1887
  1. Home
  2. A-Z Publications
  3. Geophysical Prospecting
  4. Volume 64, Issue 6
  5. Article
Volume 64, Issue 6
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

In many cases, seismic measurements are coarsely sampled in at least one dimension. This leads to aliasing artefacts and therefore to problems in the subsequent processing steps. To avoid this, seismic data reconstruction can be applied in advance. The success and reliability of reconstruction methods are dependent on the assumptions they make on the data. In many cases, wavefields are assumed to (locally) have a linear space–time behaviour. However, field data are usually complex, with strongly curved events. Therefore, in this paper, we propose the double focal transformation as an efficient way for complex data reconstruction. Hereby, wavefield propagation is formulated as a transformation, where one‐way propagation operators are used as its basis functions. These wavefield operators can be based on a macro velocity model, which allows our method to use prior information in order to make the data decomposition more effective. The basic principle of the double focal transformation is to focus seismic energy along source and receiver coordinates simultaneously. The seismic data are represented by a number of localized events in the focal domain, whereas aliasing noise spreads out. By imposing a sparse solution in the focal domain, aliasing noise is suppressed, and data reconstruction beyond aliasing is achieved. To facilitate the process, only a few effective depth levels need to be included, preferably along the major boundaries in the data, from which the propagation operators can be calculated. Results on 2D and 3D synthetic data illustrate the method's virtues. Furthermore, seismic data reconstruction on a 2D field dataset with gaps and aliased source spacing demonstrates the strength of the double focal transformation, particularly for near‐offset reflections with strong curvature and for diffractions.

© 2016 European Association of Geoscientists & Engineers © 2016 European Association of Geoscientists & Engineers
Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12362
2016-05-13
2024-04-26

  • From This Site

    /content/journals/10.1111/1365-2478.12362
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. AbramowitzM. and StegunI.A.1970. Handbook of Mathematical Function: With Formulas, Graphs, and Mathematical Tables. Dover Publications, Inc.
     [Google Scholar]
  2. BagainiC. and SpagnoliniU.1996. 2‐D continuation operators and their applications. Geophysics61(6), 1846–1858.
     [Google Scholar]
  3. BerkhoutA.J.1982. Seismic Migration: Imaging of Acoustic Energy by Wave Field Extrapolation, A: Theoretical Aspects, 2nd edn. Elsevier.
     [Google Scholar]
  4. BerkhoutA.J.1987. Applied Seismic Wave Theory. Elsevier.
     [Google Scholar]
  5. BerkhoutA.J.1997. Pushing the limits of seismic imaging, part II: integration of prestack migration, velocity estimation and AVO analysis. Geophysics62(3), 954–969.
     [Google Scholar]
  6. BerkhoutA.J.2006. Seismic processing in the inverse data space. Geophysics71(4), A29–A33.
     [Google Scholar]
  7. BerkhoutA.J. and VerschuurD.J.2006. Focal transformation: an imaging concept for signal restoration and noise removal. Geophysics71(6), A55–A59.
     [Google Scholar]
  8. BerkhoutA.J., VerschuurD.J. and RomijnR.2004. Reconstruction of seismic data using the focal transformation. 74th SEG meeting, Denver, USA, Expanded Abstracts, 1993–1996.
  9. BiondiB., FomelS. and CheminguiN.1998. Azimuth moveout for 3D prestack imaging. Geophysics63(2), 574–588.
     [Google Scholar]
  10. CaryP.1999. Common‐offset‐vector gathers: an alternative to cross‐spreads for wide‐azimuth 3D surveys. 69th SEG meeting, Expanded Abstracts, 1496–1499.
  11. de BruinC.G.M., WapenaarC.P.A. and BerkhoutA.J.1990. Angle‐dependent reflectivity by means of prestack migration. Geophysics55(9), 1223–1234.
     [Google Scholar]
  12. DeregowskiS.M.1986. What is DMO? First Break4, 7–24.
     [Google Scholar]
  13. DoulgerisP., MahdadA. and BlacquiereG.2009. An R‐based overview of the WRW concept. 3rd International Conference and Exhibition, Nafplion, Greece, June 21–26, 2009.
  14. DoulgerisP., VerschuurD.J. and BlacquiereG.2012. Separation of blended data by sparse inversion utilizing surface‐related multiples. 74th EAGE Annual International Meeting, Expanded Abstracts, A041.
  15. DragosetW.H.1999. A practical approach to surface multiple attenuation. The Leading Edge18(1), 104–108.
     [Google Scholar]
  16. DuijndamA., SchonewilleM. and HindriksC.1999. Reconstruction of band‐limited signals, irregularly sampled along one spatial direction. Geophysics64(2), 524–538.
     [Google Scholar]
  17. FokkemaJ.T. and van den BergP.M.1993. Seismic Applications of Acoustic Reciprocity. Elsevier Science Publishers B.V.
     [Google Scholar]
  18. GisolfA. and VerschuurD.J.2010. The Principles of Quantitative Acoustical Imaging. EAGE Publications B.V.
     [Google Scholar]
  19. HennenfentG. and HerrmannF.J.2008. Simply denoise: wavefield reconstruction via jittered undersampling. Geophysics73(3), V19–V28.
     [Google Scholar]
  20. HennenfentG., FenelonL., and HerrmannF.J.2010. Nonequispaced curvelet transform for seismic data reconstruction: A sparsity‐promoting approach. Geophysics75(6), WB203–WB210.
     [Google Scholar]
  21. HerrmannP., MojeskyT., MagasanM., and HugonnetP.2000. De‐aliased, high‐resolution Radon transforms. 70th 70th SEG meeting, Calgary, Canada, Expanded abstracts, 1953–1956.
  22. KabirM.M.N. and VerschuurD.J.1995. Restoration of missing offsets by parabolic radon transform. Geophysical Prospecting43(3), 347–368.
     [Google Scholar]
  23. KinnegingN.K., BudejickyV., WapenaarC.P.A. and BerkhoutA.J.1989. Efficient 2D and 3D shot record redatuming. Geophysical Prospecting37(5), 493–530.
     [Google Scholar]
  24. KontakisA. and VerschuurD.J.2014. Deblending via sparsity‐constrained inversion in the focal domain. 76th EAGE meeting, Amsterdam, Netherlands, Expanded Abstracts, Th ELI2 02.
  25. KontakisA. and VerschuurD.J.2015. Deblending via a hybrid focal and linear Radon transform. 77th EAGE meeting, Madrid, Spain, Expanded Abstracts, We N101 02.
  26. KuehlH.2002. Least‐squares wave‐equation migration/inversion . Ph.D. thesis. University of Alberta, Edmonton, Canada.
  27. KutschaH.2014. The double focal transformation and its application to data reconstruction . Ph.D. thesis. Delft University of Technology, The Netherlands.
  28. KutschaH. and VerschuurD.J.2012. Data reconstruction via sparse double focal transformation: An overview. IEEE Signal Processing Magazine29(4), 53–60.
     [Google Scholar]
  29. KutschaH., VerschuurD.J. and BerkhoutA.2010. High resolution double focal transformation and its application to data reconstruction. 80th SEG meeting, Denver, USA, Expanded Abstracts 2010, 3589–3593.
  30. LopezG.A. and VerschuurD.J.2013. 3D primary estimation by sparse inversion using the focal domain parameterization. 83rd SEG meeting, Houston, TX, Expanded Abstracts, 4172–4175.
  31. NaghizadehM.2012. Seismic data interpolation and denoising in the frequency‐wavenumber domain. Geophysics77(2), V71–V80.
     [Google Scholar]
  32. NaghizadehM. and SacchiM.D.2010. Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data. Geophysics75(6), WB189–WB202.
     [Google Scholar]
  33. NemethT., WuC. and SchusterG.1999. Least squares migration of incomplete reflection data. Geophysics64(1), 208–221.
     [Google Scholar]
  34. SchonewilleM., KlaedtkeA., and VignerA.2009. Anti alias anti leakage Fourier transform. 79th SEG meeting, Expanded Abstracts, 3249–3253.
  35. SpagnoliniU. and OpreniS.1996. 3D shot continuation operator. 66th SEG Meeting, Denver, USA, Expanded Abstracts, 439–442.
  36. TradD.O.2002. Accurate interpolation with high‐resolution time‐variant radon transforms. Geophysics67(2), 644–656.
     [Google Scholar]
  37. TradD.O.2003. Interpolation and multiple attenuation with migration operators. Geophysics68, 2043–2054.
     [Google Scholar]
  38. TradD.O.2009. Five‐dimensional interpolation: Recovering from acquisition constraints. Geophysics74(6), V123–V132.
     [Google Scholar]
  39. TradD.O., UlrychT. and SacchiM.2003. Latest views of the sparse radon transform. Geophysics68, 386–399.
     [Google Scholar]
  40. van denBerg E. and FriedlanderM.P.2008. Probing the Pareto frontier for basis pursuit solutions. SIAM Journal on Scientific Computing31(2), 890–912.
     [Google Scholar]
  41. van WijngaardenA.J.1998. Imaging and characterization of angle‐dependent seismic reflection data . Ph.D. thesis. Delft University of Technology, The Netherlands.
  42. VerschuurD.J., VrolijkJ.W. and TsingasC.2012. 4D reconstruction of wide azimuth (waz) data using sparse inversion of hybrid radon transforms. 82nd SEG meeting, Las Vegas, USA, 1–5.
  43. WangJ., NgM. and PerzM.2010. Seismic data interpolation by greedy local radon transform. Geophysics75(6), WB225–WB234.
     [Google Scholar]
  44. XuS., ZhangY., PhamD. and LambareG.2005. Antileakage Fourier transform for seismic data regularization. Geophysics70(4), V87–V95.
     [Google Scholar]
  45. ZwartjesP.M., and GisolfA.2006. Fourier reconstruction of marine‐streamer data in four spatial coordinates. Geophysics71(6), V171–V186.
     [Google Scholar]
  46. ZwartjesP.M. and GisolfA.2007. Fourier reconstruction with sparse inversion. Geophysical Prospecting55(2), 199–221.
     [Google Scholar]
  47. ZwartjesP.M. and SacchiM.2007. Fourier reconstruction of nonuniformly sampled, aliased seismic data. Geophysics72(1), V21–V32.
     [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12362
Loading
The utilization of the double focal transformation for sparse data representation and data reconstruction
Geophysical Prospecting 64, 1498 (2016); https://doi.org/10.1111/1365-2478.12362
/content/journals/10.1111/1365-2478.12362
/content/journals/10.1111/1365-2478.12362
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Coarse sampling; Inverse problem; Noise attenuation; Reconstruction; Seismics; Sparse inversion

Most Cited This Month Most Cited RSS feed

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