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Seismic imaging in the curvelet domain: achievements and perspectives

Seismic imaging in the curvelet domain: achievements and perspectives. Hervé Chauris (1) & Jianwei Ma (1,2) EAGE 2009 - Amsterdam. Centre de Géosciences, Mines ParisTech, France Institute of Seismic Exploration, School of Aerospace, Tsinghua University, Beijing, China.

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Seismic imaging in the curvelet domain: achievements and perspectives

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  1. Seismic imaging in the curvelet domain: achievements and perspectives Hervé Chauris(1) & Jianwei Ma(1,2) EAGE 2009 - Amsterdam • Centre de Géosciences, Mines ParisTech, France • Institute of Seismic Exploration, School of Aerospace, Tsinghua University, Beijing, China

  2. Locally coherent events Time common-offset section Same section after depth migration

  3. Locally coherent events Context : seismic modeling / migration Diffraction point Globally coherent event Locally coherent event

  4. Curvelets and other …lets Taking into account band-limited data:  Curvelet Ridgelet Contourlet Shearlet Wavelet EPW Surfacelet Seislet Bandlet, …

  5. Potential of curvelets Seismic data Single curvelet

  6. Introduction – Curvelets Curvelets for different coefficients cμ(x,z) shift rotation stretch

  7. Content Introduction – what are curvelets Curvelets and seismic processing tasks • pre-/post-processing • seismic migration • seismic demigration/migration – velocity estimation Conclusions

  8. Curvelets and seismic applications Review: • Ma and Plonka, 2009 • Workshop EAGE 2007 (London), Chauris and Douma Data denoising, interpolation and compression • Hennenfent and Herrmann, 2006 Droujinine et al., 2007 • Herrmann et al., 2008a Sacchi et al., 2007 • Herrmann et al., 2008b Fomel, 2007 • Lin and Herrmann, 2007 • Neelamani et al, 2008 Seismic modeling and migration • Douma and de Hoop, 2007 • Chauris, 2006 Velocity model estimation • Chauris and Nguyen, 2007 • Chauris and Nguyen, 2008 redundant transform

  9. Seismic propagation/migration Theoretical results • Candes and Donoho, 2003 Practical results • Douma and de Hoop, 2006 • Douma and de Hoop, 2007 • Chauris, 2006

  10. Use of digital curvelets Fast curvelet transform Migrated section in initial model Curvelet processing Fast inverse curvelet transform Perturbed section

  11. Migration in heterogeneous models Smooth heterogeneous 2-D model Kirchhoff migration First-order curvelet migration

  12. Migration in heterogeneous models First-order curvelet migration Kirchhoff migration

  13. Kirchhoff migration of a few curvelets Migration in heterogeneous models First-order approximation not good enough

  14. Demigration/migration Sensitivity of the migrated result with respect to the velocity model Initial velocity model Triplicated ray field Velocity perturbation (up to 200 m/s)

  15. Demigration/migration Sensitivity of a migrated image with respect to the background velocity model Given velocity model Migration ? Local velocity perturbation Migration

  16. Input data Ray+Born 2-D synthetic data set (offsets from 0 to 2 km) Offset 600 m Initial image

  17. Initial image Predicted image Exact image Demigration/migration Sensitivity of the migrated result with respect to the velocity model

  18. Demigration/migration Depth difference reduced from 60 m to less than 2 m Initial / exact Predicted / exact

  19. Demigration/migration Sensitivity of the migrated result with respect to the velocity model Unperturbed part Modified part

  20. Common Image Gathers The prediction takes into account the lateral velocity variations Prediction with curvelets Exact Reference image

  21. Demigration/migration Sensitivity of a migrated image with respect to the background velocity model Given velocity model Migration ? Local velocity perturbation Migration

  22. Velocity estimation Sensitivity of a migrated image with respect to the background velocity model Given velocity model Migration Improved seismic section ? Optimal velocity perturbation? Migration Cost function

  23. DSO in curvelet domain Feasibility study 2-D synthetic ray+Born data set Initial After 1 iteration Exact

  24. DSO in curvelet domain Stack of offsets between 100 and 800 m Initial After 1 iteration Exact

  25. Conclusions & perspectives Seismic imaging operators: • Curvelets more suited for demigration/migration than for migration or demigration (modeling) alone • Applications limited to smooth background velocity models A similar analysis should be conducted for (non-smooth) general background velocity models (without the use of geometrical optics) Perspectives: new transform (e.g. with explicit curvature)?

  26. Acknowledgements We would like to thank F. ten Kroode (Shell E&P) for fruitful discussions and support M. Noble and P. Podvin (Mines ParisTech) Shell E&P for partly funding the project

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