Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob...
-
Upload
beau-earls -
Category
Documents
-
view
219 -
download
0
Transcript of Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob...
![Page 1: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/1.jpg)
Elastodynamic reciprocity theorems for time-lapse seismic methods
Kees WapenaarMenno DillenJacob Fokkema
Centre for Technical GeoscienceDelft University of Technology
![Page 2: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/2.jpg)
Review of reciprocity theorems and seismic applications
Kees WapenaarMenno DillenJacob Fokkema
Centre for Technical GeoscienceDelft University of Technology
![Page 3: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/3.jpg)
‘State A’
‘State B’
A
A
B
B
),(),( tptp ABBA xx
![Page 4: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/4.jpg)
‘State A’
‘State B’
A
A
B
B
),(),( ABBA PP xx
![Page 5: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/5.jpg)
![Page 6: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/6.jpg)
‘State A’
‘State B’
),(),( ABBA PP xx
![Page 7: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/7.jpg)
‘State A’
‘State B’
),(),( ABBA PP xx
![Page 8: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/8.jpg)
‘State A’
‘State B’
V
kBAkBkAABBA nPVVPPP xxx 2,, d}{),(),(
Vn
![Page 9: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/9.jpg)
State A State BPA, Vk,A
QA,Fk,A
A, A
PB, Vk,B
QB,Fk,B
B, B
Wave fields
Sources
Medium
‘State B’‘State A’
QAQB
PA
PB
V n
V
V n
V
A, A B, B
![Page 10: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/10.jpg)
‘State B’‘State A’
QAQB
PA
PB
V
BABkAkBkAkBA
V
BkAkBA
V
kBAkBkA
PQVFFVQP
VVPPjnPVVP
x
xx
3,,,,
3,,
2,,
d}{
d}{d}{ 0 0
0 0
)( Axx )( Bxx
V n
V
V n
V
![Page 11: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/11.jpg)
‘State B’‘State A’
QAQB
PA
PB
V
BABkAkBkAkBA
V
BkAkBA
V
kBAkBkA
PQVFFVQP
VVPPjnPVVP
x
xx
3,,,,
3,,
2,,
d}{
d}{d}{
V n
V
V n
V
![Page 12: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/12.jpg)
‘State B’‘State A’
V
BijAijBiAiBiAiBijAij
V
BiAiijklBklAij
V
jBijAiBiAij
THVFFVHT
VVsTTjnTVVT
x
xx
3,,,,,,,,
3,,,,
2,,,,
d}{
d}{d}{
V n
V
V n
V
![Page 13: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/13.jpg)
1872, Betti: Elastostatic fields
1873, Rayleigh: Acoustic time-harmonic fields
1959, Knopoff and Gangi: Elastodynamic fields in inhomogeneous anisotropic media
Some history
1966, De Hoop: visco-elastic anisotropic media
1993, Fokkema and van den Berg: applications in seismic processing
(source: Arntsen and Carcione, Geophysics, 2000)
![Page 14: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/14.jpg)
‘State A’
‘State B’
V
kBAkBkAABBA nPVVPPP xxx 2,, d}{),(),(
Vn
![Page 15: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/15.jpg)
‘State B’
V
kBAkBkAABBA nPVVPPP xxx 2,, d}{),(),(
‘State A’
![Page 16: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/16.jpg)
‘State A’ ‘State B’
Multiple elimination (van Borselen et al., 1996)
V
kBAkBkAABBA nPVVPPP xxx 2,, d}{),(),(
![Page 17: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/17.jpg)
‘State A’ ‘State B’
Multiple elimination (van Borselen et al., 1996)
![Page 18: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/18.jpg)
‘State B’‘State A’
V n
V
V n
V
V
jBijAiBiAijABiAiBAiBi nTVVTVfVf xxx 2,,,,,,,, d}{),(),(
Aif ,
AiV ,
BiV ,Bif ,
Surface wave suppression (van Zanen et al., 2000)
![Page 19: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/19.jpg)
‘State A’ ‘State B’
V
jBijAiBiAijABiAiBAiBi nTVVTVfVf xxx 2,,,,,,,, d}{),(),(
Surface wave suppression (van Zanen et al., 2000)
![Page 20: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/20.jpg)
‘State A’ ‘State B’
Surface wave suppression (van Zanen et al., 2000)
![Page 21: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/21.jpg)
‘State B’‘State A’
QAQB
PA
PB
V
BABkAkBkAkBA
V
BkAkBA
V
kBAkBkA
PQVFFVQP
VVPPjnPVVP
x
xx
3,,,,
3,,
2,,
d}{
d}{d}{
V n
V
V n
V
Time-lapse seismic (Dillen et al, 2000)
![Page 22: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/22.jpg)
‘State B’‘State A’
QBPB
V
BABkAkBkAkBA
V
BkAkBA
V
kBAkBkA
PQVFFVQP
VVPPjnPVVP
x
xx
3,,,,
3,,
2,,
d}{
d}{d}{
V n
V
Time-lapse seismic (Dillen et al, 2000)
![Page 23: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/23.jpg)
V
BABkAkBkAkBA
V
BkAkBA
V
kBAkBkA
PQVFFVQP
VVPPjnPVVP
x
xx
3,,,,
3,,
2,,
d}{
d}{d}{
‘State A’ ‘State B’
Time-lapse seismic (Dillen et al, 2000)
![Page 24: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/24.jpg)
State A State B
xA xA
xB xB
),x(),x( ABBA PP
Acoustic reciprocity for one-way wave fields
![Page 25: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/25.jpg)
V
BABABABA
V
HBABA n
x
x
3
23
d}{
d}{
PSPSSPSP
PPPP
V
BABkAkBkAkBA
V
kBAkBkA
PQVFFVQP
nPVVP
x
x
3,,,,
2,,
d}{
d}{
Acoustic reciprocity for full (two-way) wave fields
Acoustic reciprocity for one-way wave fields
![Page 26: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/26.jpg)
A BA B
03x
13x
23x
33x
03x
13x
23x
33x
HRBSA x)x,x()x,x( 2d PP
HRBSA x)x,x()x,x( 2dPP
Fokkema and van den Berg (1996) Dillen (2000, Ph.d thesis) Wapenaar et al. (2000, SEG)
B A
Application in time-lapse seismic
![Page 27: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/27.jpg)
A BA B
03x
13x
23x
33x
03x
13x
23x
33x
HRBSA x)x,x()x,x( 2d PP
HRBSA x)x,x()x,x( 2dPP
Fokkema and van den Berg (1996) Dillen (2000, Ph.d thesis) Wapenaar et al. (2000, SEG)
B A
Application in time-lapse seismic
![Page 28: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/28.jpg)
Difference data
Application in time-lapse seismic
![Page 29: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/29.jpg)
Boundary integral
Application in time-lapse seismic
![Page 30: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/30.jpg)
Conclusions
Source - receiver reciprocity is a special caseof general reciprocity
General reciprocity theorems formulate a relationbetween wave fields, sources and medium parameters in two different states
- Acoustic and elastodynamic
- Two-way and one-way
Applications:
- Multiple elimination- Surface wave suppression- Time-lapse seismic- Etc.
![Page 31: Elastodynamic reciprocity theorems for time-lapse seismic methods Kees Wapenaar Menno Dillen Jacob Fokkema Centre for Technical Geoscience Delft University.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551a71d5550346b52d8b4fa2/html5/thumbnails/31.jpg)