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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2009, Volume 12, Number 3, Pages 325–339 (Mi sjvm20)  
This article is cited in 2 scientific papers (total in 2 papers)

Calculation formulas of linear geometrical spreading at ray tracing in a 3D block-inhomogeneous gradient medium

V. A. Tsetsocho, A. V. Belonosovaa, A. S. Belonosova

a Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences
Full-text PDF (231 kB) Citations (2)
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Abstract: In this paper, recurrent formulas, suitable for direct programming, to calculate a linear geometrical spreading of the central field of seismic rays in a 3D block-gradient medium needed for organizing shooting to area observation systems have been obtained.
For recalculation formulas through the interface, a new representation using a special operator of nonorthogonal projection allowing an additive separation of terms depending only on the ray curvature, the boundary curvature, and the variable character of the velocities ratio along the boundary, has been found.
Formulas for partial derivatives of the eikonal via linear and angular geometrical spreading are presented.
Key words: ray method, geometrical spreading, ray tracing, 3D shooting.
Received: 26.12.2008
English version:
Numerical Analysis and Applications, 2009, Volume 2, Issue 3, Pages 260–271
DOI: https://doi.org/10.1134/S1995423909030070
Bibliographic databases:
UDC: 550.834.681.3
Language: Russian
Citation: V. A. Tsetsocho, A. V. Belonosova, A. S. Belonosov, “Calculation formulas of linear geometrical spreading at ray tracing in a 3D block-inhomogeneous gradient medium”, Sib. Zh. Vychisl. Mat., 12:3 (2009), 325–339; Num. Anal. Appl., 2:3 (2009), 260–271
Citation in format AMSBIB
\Bibitem{TseBelBel09}
\by V.~A.~Tsetsocho, A.~V.~Belonosova, A.~S.~Belonosov
\paper Calculation formulas of linear geometrical spreading at ray tracing in a~3D block-inhomogeneous gradient medium
\jour Sib. Zh. Vychisl. Mat.
\yr 2009
\vol 12
\issue 3
\pages 325--339
\mathnet{http://mi.mathnet.ru/sjvm20}
\transl
\jour Num. Anal. Appl.
\yr 2009
\vol 2
\issue 3
\pages 260--271
\crossref{https://doi.org/10.1134/S1995423909030070}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-71449096877}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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