Volume 56 Number 1
  • E-ISSN: 1365-2478



In this paper, source‐receiver migration based on the double‐square‐root one‐way wave equation is modified to operate in the two‐way vertical traveltime (τ) domain. This tau migration method includes reasonable treatment for media with lateral inhomogeneity. It is implemented by recursive wavefield extrapolation with a frequency‐wavenumber domain phase shift in a constant background medium, followed by a phase correction in the frequency‐space domain, which accommodates moderate lateral velocity variations. More advanced τ‐domain double‐square‐root wave propagators have been conceptually discussed in this paper for migration in media with stronger lateral velocity variations. To address the problems that the full 3D double‐square‐root equation prestack tau migration could meet in practical applications, we present a method for downward continuing common‐azimuth data, which is based on a stationary‐phase approximation of the full 3D migration operator in the theoretical frame of prestack tau migration of cross‐line constant offset data. Migrations of synthetic data sets show that our tau migration approach has good performance in strong contrast media. The real data example demonstrates that common‐azimuth prestack tau migration has improved the delineation of the geological structures and stratigraphic configurations in a complex fault area.

Prestack tau migration has some inherent robust characteristics usually associated with prestack time migration. It follows a velocity‐independent anti‐aliasing criterion that generally leads to reduction of the computation cost for typical vertical velocity variations. Moreover, this τ‐domain source‐receiver migration method has features that could be of help to speed up the convergence of the velocity estimation.


Article metrics loading...

Loading full text...

Full text loading...


  1. AlkhalifahT.2000. Prestack phase‐shift migration of separate offsets. Geophysics65, 1179–1194.
    [Google Scholar]
  2. AlkhalifahT., FomelS. and BiondiB.2001. The space‐time domain: Theory and modelling for anisotropic media. Geophysical Journal International144, 105–113.
    [Google Scholar]
  3. AlkhalifahT.2003. Tau migration and velocity analysis: Theory and synthetic examples. Geophysics68, 1331–1339.
    [Google Scholar]
  4. BiondiB.2003. Narrow‐azimuth migration of marine streamer data. 73rd SEG meeting, Dallas , Texas , USA , Expanded Abstracts, 897–900.
  5. BiondiB. and PalacharlaG.1996. 3D prestack migration of common‐azimuth data. Geophysics61, 1822–1832.
    [Google Scholar]
  6. BiondiB., ClappR.G., FomelS. and AlkhalifahT.1998. Robust reflection tomography in the time domain. 68th SEG meeting, New Orleans , Louisiana , USA , Expanded Abstracts, 1847–1850.
  7. BleisteinN.1984. Mathematical Methods for Wave Phenomena . Academic Press.
    [Google Scholar]
  8. ChengJ.B., WangH.Z., MaZ.T. and YangS.Q.2003. Crossline common‐offset migration for narrow azimuth data set. 73rd SEG meeting, Dallas , Texas , USA , 901–904.
  9. ClaerboutJ.F.1985. Imaging the Earth's Interior . Blackwell.
    [Google Scholar]
  10. ClappR. and BiondiB.2000. Tau domain migration velocity analysis using angle CRP gathers and geologic constrains. 70th SEG meeting, Calgary , Canada , 926–929.
  11. ClaytonR.W. and StoltR.H.1981. A Born‐WKBJ inversion method for acoustic reaction data. Geophysics46, 1559–1567.
    [Google Scholar]
  12. DablainM.A.1986. The application of high‐order differencing to the scalar wave equation. Geophysics51, 54–66.
    [Google Scholar]
  13. DeregowskiS.M. and RoccaF.1981. Geometric optics and wave theory of constant offset sections in layered media. Geophysical Prospecting29, 374–406.
    [Google Scholar]
  14. EtrisE.L., CrabtreeN.J., DewarJ. and PickfordS.2001. True depth conversion: More than a pretty picture. CSEG Recorder11, 11–22.
    [Google Scholar]
  15. FowlerP.J.1997. A comparative overview of prestack time migration methods. 67th SEG meeting, Dallas , Texas , USA , 1571–1574
  16. HuangL.J. and WuR.S.1996. Prestack depth migration with acoustic screen propagators. 66th SEG meeting, Denver , Colorado , USA , Expanded Abstracts, 415–418.
  17. HuangL.J., MichaelC.F. and WuR.S.1999. Extended local Born Fourier migration method. Geophysics64, 1524–1534.
    [Google Scholar]
  18. JinS.W., MosherC.C. and WuR.S.2002. Offset‐domain pseudoscreen prestack depth migration. Geophysics67, 1895–1902.
    [Google Scholar]
  19. KessingerW.1992. Extended split‐step Fourier migration. 62nd SEG meeting, New Orleans , Louisiana , USA , Expanded Abstracts, 917–920.
  20. PestanaR., StoffaP. and SantosJ.R.2000. Plane wave prestack time migration. 70th SEG meeting, Calgary , Canada , Expanded Abstracts, 810–813.
  21. PopoviciA.M.1996. Prestack migration by split‐step DSR. Geophysics61, 1412–1416.
    [Google Scholar]
  22. PruchaM., BiondiB. and SymesW.1999. Angle‐domain common‐image gathers by wave‐equation. 69th SEG meeting, Houston , Texas , USA , Expanded Abstracts, 824–827.
  23. SchultzP. 1999. The Seismic Velocity Model as an Interpretation Asset. SEG Distinguished Instructor Short Course.
  24. StolkC.C. and De HoopM.V.2001. Seismic inverse scattering in the ‘wave‐equation’ approach. Preprint 2001‐047, The Mathematical Sciences Research Institute, http://msri.org/publications/preprints/2001.html.
  25. StolkC.C. and SymesW.W.2004. Kinematic artefacts in prestack depth migration. Geophysics69, 562–575.
    [Google Scholar]
  26. StolkC.C., De HoopM.V. and SymesW.W.2005. Kinematics of prestack source‐receiver migration. 75th SEG meeting, Houston , Texas , USA , Expanded Abstracts, 1866–1869.
  27. SunH.C., HuangL.J. and FehlerM.C.2005. Globally optimized Fourier finite‐difference migration in the offset domain. 75th SEG meeting, Houston , Texas , USA , 1858–1861.
  28. WuR.S. and De HoopM.V.1996. Accuracy analysis of screen propagators for wave extrapolation using a thin‐slab model. 66th SEG meeting, Denver , Colorado , USA , 419–422.

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