analiza, v. 1, Fizmatgiz, M., 1963