1. Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University of Technology

2. Review of reciprocity theorems and seismic applications Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University of Technology

3. ‘State A’ ‘State B’ A A B B

4. ‘State A’ ‘State B’ A A B B

6. ‘State A’ ‘State B’

7. ‘State A’ ‘State B’

8. ‘State A’ ‘State B’ n

9. State AState B P A, V k,A Q A,F k,A  A,  A P B, V k,B Q B,F k,B  B,  B Wave fields Sources Medium ‘State B’ ‘State A’ QAQA QBQB PAPA PBPB VnVn  A,  A  B,  B

10. ‘State B’ ‘State A’ QAQA QBQB PAPA PBPB 00 00 VnVn

11. ‘State B’ ‘State A’ QAQA QBQB PAPA PBPB VnVn

12. ‘State B’ ‘State A’ VnVn

13. 1872, Betti: Elastostatic fields 1873, Rayleigh: Acoustic time-harmonic fields 1959, Knopoff and Gangi: Elastodynamic fields in inhomogeneous anisotropic media Some history 1966, De Hoop: visco-elastic anisotropic media 1993, Fokkema and van den Berg: applications in seismic processing (source: Arntsen and Carcione, Geophysics, 2000)

14. ‘State A’ ‘State B’ n

15. ‘State A’

16. ‘State B’ Multiple elimination (van Borselen et al., 1996)

17. ‘State A’‘State B’ Multiple elimination (van Borselen et al., 1996)

18. ‘State B’ ‘State A’ VnVn Surface wave suppression (van Zanen et al., 2000)

19. ‘State A’ ‘State B’ Surface wave suppression (van Zanen et al., 2000)

20. ‘State A’ ‘State B’ Surface wave suppression (van Zanen et al., 2000)

21. ‘State B’ ‘State A’ QAQA QBQB PAPA PBPB VnVn Time-lapse seismic (Dillen et al, 2000)

22. ‘State B’ ‘State A’ QBQB PBPB Vn Time-lapse seismic (Dillen et al, 2000)

23. ‘State A’ ‘State B’ Time-lapse seismic (Dillen et al, 2000)

24. State AState B xAxA xAxA xBxB xBxB Acoustic reciprocity for one-way wave fields

25. Acoustic reciprocity for full (two-way) wave fields Acoustic reciprocity for one-way wave fields

26. AB AB Fokkema and van den Berg (1996) Dillen (2000, Ph.d thesis) Wapenaar et al. (2000, SEG) B A   Application in time-lapse seismic

27. AB AB Fokkema and van den Berg (1996) Dillen (2000, Ph.d thesis) Wapenaar et al. (2000, SEG) B A   Application in time-lapse seismic

28. Difference data Application in time-lapse seismic

29. Boundary integral Application in time-lapse seismic

30. Conclusions Source - receiver reciprocity is a special case of general reciprocity General reciprocity theorems formulate a relation between wave fields, sources and medium parameters in two different states - Acoustic and elastodynamic - Two-way and one-way Applications: - Multiple elimination - Surface wave suppression - Time-lapse seismic - Etc.