relations between reflection and transmission responses of 3-d inhomogeneous media kees wapenaar...
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Relations between reflection and transmission responses of 3-D inhomogeneous media
Kees Wapenaar
Department of Applied Earth Sciences Centre for Technical Geoscience Delft University of Technology
Dallas SEG 2003October 29
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Claerbout, 1968 SEG, 2002‘Acoustic daylight imaging’
T R Berkhout, 1982‘Multiple elimination’
0R R
Imaging ‘from below’
0 0R R
R R Schuster, 2001‘Seismic interferometry’
0 0R T Herman, 1992Wapenaar, 1993‘True amplitude imaging’
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Claerbout, 1968 SEG, 2002‘Acoustic daylight imaging’
T R Berkhout, 1982‘Multiple elimination’
0R R
Imaging ‘from below’
0 0R R
R R Schuster, 2001‘Seismic interferometry’
0 0R T Herman, 1992Wapenaar, 1993‘True amplitude imaging’
One-way reciprocity theorems
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‘State A’
‘State B’
A
A
B
B
),(),( tptp ABBA xx
Reciprocity interrelates states A and B
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‘State A’
‘State B’
A
A
B
B
),(),( ABBA PP xx
Reciprocity interrelates states A and B
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‘State A’ ‘State B’
AP
AP
BP
BP
Downgoing waves
AP
AP
BP
BP
and upgoing waves
One-way reciprocity theorems
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‘State A’ ‘State B’
Convolution-type propagation invariant:
AP
AP
BP
BP
D D
2{ }dA B A B
D
P P P P
x constant
One-way reciprocity theorems
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‘State A’ ‘State B’
0D 0D
mDmD
AP
AP
BP
BP
AP
AP
BP
BP
Convolution-type reciprocity theorem:
One-way reciprocity theorems
0
2 2{ }d { }dm
A B A B A B A B
D D
P P P P P P P P
x x
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‘State A’ ‘State B’
Correlation-type propagation invariant:
*AP *
AP
BP
BP
D D
* * 2{ }dA B A B
D
P P P P
x constant
One-way reciprocity theorems
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‘State A’ ‘State B’
0D 0D
mDmD
BP
BP
*AP *
AP
BP
BP
0
* * 2 * * 2{ }d { }dm
A B A B A B A B
D D
P P P P P P P P
x x
Correlation-type reciprocity theorem:
*AP *
AP
One-way reciprocity theorems
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‘State A’ ‘State B’
Derivation of relations between reflection and transmission responses
States A and B with or without free surface
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‘State A’ ‘State B’
Derivation of relations between reflection and transmission responses
States A and B with or without free surface Convolution- or correlation-type reciprocity
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‘State A’ ‘State B’
Derivation of relations between reflection and transmission responses
States A and B with or without free surface Convolution- or correlation-type reciprocity Sources at upper or lower boundary
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Ax Bx
‘State A’
Ax Bx
‘State B’
States A and B without free surface Convolution-type reciprocity Sources at upper boundary
One-way source-receiver reciprocity
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Ax Bx
‘State A’
Ax Bx
‘State B’
0 ( , )BR x x0 ( , )AR x x
0
2 2{ }d { }dm
A B A B A B A B
D D
P P P P P P P P
x x
( )A x - x ( )B x - x
0 0
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Ax Bx
‘State A’
Ax Bx
‘State B’
0 ( , )A BR x x0 ( , )B AR x x
0 0( , ) ( , )B A A BR R x x x x
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States A and B without free surface Convolution-type reciprocity Sources at lower boundary
Ax Bx Ax Bx
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Ax Bx Ax Bx
0 ( , )A BR x x0 ( , )B AR x x
0 0( , ) ( , )B A A BR R x x x x
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States A and B without free surface Convolution-type reciprocity Source A at lower and source B at upper boundary
Ax
Bx
Ax
Bx
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Ax
Bx
Ax
Bx
0 ( , )A BT x x
0 ( , )B AT x x
0 0( , ) ( , )B A A BT T x x x x
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Ax Bx
‘State A’
Ax Bx
‘State B’
States A and B with free surface Convolution-type reciprocity Sources at upper boundary
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Ax Bx
‘State A’
Ax Bx
‘State B’
( , )A BR x x( , )B AR x x
( , ) ( , )B A A BR R x x x x
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States A and B with free surface Convolution-type reciprocity Sources at lower boundary
Ax Bx Ax Bx
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Ax Bx Ax Bx
( , )A BR x x( , )B AR x x
( , ) ( , )B A A BR R x x x x
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States A and B with free surface Convolution-type reciprocity Source A at lower and source B at upper boundary
Ax
Bx
Ax
Bx
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Ax
Bx
Ax
Bx
( , )A BT x x
( , )B AT x x
( , ) ( , )B A A BT T x x x x
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Summary of one-way source-receiver reciprocity
Without free surface:
0 0( , ) ( , )B A A BR R x x x x
0 0( , ) ( , )B A A BR R x x x x
0 0( , ) ( , )B A A BT T x x x x
With free surface:
( , ) ( , )B A A BR R x x x x( , ) ( , )B A A BR R x x x x
( , ) ( , )B A A BT T x x x x
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Ax Bx
‘State A’
Ax Bx
‘State B’
States A and B without free surface Correlation-type reciprocity Sources at upper boundary
From reflection to transmission
x x
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Ax Bx Ax Bx
0 ( , )AT x x
x x
0 ( , )ABR x x
0 ( , )BT x x
0 ( , )BAR x x
* 20 0{ ( , )} ( , )d ( )
m
A B B A
D
T T
x x x x x x x
0
* 20 0{ ( , )} ( , )dA B
D
R R
x x x x x
0D 0D
mDmD
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Ax Bx Ax Bx
0 ( , )AT x x
x x
0 ( , )ABR x x
0 ( , )BT x x
0 ( , )BAR x x
0D 0D
mDmD
Herman, 1992 Wapenaar and Herrmann, 1993 Application in inverse wave field extrapolation
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Ax Bx
‘State A’
Ax Bx
‘State B’
States A and B with free surface Correlation-type reciprocity Sources at lower boundary
From transmission to reflection
x x
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Ax Bx Ax Bx
x x
( ),AT x x ( ),BT x x
* 2{ ( , )} ( , )dm
A B
D
T T
x x x x x
( , ) ( )2 ReA B A B
R x x x - x
0D 0D
mDmD
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1500 m/s
2000 m/s
Acoustic daylight imaging
Syncline model
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Acoustic daylight imaging
* 2{ ( , )} ( , )dm
A B
D
T T
x x x x x( ),AT x x
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Acoustic daylight imaging
*{ ( )} ( )obs A obs BT T x x( )AobsT x
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Acoustic daylight imaging
Poster presentation Draganov et al.
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Ax Bx
‘State A’
Ax Bx
‘State B’
State A without and state B with free surface Convolution-type reciprocity Sources at upper boundary
Multiple elimination
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Ax Bx Ax Bx
( , )A BR x x0 ( , )B AR x x
0 ( , ) ( , )B A A BR R x x x x
0
20{ ( , ) ( , )}dA B
D
R R
x x x x x
Berkhout, 1982; Verschuur, Berkhout and Wapenaar, 1992 Fokkema and van den Berg, 1993, Van Borselen et al, 1996
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Multiple elimination (van Borselen et al., 1996)
( , )A BR x x 0 ( , )B AR x x
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Ax Bx
‘State A’
Ax Bx
‘State B’
State A without and state B with free surface Correlation-type reciprocity Sources at upper boundary
Seismic interferometry
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Ax Bx Ax Bx
( , )A BR x x0 ( , )B AR x x
0
* 2
0( , ) ( ) { ( , )} ( , )dA B A B B
D
AR R R
x x x - x x x x x x
* 20{ ( , )} ( , )d
m
A B
D
T T
x x x x x
Schuster, 2001, EAGE
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( , )A BR x x0
* 2
0{ ( , )} ( , )d
B
D
AR R
x x x x x
Seismic interferometry
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Ax
Bx
‘State A’
Ax
Bx
‘State B’
States A and B without free surface Correlation-type reciprocity Source A at upper and source B at lower boundary
Reflection ‘from below’
x
x
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Ax
Bx
Ax
Bxx
x0 ( , )AR x x
0 ( , )B AT x x
0 ( , )A BT x x
0 ( , )BR x x
* 20 0{ ( , )} ( , )d
m
A B
D
T R
x x x x x
0
* 20 0{ ( , )} ( , )dA B
D
R T
x x x x x
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‘State A’ ‘State B’
Derivation of relations between reflection and transmission responses
States A and B with or without free surface
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‘State A’ ‘State B’
Derivation of relations between reflection and transmission responses
States A and B with or without free surface Convolution- or correlation-type reciprocity
![Page 48: Relations between reflection and transmission responses of 3-D inhomogeneous media Kees Wapenaar Department of Applied Earth Sciences Centre for Technical](https://reader035.vdocument.in/reader035/viewer/2022062312/551643a7550346c6758b54ff/html5/thumbnails/48.jpg)
‘State A’ ‘State B’
Derivation of relations between reflection and transmission responses
States A and B with or without free surface Convolution- or correlation-type reciprocity Sources at upper or lower boundary
![Page 49: Relations between reflection and transmission responses of 3-D inhomogeneous media Kees Wapenaar Department of Applied Earth Sciences Centre for Technical](https://reader035.vdocument.in/reader035/viewer/2022062312/551643a7550346c6758b54ff/html5/thumbnails/49.jpg)
Claerbout, 1968 SEG, 2002‘Acoustic daylight imaging’
T R Berkhout, 1982‘Multiple elimination’
0R R
Imaging ‘from below’
0 0R R
R R Schuster, 2001‘Seismic interferometry’
0 0R T Herman, 1992Wapenaar, 1993‘True amplitude imaging’
One-way reciprocity theorems
![Page 50: Relations between reflection and transmission responses of 3-D inhomogeneous media Kees Wapenaar Department of Applied Earth Sciences Centre for Technical](https://reader035.vdocument.in/reader035/viewer/2022062312/551643a7550346c6758b54ff/html5/thumbnails/50.jpg)
Monitoring the universe by an array of telescopes
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Monitoring the subsurface by an array of geophones
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Combined monitoring the universe and the subsurface:Different applications; shared infrastructure
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25% of antennas in central core
High speed data transport
Antenna cluster (Station)
Central processor
X
Shared infrastructure (1)
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Shared infrastructure (2)
1 3 0 0 0 D a ta F a b ric s
o n-line hyb rid d ata p ro c es s ing c lus terU s er p o s t p ro c es s ing
D ata P ro c es s ing P lant
C o ntro l C enter(s )