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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Rank 59 out of 312 in category Mathematics and 93 out of 254 in Applied Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

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1569-3945
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Iterative continuation of wave fields and inverse problems

G. M. Tsibulchik

Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of Russian Academy of Science, Acad. Lavrent'ev Avenue, 6, Novosibirsk, 630090, Russia. E-mail:

Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 12, Issue 5, Pages 549–555, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/1569394042531323,

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An iterative process of continuation of wave fields is proposed to invert the wave equation. Inverse problems of two types are analyzed, namely: the problem of reconstruction of the right-hand side of the wave equation describing the wave sources and the inverse problem of wave scattering in an inhomogeneous medium. The latter problem is of great practical importance for applications. It is shown that for an observation system in which a source point coincides with a receiver point (the so-called "scheme of central rays" in seismic prospecting), the scattering problem is reduced to the Cauchy problem on a space-like surface and in an inhomogeneous reference medium. The solution of this problem is obtained by wave continuation at each iteration step with the reference velocity values specified at the previous step.

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