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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 379, Pages 88–102 (Mi znsl3839)  
This article is cited in 4 scientific papers (total in 4 papers)

Comparison of the Hill's method with the seismic depth migration by the Gaussian beam summation method

M. M. Popov, P. M. Popov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (853 kB) Citations (4)
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Abstract: The mathematical basement of the Hill's method of prestack depth migration is analyzed. It is shown that this method should be classified as the ray based Kirchhoff migration with so called “fat” rays, that is where the rays are substituted by isolated Gaussian beams centered on the rays and associated somehow with the input data on the seismic surface. That makes essential difference with our approach to seismic depth migration based on Gaussian beam summation method. We display on numerical examples the results of implementation of basic Hill's idea in the wave field computations. Bibl. 10 titles.
Key words and phrases: seismic depth migration, ray method, Gaussian beams.
Received: 15.10.2010
English version:
Journal of Mathematical Sciences (New York), 2011, Volume 173, Issue 3, Pages 291–298
DOI: https://doi.org/10.1007/s10958-011-0251-8
Bibliographic databases:
Document Type: Article
UDC: 550.341
Language: Russian
Citation: M. M. Popov, P. M. Popov, “Comparison of the Hill's method with the seismic depth migration by the Gaussian beam summation method”, Mathematical problems in the theory of wave propagation. Part 39, Zap. Nauchn. Sem. POMI, 379, POMI, St. Petersburg, 2010, 88–102; J. Math. Sci. (N. Y.), 173:3 (2011), 291–298
Citation in format AMSBIB
\Bibitem{PopPop10}
\by M.~M.~Popov, P.~M.~Popov
\paper Comparison of the Hill's method with the seismic depth migration by the Gaussian beam summation method
\inbook Mathematical problems in the theory of wave propagation. Part~39
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 379
\pages 88--102
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3839}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 173
\issue 3
\pages 291--298
\crossref{https://doi.org/10.1007/s10958-011-0251-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952247689}
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  • https://www.mathnet.ru/eng/znsl/v379/p88
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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