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Seismic interferometry: Who needs a seismic source?

Seismic interferometry: Who needs a seismic source?. Roel Snieder Center for Wave Phenomena Colorado School of Mines email rsnieder@mines.edu http://www.mines.edu/~rsnieder download publications from: http://www.mines.edu/~rsnieder/Publications.html. F. (Einstein, 1905).

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Seismic interferometry: Who needs a seismic source?

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  1. Seismic interferometry:Who needs a seismic source? Roel Snieder Center for Wave Phenomena Colorado School of Mines email rsnieder@mines.edu http://www.mines.edu/~rsnieder download publications from: http://www.mines.edu/~rsnieder/Publications.html

  2. F (Einstein, 1905) Fluctuation-dissipation theorem (Kubo, Rep. Prog. Phys., 29, 255-284, 1966)

  3. Very Long Baseline Interferometry http://www.lupus.gsfc.nasa.gov/brochure/bintro.html

  4. Distance between USA and Germany http://www.lupus.gsfc.nasa.gov/brochure/btoday2.html

  5. Pseudo-random source Piezo-electric vibrator from CGG

  6. Coda wave interferometry 45°C 50°C (Snieder et al., Science, 295, 2253-2255, 2002)

  7. 1D example

  8. Cross-correlation • sum of causal and acausal response • uncorrelated left- and rightgoing waves

  9. Right-going wave only

  10. Right-going wave only

  11. DC-component must vanish

  12. Need to extend this to include: • heterogeneous media • - more space dimensions

  13. Derivation based on normal-modes (Lobkis and Weaver, JASA, 110, 3011-3017, 2001)

  14. Displacement response Heaviside function

  15. Velocity response

  16. Uncorrelated excitation

  17. Correlation

  18. Correlation as sum over modes

  19. For uncorrelated modes

  20. For uncorrelated modes

  21. Correlation Green’s function

  22. Correlation Green’s function

  23. Correlation Green’s function

  24. Correlation and Green’s function • sum of causal and acausal Green’s function • holds for arbitrary heterogeneity

  25. Dealing with with acausal Green’s function • truncate correlation for t<0 • average correlation for t<0 and t>0

  26. Displacement instead of velocity Conclusion: time derivative may appear

  27. (Weaver and Lobkis, Ultrasonics, 40, 435-439, 2002)

  28. (Weaver and Lobkis, Ultrasonics, 40, 435-439, 2002)

  29. Representation theorem

  30. Acoustic waves Green’s function:

  31. Time reversal = complex conjugation Time-reversed solution

  32. Time-reversal When is a solution. then is a solution as well N.B. this does not hold in the presence of attenuation

  33. Representation theorem replace:

  34. Left hand side reciprocity

  35. Right hand side

  36. For spherical surface far away Radiation condition:

  37. Virtual-sources (Wapenaar, Fokkema, and Snieder, JASA, 118, 2783-2786 2005 heuristic derivation: Derode et al., JASA, 113, 2973-2976, 2003)

  38. Computing synthetic seismograms (Van Manen et al., Phys. Rev. Lett., 94, 164301,2005)

  39. Field example of virtual sources complicated overburden reservoir (Bakulin and Calvert, SEG expanded abstracts, 2477-2480, 2004)

  40. Peace River 4D VSP Component used, along-the-well (450)

  41. Image from virtual sources top bottom

  42. Virtual source Surface

  43. Virtual-sources (Wapenaar, Fokkema, and Snieder, JASA, 118, 2783-2786 2005 heuristic derivation: Derode et al., JASA, 113, 2973-2976, 2003)

  44. Excitation by uncorrelated sources on surface • Uncorrelated sources can be: • sequential shots • uncorrelated noise

  45. Response to uncorrelated noise

  46. Green’s function from uncorrelated sources (For elastic waves: Wapenaar, Phys. Rev. Lett, 93, 254301, 2004)

  47. Raindrop model • Sources can be: • real sources • secondary sources (scatterers)

  48. Response to random sources

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