1887
Volume 63, Issue 1
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Most modern seismic imaging methods separate input data into parts (shot gathers). We develop a formulation that is able to incorporate all available data at once while numerically propagating the recorded multidimensional wavefield forward or backward in time. This approach has the potential for generating accurate images free of artiefacts associated with conventional approaches. We derive novel high‐order partial differential equations in the source–receiver time domain. The fourth‐order nature of the extrapolation in time leads to four solutions, two of which correspond to the incoming and outgoing P‐waves and reduce to the zero‐offset exploding‐reflector solutions when the source coincides with the receiver. A challenge for implementing two‐way time extrapolation is an essential singularity for horizontally travelling waves. This singularity can be avoided by limiting the range of wavenumbers treated in a spectral‐based extrapolation. Using spectral methods based on the low‐rank approximation of the propagation symbol, we extrapolate only the desired solutions in an accurate and efficient manner with reduced dispersion artiefacts. Applications to synthetic data demonstrate the accuracy of the new prestack modelling and migration approach.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12162
2014-10-08
2019-12-09
Loading full text...

Full text loading...

References

  1. Alkhalifah, T.1998. Acoustic approximations for processing in transversely isotropic media: Geophysics, 63, 623–631.
    [Google Scholar]
  2. Alkhalifah, T. and FomelS.2010. Source‐receiver two‐way wave extrapolation for prestack exploding‐reflector modeling and migration: SEG, Expanded Abstracts, 29, 2950–2955.
    [Google Scholar]
  3. AlkhalifahT. and FomelS.2011a. Angle gathers in wave‐equation imaging for transversely isotropic media: Geophysical Prospecting, 59, 422–431.
    [Google Scholar]
  4. AlkhalifahT. and FomelS.2011b. A stable implementation of the prestack exploding reflector modeling and migration: SEG Technical Program Expanded Abstracts, 30, 3851–3855.
    [Google Scholar]
  5. Baysal, E., D.D.Kosloff and J.W.C.Sherwood1983. Reverse time migration: Geophysics, 48, 1514–1524.
    [Google Scholar]
  6. Biondi, B.2002. Reverse time migration in midpoint‐offset coordinates: SEP‐Report, 111, 149–156.
    [Google Scholar]
  7. Claerbout, J.F.1985. Imaging the Earth's Interior: Blackwell Scientific Publications.
    [Google Scholar]
  8. Courant, R., K.Friedrichs and H.Lewy1928. Uber die partiellen differenzengleichungen der mathematischen physik: Mathematische Annalen, 100, 32–74.
    [Google Scholar]
  9. de Hoop, M.V., J.H.L.Rousseau and B.L.Biondi2003. Symplectic structure of wave‐equation imaging: a path‐integral approach based on the double‐square‐root equation: Geophysical Journal International, 153, 52–74.
    [Google Scholar]
  10. Duchkov, A. and M.V.de Hoop2009. Extended isochron rays in prestack depth migration, in 79th Annual International Meeting: Society of Exploration Geophysics3610–3614.
    [Google Scholar]
  11. Etgen, J. and S.Brandsberg‐Dahl2009. The pseudo‐analytical method: application of pseudo‐Laplacians to acoustic and acoustic anisotropic wave propagation, in 79th Annual International Meeting: Society of Exploration Geophysics2552–2556.
    [Google Scholar]
  12. Fomel, S.2011. Theory of 3‐D angle gathers in wave‐equation seismic imaging: Journal of Petroleum Exploration and Production Technology, 1, no. 1, 11–16.
    [Google Scholar]
  13. Fomel, S., L.Ying and X.Song2012. Seismic wave extrapolation using lowrank symbol approximation: Geophysical Prospecting, page in press.
    [Google Scholar]
  14. Fowler, P.J.1997. A comparative overview of prestack time migration methods: A comparative overview of prestack time migration methods: 67th Annual International Meeting: Society of Exploration Geophysics1571–1574.
    [Google Scholar]
  15. French, W.S.1974. Two‐dimensional and three‐dimensional migration of model‐experiment reflection profiles: Geophysics, 39, 265–277.
    [Google Scholar]
  16. Gazdag, J. and P.Sguazzero1984. Migration of seismic data by phase‐shift plus interpolation: Geophysics, 49, 124–131.
    [Google Scholar]
  17. Loewenthal, D., L.Lu, R.Roberson and J.Sherwood. 1976. The wave equation applied to migration: Geophysical Prospecting , 24, 380–399.
    [Google Scholar]
  18. Popovici, A.M.1996. Prestack migration by split‐step DsR: Geophysics, 61, 1412–1416.
    [Google Scholar]
  19. Sava, P. and B.Biondi2004. Wave‐equation migration velocity analysis. I. Theory: Geophysical Prospecting, 52, 593–606.
    [Google Scholar]
  20. Sava, P.C., B.Biondi and J.Etgen2005. Wave‐equation migration velocity analysis by focusing diffractions and reflections: Geophysics, 70, U19–U27.
    [Google Scholar]
  21. Sava, P.C. and S.Fomel2003. Angle‐domain common‐image gathers by wavefield continuation methods: Geophysics, 68, 1065–1074.
    [Google Scholar]
  22. SavaP.C. and FomelS.2005. Coordinate‐independent angle‐gathers for wave equation migration, in 75th Annual International Meeting: Society of Exploration Geophysics, 2052–2055.
    [Google Scholar]
  23. Song, X. and S.Fomel. 2011. Fourier finite‐difference wave propagation: Geophysics, 76, T123–T129.
    [Google Scholar]
  24. Versteeg, R.1994. The Marmousi experience: velocity model determination on a synthetic complex data set: The Leading Edge, 13, 927–936.
    [Google Scholar]
  25. Yilmaz, O.1979. Prestack partial migration: PhD thesis, Stanford University.
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12162
Loading
/content/journals/10.1111/1365-2478.12162
Loading

Data & Media loading...

  • Article Type: Research Article
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