Codas in reflection and transmission responses and their mutual relations

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

9. 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

10. Claerbout, 1968 :

11. 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’’

12. Reciprocity for one-way wave fields

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

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

16. 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

17. Syncline model

18. Reflection response Transmission response

19. Syncline model

20. Transmission response (fixed , variable )

21. (variable )

22. Syncline model

23. (variable )

25. Causal part of

26. Directly modeled reflection response

27. Syncline model with extra layer

28. Transmission response with coda

29. Reflection response with coda

30. 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

31. 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)

32. = • 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)

33. 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)