1887
  1. Home
  2. A-Z Publications
  3. Geophysical Prospecting
  4. Volume 61, Issue 3
  5. Article
Volume 61, Issue 3
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

I introduce a new explicit form of vertical seismic profile (VSP) traveltime approximation for a 2D model with non‐horizontal boundaries and anisotropic layers. The goal of the new approximation is to dramatically decrease the cost of time calculations by reducing the number of calculated rays in a complex multi‐layered anisotropic model for VSP walkaway data with many sources. This traveltime approximation extends the generalized moveout approximation proposed by Fomel and Stovas. The new equation is designed for borehole seismic geometry where the receivers are placed in a well while the sources are on the surface. For this, the time‐offset function is presented as a sum of odd and even functions. Coefficients in this approximation are determined by calculating the traveltime and its first‐ and second‐order derivatives at five specific rays. Once these coefficients are determined, the traveltimes at other rays are calculated by this approximation. Testing this new approximation on a 2D anisotropic model with dipping boundaries shows its very high accuracy for offsets three times the reflector depths. The new approximation can be used for 2D anisotropic models with tilted symmetry axes for practical VSP geometry calculations. The new explicit approximation eliminates the need of massive ray tracing in a complicated velocity model for multi‐source VSP surveys. This method is designed not for NMO correction but for replacing conventional ray tracing for time calculations.

© 2012 European Association of Geoscientists & Engineers
Loading

Article metrics loading...

/content/journals/10.1111/j.1365-2478.2012.01100.x
2012-10-15
2024-04-28

  • From This Site

    /content/journals/10.1111/j.1365-2478.2012.01100.x
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. AlkhalifahT.2000. The offset‐midpoint traveltime equation for transversely isotropic media. Geophysics 65, 1316–1325.
    [Google Scholar]
  2. AlkhalifahT.2011. Traveltime approximations for transversely isotropic media with an inhomogeneous background. Geophysics 76, WA31–42.
    [Google Scholar]
  3. AlkhalifahT. and SavaP.2010. A transversely isotropic medium with a tilted symmetry axis normal to the reflector. Geophysics , A19–A24.
    [Google Scholar]
  4. AlkhalifahT. and TsvankinI.1995. Velocity analysis for transversely isotropic media. Geophysics 60, 1550–1566.
    [Google Scholar]
  5. BliaE.A.1983. Reflected wave's traveltime curve in flat‐bedded medium with transverse layers and their interpretation. Soviet Geology and Geophysics N2, 91–95.
    [Google Scholar]
  6. BliasE.A.2009. Long‐offset NMO approximations for a layered VTI model: Model study. 79th Annual International Meeting, SEG, 3745–3748.
  7. 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]
  8. CervenyV.2001. Seismic Ray Theory . Cambridge University Press.
    [Google Scholar]
  9. FomelS. and StovasA.2010. Generalized nonhyperbolic moveout approximation. Geophysics 75, U9–U18.
    [Google Scholar]
  10. FowlerP.J.2003. Practical VTI approximations: A systematic anatomy. Journal of Applied Geophysics 54, 347–367.
    [Google Scholar]
  11. HakeH., HelbigK. and MesdagC.S.1984. Three‐term Taylor series for t2– x2 curves over layered transversely isotropic ground. Geophysical Prospecting 32, 828–850.
    [Google Scholar]
  12. MalovichkA.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]
  13. PeiD., CornishB., ZhouR., QuinnD. and WilliamsonR.2011. A VFSA Method of Travel Time Inversion for Layer Interval Anisotropy Estimation Using Walk‐away VSP. Borehole Geophysics Workshop, Istanbul , BGP05.
  14. TanerM.T. and KoehlerF.1969. Velocity spectra – Digital computer derivation and applications of velocity functions. Geophysics 34, 859–881. (Errata in GEO‐36–4‐0787).
     [Google Scholar]
  15. ThomsenL.1986. Weak elastic anisotropy. Geophysics 51, 1954–1966.
    [Google Scholar]
  16. TsvankinI. and GrechkaV.2011. Seismology of Azimuthally Anisotropic Media and Seismic Fracture Characterization, 491. SEG, Tulsa .
  17. TsvankinI. and ThomsenL.1994. Nonhyperbolic reflection moveout in anisotropic media. Geophysics 59, 1290–1304.
    [Google Scholar]
  18. UrsinB. and StovasA.2006. Traveltime approximations for a layered transversely isotropic medium. Geophysics 71, D23–D33.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/j.1365-2478.2012.01100.x
Loading
Moveout approximation for vertical seismic profile geometry in a 2D model with anisotropic layers
Geophysical Prospecting 61, 574 (2013); https://doi.org/10.1111/j.1365-2478.2012.01100.x
/content/journals/10.1111/j.1365-2478.2012.01100.x
/content/journals/10.1111/j.1365-2478.2012.01100.x
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Anisotropic; Moveout

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error