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Codas in reflection and transmission responses and their mutual relations

Codas in reflection and transmission responses and their mutual relations. Kees Wapenaar Deyan Draganov Jan Thorbecke Jacob Fokkema. Centre for Technical Geoscience Delft University of Technology. Contents. 1-D relations From transmission to reflection

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Codas in reflection and transmission responses and their mutual relations

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  1. Codas in reflection and transmission responses and their mutual relations Kees Wapenaar Deyan Draganov Jan Thorbecke Jacob Fokkema Centre for Technical Geoscience Delft University of Technology

  2. Contents • 1-D relations • From transmission to reflection • From reflection to transmission • 3-D relations • Claerbout’s conjecture • One-way reciprocity theorem • From transmission to reflection • From reflection to transmission • 2-D examples • Discussion of applications

  3. Claerbout, 1968 :

  4. Reflection response Transmission response

  5. With free surface :

  6. 0 0 Without free surface :

  7. Transmission response Reflection response

  8. Contents • 1-D relations • From transmission to reflection • From reflection to transmission • 3-D relations • Claerbout’s conjecture • One-way reciprocity theorem • From transmission to reflection • From reflection to transmission • 2-D examples • Discussion of applications

  9. Claerbout, 1968 :

  10. Claerbout’s conjecture: ‘‘By crosscorrelating noise traces recorded at two locations on the surface, we can construct the wave field that would be recorded at one of the locations if there was a source at the other’’

  11. Reciprocity for one-way wave fields

  12. From transmission to reflection : 1-Dimensional : 3-Dimensional :

  13. = From reflection to transmission : 1-Dimensional : 3-Dimensional :

  14. Contents • 1-D relations • From transmission to reflection • From reflection to transmission • 3-D relations • Claerbout’s conjecture • One-way reciprocity theorem • From transmission to reflection • From reflection to transmission • 2-D examples • Discussion of applications

  15. Syncline model

  16. Reflection response Transmission response

  17. Syncline model

  18. Transmission response (fixed , variable )

  19. (variable )

  20. Syncline model

  21. (variable )

  22. Causal part of

  23. Directly modeled reflection response

  24. Syncline model with extra layer

  25. Transmission response with coda

  26. Reflection response with coda

  27. Contents • 1-D relations • From transmission to reflection • From reflection to transmission • 3-D relations • Claerbout’s conjecture • One-way reciprocity theorem • From transmission to reflection • From reflection to transmission • 2-D examples • Discussion of applications

  28. From transmission to reflection • Acoustic daylight imaging (Rickett and Claerbout , 1999) • From reflection to transmission • Construction of inverse propagation operators (Herman, 1992, Wapenaar and Herrmann, 1993) • From reflection to reflection • Interferometric imaging (Schuster, 2001)

  29. = • From transmission to reflection • Acoustic daylight imaging (Rickett and Claerbout , 1999) • From reflection to transmission • Construction of coda in inverse propagation operators (Herman, 1992, Wapenaar and Herrmann, 1993) • From reflection to reflection • Interferometric imaging (Schuster, 2001)

  30. From transmission to reflection • Acoustic daylight imaging (Rickett and Claerbout , 1999) • From reflection to transmission • Construction of coda in inverse propagation operators (Herman, 1992, Wapenaar and Herrmann, 1993) • From reflection to reflection • Interferometric imaging (Schuster, 2001)

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