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Greens function representations for seismic interferometry Kees Wapenaar 75 th SEG meeting, Houston November 8, 2005 Slide 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) Slide 3 Rayleighs reciprocity theorem: Slide 4 State A Slide 5 Rayleighs reciprocity theorem: State A State B Slide 6 Rayleighs reciprocity theorem: Time-reversal: Slide 7 Rayleighs reciprocity theorem: Time-reversal: Slide 8 Rayleighs reciprocity theorem: State A Slide 9 Rayleighs reciprocity theorem: State B Slide 10 Slide 11 Monopole at x Slide 12 Dipole at x Slide 13 Slide 14 High-frequency approximation Slide 15 High-frequency approximation Far-field approximation (Fraunhofer) Slide 16 High-frequency approximation Far-field approximation (Fraunhofer) Slide 17 0 Slide 18 0 Slide 19 0 Slide 20 0 Slide 21 0 Slide 22 0 Slide 23 0 Slide 24 0 Slide 25 0 Slide 26 0 Slide 27 0 Slide 28 0 Slide 29 0 Slide 30 0 Slide 31 0 Slide 32 0 Slide 33 0 Slide 34 0 Slide 35 0 Slide 36 0 Slide 37 0 Slide 38 0 Slide 39 0 Slide 40 0 Slide 41 0 Slide 42 0 Slide 43 Rayleighs reciprocity theorem: Slide 44 Free surface Slide 45 Slide 46 High-frequency approximation Slide 47 Free surface High-frequency approximation Far-field approximation (Fraunhofer) Slide 48 Free surface High-frequency approximation Far-field approximation (Fraunhofer) Slide 49 Free surface Slide 50 Uncorrelated noise sources Slide 51 Draganov and Wapenaar, Poster session PSC P1, Today Slide 52 Slide 53 Slide 54 Slide 55 Slide 56 Slide 57 Slide 58 Slide 59 Slide 60 Slide 61 Slide 62 Slide 63 Slide 64 Slide 65 Slide 66 Slide 67 Draganov et al., EAGE, 2003 Slide 68 Draganov and Wapenaar, Poster session PSC P1, Today Slide 69 From acoustic .. . to elastodynamic Slide 70 Draganov and Wapenaar, Poster session PSC P1, Today Slide 71 Slide 72 Slide 73 Conclusions Exact and approximate representations of Greens functions for seismic interferometry Main contributions come from stationary points Free surface obviates the need of closed integral along sources Uncorrelated noise sources obviates the need of integral along sources Random source distribution suppresses artefacts from scatterers below sources Straightforward extension to elastodynamic situation