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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/sjvm20
https://www.mathnet.ru/eng/sjvm/v12/i3/p325
This publication is cited in the following 2 articles:
An. G. Marchuk, “The assessment of tsunami heights above the parabolic bottom relief within the wave-ray approach”, Num. Anal. Appl., 10:1 (2017), 17–27
Galaktionova A., Belonosov A., “Computation of Seismic Wave Field Kinematics in a Three-Dimensional Heterogeneous Isotropic Medium”, Application of Mathematics in Technical and Natural Sciences, AIP Conference Proceedings, 1895, ed. Todorov M., Amer Inst Physics, 2017, UNSP 120004-1
Citation in format AMSBIB
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