Seismic interferometry, time-reversal, and reciprocity Kees Wapenaar, Jacob Fokkema and Roel Snieder

67th EAGE meeting, Madrid June 13, 2005

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)

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)

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)

Time - reversal

Huygens principle:propagatorsource

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)

Rayleighs reciprocity theorem:Time-reversal:

Rayleighs reciprocity theorem:

Rayleighs reciprocity theorem:

Dipole at x

Monopole at x

High-frequencyapproximation

High-frequencyapproximation

Far-field approximation(Fraunhofer)

High-frequencyapproximation

Far-field approximation(Fraunhofer)

Rayleighs reciprocity theorem:

Rayleighs reciprocity theorem:Free surface

Free surface

Free surfaceHigh-frequencyapproximation

Free surfaceHigh-frequencyapproximationFar-field approximation(Fraunhofer)

Free surfaceHigh-frequencyapproximationFar-field approximation(Fraunhofer)

Free surface

Free surfaceUncorrelated noise sources

Conclusions Time-reversal approach (Derode et al, 2003) leads to high-frequency far-field approximation of interferometric relations Reciprocity approach (Wapenaar, Draganov et al, 2002, 2004) leads to exact interferometric relations 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 Extension to elastodynamic situation (next speaker)

Free surface

Free surface