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Seismic interferometry, the optical theorem and a non-linear point scatterer Kees Wapenaar

Seismic interferometry, the optical theorem and a non-linear point scatterer Kees Wapenaar Evert Slob Roel Snieder Society of Exploration Geophysicists Houston, October 26, 2009. Interferometry. Non-linear. Paradox. Point scatterer. Optical theorem. Interferometry. Modeling

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Seismic interferometry, the optical theorem and a non-linear point scatterer Kees Wapenaar

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  1. Seismic interferometry, the optical theorem and a non-linear point scatterer Kees Wapenaar Evert Slob Roel Snieder Society of Exploration Geophysicists Houston, October 26, 2009

  2. Interferometry Non-linear Paradox Point scatterer Optical theorem

  3. Interferometry Modeling Inversion Interferometry Migration Non-linear Paradox Point scatterer Optical theorem

  4. Snieder, R., K.van Wijk, M.Haney, and R.Calvert, 2008, Cancellation of spurious arrivals in Green's function extraction and the generalized optical theorem: Physical Review E, 78, 036606. Halliday, D. and A.Curtis, 2009, Generalized optical theorem for surface waves and layered media: Physical Review E, 79, 056603. van Rossum, M. C. W. and T.M. Nieuwenhuizen, 1999, Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion: Reviews of Modern Physics, 71, 313--371.

  5. Term 1: a b

  6. Term 2: c d

  7. Term 3: f e

  8. Terms 1 + 2 + 3: c a f e b d

  9. Terms 1 + 2 + 3, compared with modeled G:

  10. h i h i Term 4: g g

  11. Terms 1 + 2 + 3 + 4, compared with modeled G:

  12. Terms 1 + 2 + 3, compared with modeled G:

  13. Interferometry Paradox Point scatterer Optical theorem

  14. Substitute into representation for interferometry (Snieder et al., 2008, Halliday and Curtis, 2009)…..

  15. This gives: Generalized optical theorem (Heisenberg, 1943)

  16. This gives: For comparison:

  17. Interferometry Non-linear Paradox Point scatterer Optical theorem

  18. Isotropic point scatterer:

  19. Isotropic point scatterer:

  20. (van Rossum et al, 1999) = + + + (Snieder, 1999)

  21. Interferometry Non-linear Paradox Point scatterer Optical theorem

  22. Interferometry Non-linear Paradox Point scatterer Optical theorem

  23. Terms 1 + 2 + 3: c a f e b d

  24. Terms 1 + 2 + 3 + 4, compared with modeled G:

  25. Interferometry Modeling Inversion Interferometry Migration Non-linear Paradox Point scatterer Optical theorem

  26. Modeling, inversion and interferometry in scatterering media Groenenboom and Snieder, 1995; Weglein et al., 2003; Van Manen et al., 2006

  27. Modeling, inversion and interferometry in scatterering media Groenenboom and Snieder, 1995; Weglein et al., 2003; Van Manen et al., 2006 Limiting case: Point scatterer

  28. Resolution function for seismic migration Miller et al., 1987; Schuster and Hu, 2000; Gelius et al., 2002; Lecomte, 2008 Migration deconvolution Yu, Hu, Schuster and Estill, 2006

  29. Conclusions • Born approximation is incompatible with seismic interferometry

  30. Conclusions • Born approximation is incompatible with seismic interferometry • Seismic interferometry optical theorem non-linear scatterer seismic interferometry • Consequences for modeling, inversion, interferometry and migration

  31. Conclusions • Born approximation is incompatible with seismic interferometry • Seismic interferometry optical theorem non-linear scatterer seismic interferometry • Consequences for modeling, inversion, interferometry and migration

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