Codas in reflection and transmission responses and their mutual relations Kees Wapenaar Deyan Draganov Jan Thorbecke Jacob Fokkema Centre for Technical Geoscience Delft University of Technology

Contents 1-D relations 3-D relations 2-D examples From transmission to reflection From reflection to transmission 3-D relations Claerbout’s conjecture One-way reciprocity theorem 2-D examples Discussion of applications

Claerbout, 1968 :

Reflection response Transmission response

With free surface :

Without free surface :

Transmission response Reflection response

Contents 1-D relations 3-D relations 2-D examples From transmission to reflection From reflection to transmission 3-D relations Claerbout’s conjecture One-way reciprocity theorem 2-D examples Discussion of applications

Claerbout, 1968 :

Claerbout’s conjecture: ‘‘By crosscorrelating noise traces recorded at two locations on the surface, we can construct the wave field that would be recorded at one of the locations if there was a source at the other’’

Reciprocity for one-way wave fields

From transmission to reflection : 1-Dimensional : 3-Dimensional :

From reflection to transmission : 1-Dimensional : 3-Dimensional : =

Contents 1-D relations 3-D relations 2-D examples From transmission to reflection From reflection to transmission 3-D relations Claerbout’s conjecture One-way reciprocity theorem 2-D examples Discussion of applications

Syncline model

Reflection response Transmission response

Syncline model

Transmission response (fixed , variable )

(variable )

Syncline model

(variable )

Causal part of

Directly modeled reflection response

Syncline model with extra layer

Transmission response with coda

Reflection response with coda

Contents 1-D relations 3-D relations 2-D examples From transmission to reflection From reflection to transmission 3-D relations Claerbout’s conjecture One-way reciprocity theorem 2-D examples Discussion of applications

From transmission to reflection Acoustic daylight imaging (Rickett and Claerbout , 1999) From reflection to transmission Construction of inverse propagation operators (Herman, 1992, Wapenaar and Herrmann, 1993) From reflection to reflection Interferometric imaging (Schuster, 2001)

= From transmission to reflection From reflection to transmission Acoustic daylight imaging (Rickett and Claerbout , 1999) From reflection to transmission Construction of coda in inverse propagation operators (Herman, 1992, Wapenaar and Herrmann, 1993) From reflection to reflection Interferometric imaging (Schuster, 2001) =

From transmission to reflection Acoustic daylight imaging (Rickett and Claerbout , 1999) From reflection to transmission Construction of coda in inverse propagation operators (Herman, 1992, Wapenaar and Herrmann, 1993) From reflection to reflection Interferometric imaging (Schuster, 2001)