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Volume 63, Issue 2
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Seismic diffracted waves carry valuable information for identifying geological discontinuities. Unfortunately, the diffraction energy is generally too weak, and standard seismic processing is biased to imaging reflection. In this paper, we present a dynamic diffraction imaging method with the aim of enhancing diffraction and increasing the signal‐to‐noise ratio. The correlation between diffraction amplitudes and their traveltimes generally exists in two forms, with one form based on the Kirchhoff integral formulation, and the other on the uniform asymptotic theory. However, the former will encounter singularities at geometrical shadow boundaries, and the latter requires the computation of a Fresnel integral. Therefore, neither of these methods is appropriate for practical applications. Noting the special form of the Fresnel integral, we propose a least‐squares fitting method based on double exponential functions to study the amplitude function of diffracted waves. The simple form of the fitting function has no singularities and can accelerate the calculation of diffraction amplitude weakening coefficients. By considering both the fitting weakening function and the polarity reversal property of the diffracted waves, we modify the conventional Kirchhoff imaging conditions and formulate a diffraction imaging formula. The mechanism of the proposed diffraction imaging procedure is based on the edge diffractor, instead of the idealized point diffractor. The polarity reversal property can eliminate the background of strong reflection and enhance the diffraction by same‐phase summation. Moreover,the fitting weakening function of diffraction amplitudes behaves like an inherent window to optimize the diffraction imaging aperture by its decaying trend. Synthetic and field data examples reveal that the proposed diffraction imaging method can meet the requirement of high‐resolution imaging, with the edge diffraction fully reinforced and the strong reflection mostly eliminated.

Copyright © 2015 European Association of Geoscientists & Engineers © 2014 European Association of Geoscientists & Engineers
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2014-11-07
2024-04-19

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References

  1. AsgedomE. G., GeliusL. J. and AustengA.2011. A new approach to post‐stack diffraction separation. EAGE, Expanded Abstracts.
  2. AudebertF., NicholsD., RekdalT., BiondiB., LumleyD. E. and UrdanetaH.1997. Imaging complex geological structure with single‐arrival Kirchhoff prestack depth migration. Geophysics62(5), 1533–1543.
     [Google Scholar]
  3. BakerB. B. and CopsonE. T.1939. The mathematical theory of Huygens' principle. Oxford University Press.
     [Google Scholar]
  4. BansalR. and ImhofM.G.2005. Diffraction enhancement in prestack seismic data. Geophysics70(3), V73–V79.
     [Google Scholar]
  5. BerkovitchA., BelferI., HassinY. and LandaE.2009. Diffraction imaging by multifocusing. Geophysics74(6), WCA75–WCA81.
     [Google Scholar]
  6. BerryhillJ. R.1977. Diffraction response for nonzero separation of source and receiver. Geophysics42(6), 1158–1176.
     [Google Scholar]
  7. BurgD.W. and VerdelA.R.2011. Depth migration of edge diffractions by adaptive weighting of migration operator amplitudes. EAGE, Expanded Abstracts.
  8. ClemmowP. C.1950. A note on the diffraction of a cylindrical wave by a perfectly conducting half plane. The Quarterly Journal of Mechanics and Applied Mathematics3, 377–384.
     [Google Scholar]
  9. ClemmowP. C.1951. A Method for the Exact Solution of a Class of Two‐Dimensional Diffraction Problems. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences205, 286–308.
     [Google Scholar]
  10. CopsonE. T.1950. Diffraction by a plane screen. Proceedings of the Royal Society of London202, 277–284.
     [Google Scholar]
  11. DellS. and GajewskiD.2011. Common‐reflection‐surface‐based workflow for diffraction imaging. Geophysics76, S187–S195.
     [Google Scholar]
  12. DeregowskiS. M. and BrownS. M.1983. A theory of acoustic diffractions applied to 2‐D models. Geophysical Prospecting31, 293–333.
     [Google Scholar]
  13. FelsenL. B.1984. Geometrical theory of diffraction, evanescent wave, complex rays and Gaussian beams. Geophysical Journal of the Royal Astronomical Society79, 77–88.
     [Google Scholar]
  14. FomelS.2002. Applications of plane‐wave destruction filters. Geophysics67, 1946–1960.
     [Google Scholar]
  15. FomelS., LandaE. and TanerM. T.2006. Post‐stack velocity analysis by separation and imaging of seismic diffraction. 76th SEG meeting, New Orleans,Lousiana, USA, Expanded Abstracts, 2559–2563.
  16. FomelS., LandaE. and TanerM. T.2007. Poststack velocity analysis by separation and imaging of seismic diffractions. Geophysics72(6), U89–U94.
     [Google Scholar]
  17. GelchinskyB. Ja.1982. Scattering of waves by a quasi‐thin body of arbitrary shape. Geophysical Journal of the Royal Astronomical Society71(2), 425–453.
     [Google Scholar]
  18. GeoltrainS. and BracJ.1993. Can we image complex structures with first‐arrival traveltimes?Geophysics58(4), 564–575.
     [Google Scholar]
  19. GoodmanJ. W.1968. Introduction to fourier optics. Mcgraw‐hill, New York.
     [Google Scholar]
  20. GrayS. H. and MayW. P., 1994. Kirchhoff migraton using eikonal equation traveltimes. Geophysics59(5), 810–817.
     [Google Scholar]
  21. HagedoornJ. G.1954. A process of seismic reflection interpretation. Geophysical Prospecting2(2), 85–127.
     [Google Scholar]
  22. HarlanW., ClaerboutJ. and RoccaF.1984. Signal/noise separation and velocity estimation. Geophysics49(11), 1869–1880.
     [Google Scholar]
  23. HiltermanF. J.1970.Three‐dimensional seismic modeling. Geophysics35(6), 1020–1037.
     [Google Scholar]
  24. HiltermanF. J.1975. Amplitudes of seismic waves: a quick look. Geophysics40(5), 745–762.
     [Google Scholar]
  25. KanasewichE. R. and PhadkeS. M.1988. Imaging discontinuities on seismic section. Geophysics53(3), 334–345.
     [Google Scholar]
  26. KellerJ. B.1962. Geometrical theory of diffraction. Journal of the Acoustical Society of America52, 116–130.
     [Google Scholar]
  27. KellerJ. B.1985. One hundred years of diffraction theory. IEEE Transactions on Antennas and Propagation33(2), 123–126.
     [Google Scholar]
  28. KhaidukovV., LandaE. and MoserT. J.2004. Diffraction imaging by focusing and defocusing: An outlook on seismic superresolution. Geophysics69, 1478–1490.
     [Google Scholar]
  29. Klem‐MusatovK. D. and AizenbergA. M.1980. The ray method and the theory of edge waves. Geophysical Journal of the Royal Astronomical Society79(1), 35–50.
     [Google Scholar]
  30. Klem‐MusatovK.1994. Theory of Seismic Diffractions. SEG, Tulsa.
     [Google Scholar]
  31. Klem‐MusatovK., AizenbergA. M., PajchelJ. and HelleA.B.2008. Edge and tip diffractions theory and applications in seismicporspecting .SEG.
     [Google Scholar]
  32. KlokovA. and FomelS.2012. Separation and imaging of seismic diffractions using migrated dip‐angle gathers. Geophysics77(6), S131–S143.
     [Google Scholar]
  33. Kozlove., BaraskyN. and KorolevE.2004. Imaging scattering objects masked by specular reflections. SEG, Expanded Abstracts.
  34. KreyT.1952. The significance of diffraction in the investigation of faults. Geophysics17(4), 843–858.
     [Google Scholar]
  35. Kunz. B. F. J.,1960. Diffraction problems in fault Interpretation. Geophysical Prospecting8(3), 381–388.
     [Google Scholar]
  36. LandaE. and FomelS.2008. Separation, imaging, and velocity analysis of seismic diffractions using migrated dip‐angle gathers. SEG, Expanded Abstracts, 2176–2180.
  37. LandaE. and KeydarS.1998. Seismic monitoring of diffraction images for detection of local heterogeneities. Geophysics63(3), 1093–1110.
     [Google Scholar]
  38. LandaE., ShtivelmanV. and GelchinskyB.1987. A method for detection of diffracted waves on comon‐offset sections. Geophysical Prospecting35(4), 359–373.
     [Google Scholar]
  39. LewisR. M. and BoersmaJ.1969. Uniform asymptotic theory of edge diffraction. Journal of Mathematical Physics10, 2291–2305.
     [Google Scholar]
  40. LonghurstR. S.1973. Geometrical and Physical Optics. Longman, Harlow.
     [Google Scholar]
  41. MarfurtK. J., KirlinR. L., FarmerS. L. and BahorichM. S.1998. 3‐D seismic attributes using a semblance‐based coherency algorithm. Geophysics63, 1150–1165.
     [Google Scholar]
  42. MorseP. M. and FeshbachH.1953. Methods of Theoretical Physics. McGraw‐Hill, New York.
     [Google Scholar]
  43. MorseP. M. and IngardK. U.1968. Theoretical Acoustics. McGraw‐Hill, New York.
     [Google Scholar]
  44. MoserT. J. and HowardC. B., 2008. Diffraction imaging in depth. Geophysical Prospecting56(5), 627–641.
     [Google Scholar]
  45. MoserT. J.1994. Migration using the shortest‐path method. Geophysics59(7),1110–1120.
     [Google Scholar]
  46. Nichols, D. E.,1996. Maximum energy traveltimes calculated in the seismic frequency band. Geophysics61(1), 253–263.
     [Google Scholar]
  47. OpertoM. S., XuS. and LambaréG.2000. Can we quantitatively image complex structures with rays?Geophysics65(4), 1223–1238.
     [Google Scholar]
  48. ReshefM. and LandaE.2009. Post‐stack velocity analysis in the dip‐angle domain using diffractions. Geophysical Prospecting57(5), 811–821.
     [Google Scholar]
  49. TanerM. T., FomelS. and LandaE.2006. Separation and imaging of seismic diffractions using plane‐wave decomposition. SEG, Expanded Abstracts, 2006–2401.
  50. TroreyA. W.1970. A simple theory for seismic diffractions. Geophysics35, 762–784.
     [Google Scholar]
  51. TroreyA. W.1977. Diffraction theory for arbitrary source‐receiver locations. Geophysics42(6), 1177–1182
     [Google Scholar]
  52. TygelM., SchleicherJ., HubralP. and HanitzschC.1993. Multiple weights in diffraction stack migration. Geophysics59, 1820–1830.
     [Google Scholar]
  53. WangY. F. and YuanY. X.2005. Convergence and regularity of trust region methods for nonlinear ill‐posed inverse problems. Inverse Problems21, 821–838.
     [Google Scholar]
  54. WangY. F.2007. Computational Methods for Inverse Problems and Their Applications(in Chinese). Higher Education Press, Beijing.
     [Google Scholar]
  55. ZhangR. F.2004. Fresnel aperture and diffraction prestack depth migration. CDSST annual report, 1–11.
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Diffraction imaging by uniform asymptotic theory and double exponential fitting
Geophysical Prospecting 63, 338 (2015); https://doi.org/10.1111/1365-2478.12199
/content/journals/10.1111/1365-2478.12199
/content/journals/10.1111/1365-2478.12199
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  • Article Type: Research Article
Keyword(s): Diffraction amplitude; Diffraction imaging; Exponential fitting; Kirchhoff diffraction; Uniform asymptotic theory

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