Seismic interferometry: a comparison of approaches Kees Wapenaar Deyan Draganov Joost van der Neut Jan Thorbecke Delft University of Technology

Contents Essentials of seismic interferometry Interferometry with multiple sources Interferometry with multiple receivers Interferometry with multiple scatterers

Contents Essentials of seismic interferometry Interferometry with multiple sources Interferometry with multiple receivers Interferometry with multiple scatterers

Cross-correlation

Cross-correlation result is equal to impulsive reflection response

Cross-correlation

Simplifying assumptions: Direct arrival at x A correlated with primary at x B Single diffractor Primaries only x A is the specular reflection point

Contents Essentials of seismic interferometry Interferometry with multiple sources Interferometry with multiple receivers Interferometry with multiple scatterers

Simplifying assumptions: Direct arrival at x A correlated with primary at x B Single diffractor Primaries only x A is the specular reflection point

Simplifying assumptions: Direct arrival at x A correlated with primary at x B Single diffractor Primaries only x A is the specular reflection point

Cross-correlation

Timing error

Simplifying assumptions: Direct arrival at x A correlated with primary at x B Single diffractor Primaries only x A is the specular reflection point

Simplifying assumptions: Direct arrival at x A correlated with primary at x B Single diffractor Primaries only Responses of many independent sources available

Simplifying assumptions: Direct arrival at x A correlated with primary at x B Single diffractor Primaries only Responses of many independent sources available

Simplifying assumptions: Direct arrival at x A correlated with primary at x B Single diffractor Primaries only Responses of many independent sources available

SEG 2002, Theory of acoustic daylight imaging revisited, p

Simplifying assumptions: Direct arrival at x A correlated with primary at x B Single diffractor Primaries only Responses of many independent sources available

Assume mutually uncorrelated sources

SEG 2002, Theory of acoustic daylight imaging revisited, p

1500 m/s 2000 m/s

Conclusions for interferometry with multiple sources Reconstruction of reflection response Arbitrary medium Primaries and multiples Requires many sources that are mutually uncorrelated

Contents Essentials of seismic interferometry Interferometry with multiple sources Interferometry with multiple receivers Interferometry with multiple scatterers

Cross-correlation

Simplifying assumptions: Direct arrival at x A correlated with primary at x B Single diffractor Primaries only x A is the specular reflection point

Cross-correlation per receiver, followed by sum over receivers gives However ….. Position of specular reflection point is different for each diffractor, which makes this approach useless

0 t Combine with downward extrapolation and imaging Forward extrapolation of ‘source’ Inverse extrapolation of receiver Cross-correlation

0 t

t 0

Forward extrapolation of ‘source’ Inverse extrapolation of receiver Cross-correlation Integrate along receivers Repeat for all subsurface points Ghost

Schuster, EAGE, 2001 Artman et al., EAGE 2004 Draganov et al., SEG 2004, Wednesday afternoon, Poster presentation Mig P3.4

Conclusions for interferometry with multiple receivers No reconstruction of reflection response possible. Instead: imaging of subsurface reflectors Arbitrary medium Primaries only Hence, multiples are imaged as ghosts Requires small number of sources

Contents Essentials of seismic interferometry Interferometry with multiple sources Interferometry with multiple receivers Interferometry with multiple scatterers

Diffuse wavefield: Weaver and Lobkis, 2001, Phys. Rev. Lett. 87

Conclusions for interferometry with multiple scatterers Reconstruction of reflection response (Green’s function) Random medium Primaries and multiples Requires small number of sources

Multiple sources Multiple receivers Multiple scatterers Output Reflection response Imaged reflectors Green’s function Medium assumptions none random Multiples (coda) yes no yes Sources many few