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Elastodynamic reciprocity theorems for time-lapse seismic methods

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

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Elastodynamic reciprocity theorems for time-lapse seismic methods

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  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. A B A B ‘State A’ ‘State B’

  4. A B A B ‘State A’ ‘State B’

  5. ‘State A’ ‘State B’

  6. ‘State A’ ‘State B’

  7. n ‘State A’ ‘State B’

  8. V V n n State A State B Wave fields Sources Medium PA, Vk,A QA,Fk,A kA, rA PB, Vk,B QB,Fk,B kB, rB kA, rA kB, rB PB QB QA PA ‘State B’ ‘State A’

  9. V V n n 0 0 0 0 PB QB QA PA ‘State B’ ‘State A’

  10. V V n n PB QB QA PA ‘State B’ ‘State A’

  11. V V n n ‘State B’ ‘State A’

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

  13. n ‘State A’ ‘State B’

  14. ‘State A’ ‘State B’

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

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

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

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

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

  20. V V n n Time-lapse seismic (Dillen et al, 2000) PB QB QA PA ‘State B’ ‘State A’

  21. V n Time-lapse seismic (Dillen et al, 2000) PB QB ‘State B’ ‘State A’

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

  23. Acoustic reciprocity for one-way wave fields State A State B xA xA xB xB

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

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

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

  27. Difference data Application in time-lapse seismic

  28. Boundary integral Application in time-lapse seismic

  29. 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.

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