1887
Volume 64, Issue 2
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

In seismic interpretation and seismic data analysis, it is of critical importance to effectively identify certain geologic formations from very large seismic data sets. In particular, the problem of salt characterization from seismic data can lead to important savings in time during the interpretation process if solved efficiently and in an automatic manner. In this work, we present a novel numerical approach that is able to automatically segmenting or identifying salt structures from a post‐stack seismic data set with a minimum intervention from the interpreter. The proposed methodology is based on the recent theory of sparse representation and consists in three major steps: first, a supervised learning assisted by the user which is performed only once, second a segmentation process via unconstrained ℓ optimization, and finally a post‐processing step based on signal separation. Furthermore, since the second step only depends upon local information at each time, the whole process greatly benefits from parallel computing platforms. We conduct numerical experiments in a synthetic 3D seismic data set demonstrating the viability of our method. More specifically, we found that the proposed approach matches up to 98.53% with respect to the corresponding 3D velocity model available in advance. Finally, in appendixes A and B, we present a convergence analysis providing theoretical guarantees for the proposed method.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12261
2015-06-29
2020-07-11
Loading full text...

Full text loading...

References

  1. AharonM., EladM. and BrucksteinA.2006. K‐SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing54, 4311–4322.
    [Google Scholar]
  2. ArgáezM., RamirezC. and SanchezR.2011. An ℓ1 algorithm for underdetermined systems and applications. North American Fuzzy Information Processing Society annual meeting, El Paso, TX, USA, doi:10.1109/NAFIPS.2011.5752016.
  3. ArgáezM., SanchezR. and RamirezC.2012. Face recognition from incomplete measurements via ℓ1 minimization. American Journal of Computational Mathematics2, 287–294.
    [Google Scholar]
  4. AqrawiA. and AlabbasiN.2013. Seed Growing attribute for salt body segmentation in post‐stack seismic data. 75th EAGE Conference and Exhibition Incorporating SPE EUROPEC, London, UK.
  5. AqrawiA., BoeT. and BarrosS.2011. Detecting Salt domes using a dip guided 3D Sobel seismic attribute. SEG annual meeting, San Antonio, TX, USA, 1014–1018.
  6. BeckerS., BobinJ. and CandèsE., 2010. NESTA: a fast and accurate first‐order method for sparse recovery. SIAM Journal on Imaging Sciences4, 1–39.
    [Google Scholar]
  7. BubeK. and LanganR.1997. Hybrid ℓ1/ℓ2 minimization with applications to tomography. Geophysics62, 1183–1195.
    [Google Scholar]
  8. CandèsE. and RombergJ.2005. ℓ1−magic: recovery of sparse signals via convex programming [Online].
  9. CandèsE., RombergJ. and TaoT.2006. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory52, 489–509.
    [Google Scholar]
  10. CandèsE. and TaoT.2005. Decoding by linear programming. IEEE Transactions on Information Theory51, 4203–4215.
    [Google Scholar]
  11. ChenS., DonohoD. and SaundersM.2001. Atomic decomposition by basis pursuit. SIAM Review43, 129–159.
    [Google Scholar]
  12. de MatosM., YenugoM., AngeloS. and MarfurtK.2011. Integrated seismic texture segmentation and cluster analysis applied to channel delineation and chert reservoir characterization. Geophysics76, 11–21.
    [Google Scholar]
  13. DonohoD.2006. For most large underdetermined systems of linear equations, the minimal ℓ1 solution is also the sparsest solution. Communications on Pure and Applied Mathematics59, 907–934.
    [Google Scholar]
  14. DonohoD. and RaimondoM.2005. A fast wavelet algorithm for image deblurring. Australian and New Zealand Industrial and Applied Mathematics Journal46, 29–46.
    [Google Scholar]
  15. DonohoD., VetterliM., DeVoreR. and DaubechiesI.1998. Data compression and harmonic analysis. IEEE Transactions on Information Theory44, 2435–2476.
    [Google Scholar]
  16. EladM., FigueiredoM. and YiM.2010. On the role of sparse and redundant representations in image processing. Proceedings of the IEEE98, 972–982.
    [Google Scholar]
  17. FigueiredoM., NowakR. and WrightS.2007. Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE Journal of Selected Topics in Signal Processing1, 586–597.
    [Google Scholar]
  18. GaoD., 2003. Volume texture extraction for 3D seismic visualization and interpretation. Geophysics68, 1294–1302.
    [Google Scholar]
  19. HaleE., YinW. and ZhangY.2007. A fixed‐point continuation method for ℓ1‐regularized minimization with applications to compresses sensing. Rice University CAAM Technical Report, Vol. TR07‐07.
  20. HalpertA. and ClappR.2009. Salt body segmentation with dip and frequency attributes. Stanford Exploration Project, Report SEP‐136, 14 April 2009.
  21. HalpertA., ClappR. and BiondiB.2014. Salt delineation via interpreter guided 3D seismic image segmentation. Interpretation2, T79–T88.
    [Google Scholar]
  22. KimS., KohK., LustigM., BoydS. and GorinveskyD.2007. An interior‐point method for large‐scale ℓ1‐regularized least squares. IEEE Journal of Selected Topics in Signal Processing1, 606–617.
    [Google Scholar]
  23. LarrazabalG., RamirezC. and GonzalezG.2014. Automatic geobody detection using multi‐class sparse representation. 76th EAGE Conference, Amsterdam, The Netherlands.
  24. LomaskJ., ClappG. and BiondiB.2007. Application of image segmentation to tracking 3D salt boundaries. Geophysics72, 47–56.
    [Google Scholar]
  25. MairalJ., BachF., PonceJ., SapiroG. and ZissermanA.2008. Discriminative learned dictionaries for local image analysis. IEEE Conference on Computer Vision and Pattern Recognition, 1–8.
  26. RamirezC.2013. Unconstrained L1 optimization with applications to signal and image processing. PhD thesis, The University of Texas at El Paso, USA.
  27. RamirezC. and ArgáezM.2013. An ℓ1 minimization algorithm for non‐smooth regularization in image processing. Signal, Image and Video Processing, doi: 10.1007s11760‐013‐0454‐1.
  28. RamirezC., ArgáezM., GuillenP. and GonzalezG., 2012. Self‐organizing maps in seismic image segmentation. Computer Technology and Application3, 624–629.
    [Google Scholar]
  29. RodriguezP. and WohlbergB.2009. Efficient minimization method for a generalized total variation functional. IEEE Transactions on Image Processing18, 322–332.
    [Google Scholar]
  30. RubinsteinR., BrucksteinA. and EladM.2010. Dictionaries for sparse representation modeling. Proceedings of the IEEE98, 1045–1057.
    [Google Scholar]
  31. ShenB., HuW., ZhangY. and ZhangY.2009. Image inpainting via sparse representation. IEEE International Conference on Acoustics, Speech and Signal Processing, 697–700.
  32. WalletB. and PepperR.2013. Using mathematical morphology in an attribute workflow to improve the interpretability of salt bodies in the Gulf of Mexico. SEG annual meeting, Houston, TX, USA, 1324–1328.
  33. WrightJ., YangA., GaneshA., SastryS. and MaY.2009. Robust face recognition via sparse representation. IEEE Transactions on Pattern Analysis and Machine Intelligence31, 210–227.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12261
Loading
/content/journals/10.1111/1365-2478.12261
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Characterization , Geobody , Salt delineation , Seismic segmentation and Sparse representation
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