1887
Volume 33 Number 8
  • E-ISSN: 1365-2478

Abstract

A

Part I of this series starts with a brief review of the fundamental principles underlying wave field extrapolation. Next, the total wave field is split into downgoing and upgoing waves, described by a set of coupled one‐way wave equations. In cases of limited propagation angles and weak inhomogeneities these one‐way wave equations can be decoupled, describing primary waves only. For large propagation angles (up to and including 90°) an alternative choice of sub‐division into downgoing and upgoing waves is presented. It is shown that this approach is well suited for modeling as well as migration and inversion schemes for seismic data which include critical angle events.

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2006-04-27
2024-03-28
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References

  1. Abramowitz, M. and Stegun, I. A.1970, Handbook of Mathematical Functions, Dover, New York .
    [Google Scholar]
  2. Berkhout, A. J.1982, Seismic Migration, Elsevier, Amsterdam .
    [Google Scholar]
  3. Berkhout, A. J.1984, Multi‐dimensional linearized inversion and seismic migration, Geophysics49, 1881–1895.
    [Google Scholar]
  4. Brekhovskikh, L. M.1980, Waves in Layered Media, Academic Press, New York .
    [Google Scholar]
  5. Bremmer, H., 1951, The WKB approximation as the first term of a geometric‐optical series, Communications Pure and Applied Mathematics4, 105.
    [Google Scholar]
  6. Brillouin, L.1926, Remarques sur la mécanique ondulatoire, Journal de Physique et de Radium6, 353–368.
    [Google Scholar]
  7. Chapman, C. H.1976, Exact and approximate generalized ray theory in vertically inhomogeneous media, Geophysical Journal of the Royal Astronomical Society46, 201–233.
    [Google Scholar]
  8. Gazdag, J.1978, Wave equation migration with the phase shift method, Geophysics43, 1342–1351.
    [Google Scholar]
  9. Green, G.1837, On the motion of waves in a variable canal of small depth and width, Transactions of the Cambridge Philosophical Society6, 457–462.
    [Google Scholar]
  10. Jeffreys, H.1924, On certain approximate solutions of linear differential equations of the second order, Proceedings of the London Mathematical Society2, 428–436.
    [Google Scholar]
  11. Kennett, B. L. N. and Illingworth, M. R.1981, Seismic waves in a stratified half space—III, Piecewise smooth models, Geophysical Journal of the Royal Astronomical Society66, 633–675.
    [Google Scholar]
  12. Kramers, H. A.1926, Wellenmechanik und halbzahlige Quantisierung, Zeitschrift für Physik39, 828–840.
    [Google Scholar]
  13. Liouville, J.1837, Sur le développement des fonctions parties de fonctions en séries, Journal de mathématiques pures et appliquées1, 16–35.
    [Google Scholar]
  14. McHugh, J. A. M.1971, An historical survey of ordinary linear differential equations with a large parameter and turning points, Archives of the History of Exact Sciences7, 277–324.
    [Google Scholar]
  15. Olver, F. W. J.1974, Asymptotics and Special Functions, Academic Press, New York .
    [Google Scholar]
  16. Schneider, W. A.1978, Integral formulation in two and three dimensions, Geophysics43, 49–76.
    [Google Scholar]
  17. Wasow, W.1965, Asymptotic Expansions for Ordinary Differential Equations, Wiley, New York .
    [Google Scholar]
  18. Wentzel, G.1926, Eine Verallgemeinerung der Quantenbedingungen für die Zwecke der Wellenmechanik, Zeitschrift für Physik38, 518–529.
    [Google Scholar]
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  • Article Type: Research Article

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