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
•
From transmission to reflection
•
From reflection to transmission
• 3-D relations
•
Claerbout’s conjecture
•
One-way reciprocity theorem
•
From transmission to reflection
•
From reflection to transmission
• 2-D examples
• Discussion of applications
Claerbout, 1968 :
Transmission response
Reflection response
With free surface :
0
Without free surface :
0
Transmission response
Reflection response
Contents
• 1-D relations
•
From transmission to reflection
•
From reflection to transmission
• 3-D relations
•
Claerbout’s conjecture
•
One-way reciprocity theorem
•
From transmission to reflection
•
From reflection to transmission
• 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

A
P

A
P

A
P

A
P

B
P

B
P

B
P

B
P
D0
Dm
From transmission to reflection :
1-Dimensional :
3-Dimensional :
From reflection to transmission :
1-Dimensional :
3-Dimensional :
=
Contents
• 1-D relations
•
From transmission to reflection
•
From reflection to transmission
• 3-D relations
•
Claerbout’s conjecture
•
One-way reciprocity theorem
•
From transmission to reflection
•
From reflection to transmission
• 2-D examples
• Discussion of applications
Syncline model
Transmission response
Reflection response
xA
xB
D0
Dm
x
Syncline model
Transmission response (fixed x, variable x A)
(variable x )
xA
xB
D0
Dm
x
Syncline model
(variable x A )
Causal part of
Directly modeled reflection response
Syncline model with extra layer
Transmission response with coda
Reflection response with coda
Contents
• 1-D relations
•
From transmission to reflection
•
From reflection to transmission
• 3-D relations
•
Claerbout’s conjecture
•
One-way reciprocity theorem
•
From transmission to reflection
•
From reflection to transmission
• 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
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)