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Review of the Green's Theorem deghosting method

This review analyzes the Green's Theorem deghosting method for removing seismic distortion caused by ghosts. The method shows promising results even without the source wavelet. Surface integration, interpolation, and high computation power are required for field data tests.

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Review of the Green's Theorem deghosting method

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  1. Review of the Green’s Theorem deghosting method Jingfeng Zhang and Arthur B. Weglein M-OSRP 2006 Annual Meeting, June 5 ~ June 7, 2007

  2. Keypoints • Scattered field can be deghosted without source wavelet and vertical derivative of the wavefield • Field data test requirements: interpolation and extrapolation, high computation power • Derivation of the Green’s theorem deghosting, wavelet estimation and field prediction algorithms

  3. Motivation • Remove the seismic distortion due to ghosts • Angle and frequency dependent distortion, ghost notch • A pre-requisite for all of the current inverse scattering series related algorithms: FSMR, IMA, Imaging and inversion

  4. Green’s function = Green’s Theorem

  5. Configuration for actual wavefield

  6. 2 3 Deghosting algorithm 1 = + 1 2 + 3 1 2 = Weglein et al. (2002)

  7. is the image of with respect to the free surface V Wavelet estimation algorithm

  8. + 2 3 = + 1 2 + 3 V Wavelet estimation algorithm = Weglein and Secrest, (1990) 1 3 2 2 3

  9. Field prediction algorithm

  10. Field prediction algorithm

  11. Deghosting algorithm F.S. Pseudo-M.S. M.S. Earth

  12. Deghosting algorithm F.S. Pseudo-M.S. M.S. Earth

  13. Towed streamer deghosting(Numerical tests) F.S. (0,2) 6.0m M.S. 300m c1=1500m/s c2=2250m/s

  14. With source wavelet Red solid: Exact; Blue dash: deghosting result

  15. FSMR results (point receiver data) Primary At (0,2.5) 1st order FSM 2nd order FSM Using the 1st term in the ISS FSMR series

  16. FSMR results (point receiver data) At (3750,2.5) 1st order FSM Using the 1st term in the ISS FSMR series

  17. Without source wavelet Consequences: (1) Direct wave and its ghost: remains (2) Scattered field: no effect

  18. Without source wavelet Between FS and MS, the scattered field satisfies: Notice there is no source term. From similar derivation of the field prediction: compared to So (1) the absent of source wavelet has no effect on the prediction of the scattered field. (2) the term only contribute to the prediction of the direct wave and its ghost.

  19. Without source wavelet • Absent of source wavelet only cause inaccuracy in prediction of the direct wave and its ghost, while the scattered field prediction is accurate • Scattered field can be deghosted well even without source wavelet • Problems exist at places (especially for shallow water cases) where the direct wave interfere with the scattered field

  20. Field data tests • Surface integration: • Surface data measurements: data interpolation and extrapolation • Large computation power • Source wavelet • Receiver array

  21. Conclusions • Green’s theorem deghosting produce encouraging results when the source wavelet is available. Even without the source wavelet, scattered field can still be deghosted. • The surface integration requires surface data measurements and high computation power. At the same time, it provides stable results due to that integration. • Interpolation and Extrapolation, high computation power are necessary for field data tests.

  22. Acknowledgements • M-OSRP sponsors and colleagues

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