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Volume 53, Issue 3
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

The phase error between the real phase shift and the Gazdag background phase shift, due to lateral velocity variations about a reference velocity, can be decomposed into axial and paraxial phase errors. The axial phase error depends only on velocity perturbations and hence can be completely removed by the split‐step Fourier method. The paraxial phase error is a cross function of velocity perturbations and propagation angles. The cross function can be approximated with various differential operators by allowing the coefficients to vary with velocity perturbations and propagation angles. These variable‐coefficient operators require finite‐difference numerical implementation. Broadband constant‐coefficient operators may provide an efficient alternative that approximates the cross function within the split‐step framework and allows implementation using Fourier transforms alone. The resulting migration accuracy depends on the localization of the constant‐coefficient operators. A simple broadband constant‐coefficient operator has been designed and is tested with the SEG/EAEG salt model. Compared with the split‐step Fourier method that applies to either weak‐contrast media or at small propagation angles, this operator improves wavefield extrapolation for large to strong lateral heterogeneities, except within the weak‐contrast region. Incorporating the split‐step Fourier operator into a hybrid implementation can eliminate the poor performance of the broadband constant‐coefficient operator in the weak‐contrast region. This study may indicate a direction of improving the split‐step Fourier method, with little loss of efficiency, while allowing it to remain faster than more precise methods such as the Fourier finite‐difference method.

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2005-04-14
2024-04-25

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References

  1. AkiK. and RichardsP.G.1980. Quantitative Seismology . W.H. Freeman.DOI: 10.1029/97JB02757DOI: 10.1029/93JB02518
     [Google Scholar]
  2. AminzadehF., BurkhardN., KunzT., NicoletisL. and RoccaF.1995. 3‐D modeling project. 3rd report. The Leading Edge14, 125–128.DOI: 10.1190/1.1437102
     [Google Scholar]
  3. CollinsM.D.1993. A split‐step Padé solution for the parabolic equation method. Journal of the Acoustical Society of America93, 1736–1742.
    [Google Scholar]
  4. CollinsM.D.1994. Generalization of the split‐step Padé solution. Journal of the Acoustical Society of America96, 382–385.
    [Google Scholar]
  5. FuL.Y.2002. Seismogram synthesis for piecewise heterogeneous media. Geophysical Journal International150, 800–808.DOI: 10.1046/j.1365-246X.2002.01752.x
     [Google Scholar]
  6. FuL.Y.2003. Numerical study of generalized Lippmann–Schwinger integral equation including surface topography. Geophysics68, 665–671.DOI: 10.1190/1.1567236
     [Google Scholar]
  7. FuL.Y., MuY.G. and YangH.J.1997. Forward problem of nonlinear Fredholm integral equation in reference medium via velocity‐weighted wavefield function. Geophysics62, 650–656.DOI: 10.1190/1.1444173
     [Google Scholar]
  8. GazdagJ.1978. Wave equation migration with the phase‐shift method. Geophysics43, 1342–1351.DOI: 10.1190/1.1440899
     [Google Scholar]
  9. GazdagJ. and SguazzeroP.1984. Migration of seismic data by phase shift plus interpolation. Geophysics49, 124–131.DOI: 10.1190/1.1441643
     [Google Scholar]
  10. HanB.1998. A comparison of four depth‐migration methods. 68th SEG meeting, New Orleans , USA , Expanded Abstracts, 1104–1107.
  11. HardinR.H. and TappertF.D.1973. Applications of the split‐step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations. SIAM Review15, 423.
    [Google Scholar]
  12. HobbsR.W.2003. 3D Modelling of Seismic Wave Propagation using Complex Elastic Screens with Application to Mineral Exploration . Special Volume on Hardrock Geophysics. Society of Exploration Geophysicists, Tulsa , OK .
    [Google Scholar]
  13. De HoopM.V.1996. Generalization of the Bremmer coupling series. Journal of Mathematical Physics37, 3246–3282.DOI: 10.1063/1.531566
     [Google Scholar]
  14. De HoopM.V., Le RousseauJ.H. and WuR.S.2000. Generalization of the phase‐screen approximation for the scattering of acoustic waves. Wave Motion31, 43–70.DOI: 10.1016/S0165-2125(99)00026-8
     [Google Scholar]
  15. HuangL.J., FehlerM.C., RobertsP.M. and BurchC.C.1999. Extended local Rytov Fourier migration method. Geophysics64, 1535–1545.DOI: 10.1190/1.1444657
     [Google Scholar]
  16. KessingerW.1992. Extended split‐step Fourier migration. 62nd SEG meeting, New Orleans , USA , Expanded Abstracts, 917–920.
  17. KneppD.L.1983. Multiple phase‐screen calculation of the temporal behavior of stochastic waves. Proceedings of the IEEE71, 722–737.
    [Google Scholar]
  18. MartinJ.M. and FlattéS.M.1988. Intensity images and statistics from numerical simulation of wave propagation in 3‐D random media. Applied Optics27, 2111–2126.
    [Google Scholar]
  19. RistowD. and RühlT.1994. Fourier finite‐difference migration. Geophysics59, 1882–1893.DOI: 10.1190/1.1443575
     [Google Scholar]
  20. StoffaP.L., FakkemaJ.T., De Luna FreireR.M. and KessingerW.P.1990. Split‐step Fourier migration. Geophysics55, 410–421.DOI: 10.1190/1.1442850
     [Google Scholar]
  21. TappertF.D.1977. The parabolic approximation method. In: Wave Propagation and Underwater Acoustics (eds J.B.Keller and J.S.Papadakis ), Lecture Notes in Physics, Vol. 70, pp. C224–C287. Springer‐Verlag, Inc.
     [Google Scholar]
  22. ThomsonD.J. and ChapmanN.R.1983. A wide‐angle split‐step algorithm for the parabolic equation. Journal of the Acoustical Society of America74, 1848–1854.
    [Google Scholar]
  23. WildA.J. and HudsonJ.A.1998. A geometrical approach to the elastic complex screen. Journal of Geophysical Research103, 707–725.
    [Google Scholar]
  24. WuR.S.1994. Wide‐angle elastic wave one‐way propagation in heterogeneous media and an elastic wave complex‐screen method. Journal of Geophysical Research99, 751–766.
    [Google Scholar]
  25. WuR.S.1996. Synthetic seismogram in heterogeneous media by one‐return approximation. Pure and Applied Geophysics148, 155–173.DOI: 10.1007/BF00882059
     [Google Scholar]
  26. WuR.S. and JinS.1997. Windowed GSP (generalized screen propagators) migration applied to SEG/EAEG salt model data. 67th SEG meeting, Dallas , USA , Expanded Abstracts, 1746–1749.
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Broadband constant‐coefficient propagators
Geophysical Prospecting 53, 299 (2005); https://doi.org/10.1111/j.1365-2478.2005.00474.x
/content/journals/10.1111/j.1365-2478.2005.00474.x
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