Green’s function representations for seismic interferometry

1. Green’s function representations for seismic interferometry Kees Wapenaar 75th SEG meeting, Houston November 8, 2005

2. Seismic interferometry : • obtaining new seismic responses by X-correlation • Claerbout, 1968 (1-D version) • Schuster, 2001, 2004 (interferometric imaging) • Weaver and Lobkis, 2001 (diffuse wave fields) • Wapenaar, Draganov et al, 2002, 2004 (reciprocity) • Derode et al., 2003 (time-reversal) • Campillo and Paul, 2003 (surface waves) • Snieder, 2004 (stationary phase) • Bakulin and Calvert, 2004 (virtual source) • Gerstoft, Sabra et al., 2004 (surface wave tomography) • Van Manen, Robertsson & Curtis 2005 (modeling)

3. Rayleigh’s reciprocity theorem:

4. State A Rayleigh’s reciprocity theorem:

5. State A State B Rayleigh’s reciprocity theorem:

6. Time-reversal: Rayleigh’s reciprocity theorem:

7. Time-reversal: Rayleigh’s reciprocity theorem:

8. State A Rayleigh’s reciprocity theorem:

9. State B Rayleigh’s reciprocity theorem:

11. Monopole at x

12. Dipole at x

14. High-frequency approximation

15. High-frequency approximation Far-field approximation (Fraunhofer)

16. High-frequency approximation Far-field approximation (Fraunhofer)

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43. Rayleigh’s reciprocity theorem:

44. Free surface Rayleigh’s reciprocity theorem:

45. Free surface

46. High-frequency approximation Free surface

47. High-frequency approximation Free surface Far-field approximation (Fraunhofer)

48. High-frequency approximation Free surface Far-field approximation (Fraunhofer)

49. Free surface

50. Free surface Uncorrelated noise sources