1887
Volume 61 Number 6
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

This paper discusses reducing computation costs for traveltime calculations in multi‐layered anisotropic models. Fomel and Stovas (2010) suggested a two‐ray five‐parameter approximation that they named ‘generalized’ because it reduces to several known three‐parameter forms. Model tests, demonstrated by the authors, showed that this generalized approximation provided very high accuracy, implying it can be used in place of the exact moveout function in modelling, migration and traveltime inversion. However, detailed model studies show that for some models, with a high‐velocity layer, this approximation leads to significant errors. I develop a new three‐ray eight‐parameter approximation that provides higher accuracy and can replace the exact traveltime function that requires numerical ray calculations for each receiver. I call it a ‘two‐interval approximation’ because it uses two different equations for two offset intervals. Model tests show that this two‐interval approximation can bring much higher accuracy compared to the generalized approximation due to the use of an additional reference ray. The two‐interval new approximation can be used instead of exact traveltimes for many practical purposes.

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/content/journals/10.1111/1365-2478.12059
2013-08-22
2024-03-29
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References

  1. AleixoR. and SchleicherJ.2010. Traveltime approximations for q‐P waves in vertical transversely isotropic media. Geophysical Prospecting58, 191–201.
    [Google Scholar]
  2. AlkhalifahT.2000. The offset‐midpoint traveltime equation for transversely isotropic media. Geophysics65, 1316–1325.
    [Google Scholar]
  3. AlkhalifahT.2011. Traveltime approximations for transversely isotropic media with an inhomogeneous background. Geophysics76, WA31–42.
    [Google Scholar]
  4. AlkhalifahT. and SavaP.2010. A transversely isotropic medium with a tilted symmetry axis normal to the reflector. Geophysics, A19–A24.
    [Google Scholar]
  5. AlkhalifahT. and TsvankinI.1995. Velocity analysis for transversely isotropic media. Geophysics60, 1550–1566.
    [Google Scholar]
  6. BliasE.A.1983. Reflected wave's traveltime curve in flat‐bedded medium with transverse layers and their interpretation. Soviet Geology and GeophysicsN2, 91–95.
    [Google Scholar]
  7. BliasE.A.2009. Long‐offset NMO approximations for a layered VTI model: Model study. 79th SEG Annual Meeting, 3745–3748.
    [Google Scholar]
  8. BliasE.A.2013. Moveout approximation for vertical seismic profile geometry in a 2D model with anisotropic layers. Geophysical Prospecting61, 574–581.
    [Google Scholar]
  9. BolshykhS.F.1956. About an approximate representation of the reflected wave traveltime curve in the case of a multi‐layered medium. Applied Geophysics (in Russian) 15, 3–15.
    [Google Scholar]
  10. FomelS.2004. On anelliptic approximations for qP velocities in VTI media. Geophysical Prospecting52, 247–59.
    [Google Scholar]
  11. FomelS. and StovasA.2010. Generalized nonhyperbolic moveout approximation. Geophysics75, U9–U18.
    [Google Scholar]
  12. GoldinS.V.1986. Seismic Traveltime Inversion. Society of Exploration Geophysicists.
  13. GolikovP. and StovasA.2012. Accuracy comparison of nonhyperbolic moveout approximations for qP‐waves in VTI media. Journal of Geophysics and Engineering9, 428–432.
    [Google Scholar]
  14. HakeH., HelbigK. and MesdagC.S.1984. Three‐term Taylor series for t2 – x2 curves over layered transversely isotropic ground. Geophysical Prospecting32, 828–850.
    [Google Scholar]
  15. MalovichkoA.A.1978. A new representation of the traveltime curve of reflected waves in horizontally layered media. Applied Geophysics (in Russian) 91, 47–53. English translation in Sword (1987).
    [Google Scholar]
  16. PeiD., CornishB., QuinnD. and WarpinskiN.2009. Velocity calibration for microseismic monitoring: A very fast simulated annealing (VFSA) approach for joint‐objective optimization. Geophysics74, WCB47–WCB55.
    [Google Scholar]
  17. ThomsenL.1986. Weak elastic anisotropy. Geophysics51, 1954–1966.
    [Google Scholar]
  18. TsvankinI. and ThomsenL.1994. Nonhyperbolic reflection moveout in anisotropic media. Geophysics59, 1290–1304.
    [Google Scholar]
  19. UrsinB. and StovasA.2006. Traveltime approximations for a layered transversely isotropic medium. Geophysics71, D23–D33.
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): Anisotropy; Approximation; normal‐moveout; Traveltime

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