1887
Volume 67, Issue 5
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Elastic least‐squares reverse time migration has been applied to multi‐component seismic data to obtain high‐quality images. However, the final images may suffer from artefacts caused by P‐ and S‐wave crosstalk and severe spurious diffractions caused by complex topographic surface conditions. To suppress these crosstalk artefacts and spurious diffractions, we have developed a topographic separated‐wavefield elastic least‐squares reverse time migration algorithm. In this method, we apply P‐ and S‐wave separated elastic velocity–stress wave equations in the curvilinear coordinates to derive demigration equations and gradient formulas with respect to P‐ and S‐velocity. For the implementation of topographic separated‐wavefield elastic least‐squares reverse time migration, the wavefields, gradient directions and step lengths are all calculated in the curvilinear coordinates. Numerical experiments conducted with the two‐component data synthetized by a three‐topographic‐layer with anomalies model and the Canadian Foothills model are considered to verify our method. The results reveal that compared with the conventional method, our method promises imaging results with higher resolution and has a faster residual convergence speed. Finally, we carry out numerical examples on noisy data, imperfect migration velocity and inaccurate surface elevation to analyse its sensitivity to noise, migration velocity and surface elevation error. The results prove that our method is less sensitive to noise compared with the conventional elastic least‐squares reverse time migration and needs good migration velocities as other least‐squares reverse time migration methods. In addition, when implementing the proposed method, an accurate surface elevation should be obtained by global positioning system to yield high‐quality images.

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2019-04-02
2020-04-05
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References

  1. AnagawA.Y. and SacchiM.D.2012. Edge‐preserving seismic imaging using the total variation method. Journal of Geophysics and Engineering9, 138–146.
    [Google Scholar]
  2. AokiN. and SchusterG.2009. Fast least‐squares migration with a deblurring filter. Geophysics74, WCA83–WCA93.
    [Google Scholar]
  3. ClaerboutJ.1992. Earth soundings analysis: Processing versus Inversion. Black‐well Scientific.
    [Google Scholar]
  4. DaiW., FowlerP. and SchusterG.2012. Multi‐source least‐squares reverse time migration. Geophysical Prospecting60, 681–695.
    [Google Scholar]
  5. DaiW., HuangY. and SchusterG.2013. Least‐squares reverse time migration of marine data with frequency‐selection encoding. Geophysics78, S233–S242.
    [Google Scholar]
  6. DaiW. and SchusterG.2013. Plane‐wave least‐squares reverse‐time migration. Geophysics78, S165–S177.
    [Google Scholar]
  7. DaiW., WangX. and SchusterG.2011. Least‐squares migration of multisource data with a deblurring filter. Geophysics76, R135–R146.
    [Google Scholar]
  8. DuquetB., MarfurtK. and DellingerJ.2000. Kirchhoff modeling, inversion for reflectivity, and subsurface illumination. Geophysics65, 1195–1209.
    [Google Scholar]
  9. EtgenJ., GrayS.H. and ZhangY.2009. An overview of depth imaging in exploration geophysics. Geophysics74, WCA5–WCA17.
    [Google Scholar]
  10. FengZ. and SchusterG. T.2017. Elastic least‐squares reverse time migration. Geophysics82, S143–S157.
    [Google Scholar]
  11. FomelS., BerrymanJ., ClappR. and PruchaM.2002. Iterative resolution estimation in least‐squares Kirchhoff migration. Geophysical Prospecting50, 577–588.
    [Google Scholar]
  12. FornbergB.1988. The pseudospectral method: accurate representation of interfaces in elastic wave calculations. Geophysics53, 625–637.
    [Google Scholar]
  13. GardnerG.H.F., GardnerL.W. and GregoryA.R.1974. Formation velocity and density‐the diagnostic basics for stratigraphic traps. Geophysics39, 770–780.
    [Google Scholar]
  14. GuB., LiZ. and HanJ.2018. A wavefield‐separation‐based elastic least‐squares reverse time migration. Geophysics83, S279‐S297.
    [Google Scholar]
  15. HestholmS.O. and RuudB.O.1994. 2D finite‐difference elastic wave modelling including surface topography. Geophysical Prospecting42, 371–390.
    [Google Scholar]
  16. HouJ. and SymesW.W.2015. An approximate inverse to the extended born modeling operator. Geophysics80, R331–R349.
    [Google Scholar]
  17. HuangY. and SchusterG. T.2012. Multisource least‐squares migration of marine streamer data with frequency‐division encoding. Geophysical Prospecting60, 663–680.
    [Google Scholar]
  18. JastramC. and TessmerE.1994. Elastic modeling on a grid with vertically varying spacing. Geophysical Prospecting42, 357–370.
    [Google Scholar]
  19. KaserM. and IgelH.2001. Numerical simulation of 2D wave propagation on unstructured grids using explicit differential operators. Geophysical Prospecting49, 607–619.
    [Google Scholar]
  20. KomatitschD. and TrompJ.2002. Spectral‐element simulations of global seismic wave propagation‐I. Validation. Geophysical Journal International149, 390–412.
    [Google Scholar]
  21. KöhnD., De NilD., KurzmannA., PrzebindowskaA. and BohlenT.2012. On the influence of model parametrization in elastic full waveform tomography. Geophysical Journal International191, 325–345.
    [Google Scholar]
  22. KuehlH. and SacchiM.1999. Least‐squares split‐step migration using the Hartley transform. SEG Technical Program Expanded Abstracts, 1548–1551.
  23. KuehlH. and SacchiM.2001. Split‐step WKBJ least‐squares migration/inversion of incomplete data. 5th SEGJ international symposium imaging technology.
  24. KuehlH. and SacchiM.2003. Least‐squares wave‐equation migration for AVP/AVA inversion. Geophysics68, 262–273.
    [Google Scholar]
  25. LebedevV.I.1964. Difference analogues of orthogonal decompositions, basic differential operators and some boundary problems of mathematical physics. USSR Computational Mathematics and Mathematical Physics4, 36–45.
    [Google Scholar]
  26. LevanderA.R.1988. Fourth‐order finite‐difference P‐SV seismograms. Geophysics53, 1425–1436.
    [Google Scholar]
  27. MoczoP.1989. Finite‐difference technique for SH‐waves in 2‐D media using irregular grids application to the seismic response problem. Geophysical Journal International99, 321–329.
    [Google Scholar]
  28. MoczoP., BystrickyE., KristekJ., CarcioneJ.M. and BouchonM.1997. Hybrid modeling of P‐SV seismic motion at inhomogeneous viscoelastic topographic structures. Bulletin of the Seismological Society of America87, 1305–1323.
    [Google Scholar]
  29. NemethT., WuC. and SchusterG.1999. Least‐squares migration of incomplete reflection data. Geophysics64, 208–221.
    [Google Scholar]
  30. NielsenP., BergP. and SkovgaardO.1994. Using the pseudospectral technique on curved grids for 2D acoustic forward modeling. Geophysical Prospecting42, 321–341.
    [Google Scholar]
  31. PlessixR.E. and MulderW. A.2004. Frequency‐domain finite‐difference amplitude‐preserving migration. Geophysical Journal International157, 975–987.
    [Google Scholar]
  32. PlessixR.E.2006. A review of the adjoint‐state method for computing the gradient of a functional with geophysical applications. Geophysical Journal International167, 495–503.
    [Google Scholar]
  33. QuY., HuangJ., LiZ. and LiJ.2017a. A hybrid grid method in an auxiliary coordinate system for irregular fluid‐solid interface modeling. Geophysical Journal International208, 1540–1556.
    [Google Scholar]
  34. QuY., LiZ., HuangJ., LiJ. and GuanZ.2017b. Elastic full‐waveform inversion for surface topography. Geophysics82, R269–R285.
    [Google Scholar]
  35. QuY., LiZ., HuangJ. and LiJ.2018a. Multi‐scale full waveform inversion for areas with irregular surface topography in an auxiliary coordinate system. Exploration Geophysics49, 68–80.
    [Google Scholar]
  36. QuY., LiJ., HuangJ. and LiZ.2018b. Elastic least‐squares reverse time migration with velocities and density perturbation. Geophysical Journal International212, 1033–1056.
    [Google Scholar]
  37. RonenS. and LinerC.2000. Least‐squares DMO and migration. Geophysics65, 1364–1371.
    [Google Scholar]
  38. TanS. and HuangL.2014. Least‐squares reverse‐time migration with a wavefield‐separation imaging condition and updated source wavefields. Geophysics79, S195–S205.
    [Google Scholar]
  39. TessmerE. and KosloffD.1994. 3D elastic modelling with surface topography by a Chebychev spectral method. Geophysics59, 464–473.
    [Google Scholar]
  40. TessmerE., KosloffD. and BehleA.1992. Elastic wave propagation simulation in the presence of surface topography. Geophysical Journal International108, 621–632.
    [Google Scholar]
  41. VirieuxJ.1986. P‐SV wave propagation in heterogeneous media: velocity‐stress finite‐difference method. Geophysics51, 889–901.
    [Google Scholar]
  42. WangJ. and SacchiM.D.2007. High‐resolution wave‐equation amplitude‐ variation‐with‐ray‐parameter (avp) imaging with sparseness constraints. Geophysics72, S11–S18.
    [Google Scholar]
  43. XueZ., ChenY., FomelS. and SunJ.2016. Seismic imaging of incomplete data and simultaneous‐source data using least‐squares reverse time migration with shaping regularization. Geophysics81, S11–S20.
    [Google Scholar]
  44. YaoG. and JakubowiczH.2012. Non‐linear least‐squares reverse‐time migration. SEG Technical Program Expanded Abstracts, 1–5.
  45. ZhangY., JiaY. and WangS.2006. 2D nearly orthogonal mesh generation with control distortion function. Journal of Computational Physics218, 549–571.
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): Elastic , Irregular grid and Least‐squares
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