yuting duan , antoine guitton, and paul sava center for wave...
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![Page 1: Yuting Duan , Antoine Guitton, and Paul Sava Center for Wave …newton.mines.edu/paul/talks/2017_CWP_ElasticLSRTM.pdf · Elastic least-squares migration Yuting Duan , Antoine Guitton,](https://reader031.vdocuments.pub/reader031/viewer/2022022001/5c695d5e09d3f29b758d1277/html5/thumbnails/1.jpg)
Elastic least-squares migration
Yuting Duan∗, Antoine Guitton, and Paul SavaCenter for Wave Phenomena
Colorado School of Mines∗presently at Shell International Exploration and Production Inc.
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α = V 2p
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α = V 2p
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β = V 2s
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β = V 2s
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α = V 2p
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![Page 7: Yuting Duan , Antoine Guitton, and Paul Sava Center for Wave …newton.mines.edu/paul/talks/2017_CWP_ElasticLSRTM.pdf · Elastic least-squares migration Yuting Duan , Antoine Guitton,](https://reader031.vdocuments.pub/reader031/viewer/2022022001/5c695d5e09d3f29b758d1277/html5/thumbnails/7.jpg)
β = V 2s
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![Page 8: Yuting Duan , Antoine Guitton, and Paul Sava Center for Wave …newton.mines.edu/paul/talks/2017_CWP_ElasticLSRTM.pdf · Elastic least-squares migration Yuting Duan , Antoine Guitton,](https://reader031.vdocuments.pub/reader031/viewer/2022022001/5c695d5e09d3f29b758d1277/html5/thumbnails/8.jpg)
higher resolutiond
fewer artifactsd
improved amplitudes
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objective function
J =∑e
1
2‖Fm− d‖2
I F: demigration
I FT: migration
![Page 10: Yuting Duan , Antoine Guitton, and Paul Sava Center for Wave …newton.mines.edu/paul/talks/2017_CWP_ElasticLSRTM.pdf · Elastic least-squares migration Yuting Duan , Antoine Guitton,](https://reader031.vdocuments.pub/reader031/viewer/2022022001/5c695d5e09d3f29b758d1277/html5/thumbnails/10.jpg)
isotropic wave equation
u− α∇(∇ · u) + β∇× (∇× u) = f
I α = λ+2µρ
I β = µρ
I u (e, x, t): background wavefield
I f (e, x, t): source
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δα, δβ → δu
δu− α∇(∇ · δu) + β∇× (∇× δu)
= δα∇(∇ · u)− δβ∇× (∇× u)
Born
I δα: α perturbation
I δβ: β perturbation
I u: background wavefield
I δu (e, x, t): perturbed wavefield
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δα, δβ → δu
δu− α∇(∇ · δu) + β∇× (∇× δu)
= δα∇(∇ · u)− δβ∇× (∇× u)
Born
I δα: α perturbation
I δβ: β perturbation
I u: background wavefield
I δu (e, x, t): perturbed wavefield
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δα, δβ → δu
δu− α∇(∇ · δu) + β∇× (∇× δu)
= δα∇(∇ · u)− δβ∇× (∇× u)
Born
I δα: α perturbation
I δβ: β perturbation
I u: background wavefield
I δu (e, x, t): perturbed wavefield
![Page 14: Yuting Duan , Antoine Guitton, and Paul Sava Center for Wave …newton.mines.edu/paul/talks/2017_CWP_ElasticLSRTM.pdf · Elastic least-squares migration Yuting Duan , Antoine Guitton,](https://reader031.vdocuments.pub/reader031/viewer/2022022001/5c695d5e09d3f29b758d1277/html5/thumbnails/14.jpg)
δα, δβ → δu
δu− α∇(∇ · δu) + β∇× (∇× δu)
= δα∇(∇ · u)− δβ∇× (∇× u)
= [∇(∇ · u) d −∇× (∇× u)]
[δα
δβ
]= Bm
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δα, δβ → δu
δu− α∇(∇ · δu) + β∇× (∇× δu)
= δα∇(∇ · u)− δβ∇× (∇× u)
= [∇(∇ · u) d −∇× (∇× u)]
[δα
δβ
]= Bm
![Page 16: Yuting Duan , Antoine Guitton, and Paul Sava Center for Wave …newton.mines.edu/paul/talks/2017_CWP_ElasticLSRTM.pdf · Elastic least-squares migration Yuting Duan , Antoine Guitton,](https://reader031.vdocuments.pub/reader031/viewer/2022022001/5c695d5e09d3f29b758d1277/html5/thumbnails/16.jpg)
δα, δβ → δu
δu− α∇(∇ · δu) + β∇× (∇× δu)
= δα∇(∇ · u)− δβ∇× (∇× u)
= [∇(∇ · u) d −∇× (∇× u)]
[δα
δβ
]= Bm
![Page 17: Yuting Duan , Antoine Guitton, and Paul Sava Center for Wave …newton.mines.edu/paul/talks/2017_CWP_ElasticLSRTM.pdf · Elastic least-squares migration Yuting Duan , Antoine Guitton,](https://reader031.vdocuments.pub/reader031/viewer/2022022001/5c695d5e09d3f29b758d1277/html5/thumbnails/17.jpg)
δα, δβ → δu
δu− α∇(∇ · δu) + β∇× (∇× δu)
= δα∇(∇ · u)− δβ∇× (∇× u)
= [∇(∇ · u) d −∇× (∇× u)]
[δα
δβ
]= Bm
![Page 18: Yuting Duan , Antoine Guitton, and Paul Sava Center for Wave …newton.mines.edu/paul/talks/2017_CWP_ElasticLSRTM.pdf · Elastic least-squares migration Yuting Duan , Antoine Guitton,](https://reader031.vdocuments.pub/reader031/viewer/2022022001/5c695d5e09d3f29b758d1277/html5/thumbnails/18.jpg)
forward operator (demigration)
dK = KKKKKKKKKKPKKKKKBKKKm
data forward Bornextraction modeling source
I m: model perturbation
[δα
δβ
]I d: data
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forward operator (demigration)
dK = KKKKKKKKKKPKKKKKBKKKm
data forward Bornextraction modeling source
I m: model perturbation
[δα
δβ
]I d: data
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forward operator (demigration)
dK = KKKKKKKKKKPKKKKKBKKKm
data forward Bornextraction modeling source
I m: model perturbation
[δα
δβ
]I d: data
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forward operator (demigration)
dK = KKKKKKKKKKPKKKKKBKKKm
data forward Bornextraction modeling source
I m: model perturbation
[δα
δβ
]I d: data
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adjoint operator (migration)
mK = KKKBTKKKKKPTKKKKKKTKKKd
imaging backward datacondition modeling injection
I m: model perturbation
[δα
δβ
]I d: data
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adjoint operator (migration)
mK = KKKBTKKKKKPTKKKKKKTKKKd
imaging backward datacondition modeling injection
I m: model perturbation
[δα
δβ
]I d: data
![Page 24: Yuting Duan , Antoine Guitton, and Paul Sava Center for Wave …newton.mines.edu/paul/talks/2017_CWP_ElasticLSRTM.pdf · Elastic least-squares migration Yuting Duan , Antoine Guitton,](https://reader031.vdocuments.pub/reader031/viewer/2022022001/5c695d5e09d3f29b758d1277/html5/thumbnails/24.jpg)
adjoint operator (migration)
mK = KKKBTKKKKKPTKKKKKKTKKKd
imaging backward datacondition modeling injection
I m: model perturbation
[δα
δβ
]I d: data
![Page 25: Yuting Duan , Antoine Guitton, and Paul Sava Center for Wave …newton.mines.edu/paul/talks/2017_CWP_ElasticLSRTM.pdf · Elastic least-squares migration Yuting Duan , Antoine Guitton,](https://reader031.vdocuments.pub/reader031/viewer/2022022001/5c695d5e09d3f29b758d1277/html5/thumbnails/25.jpg)
imaging condition
δα =∑e,t
[∇(∇ · us)] · ur
δβ =∑e,t
[−∇× (∇× us)] · ur
I us : source wavefield
I ur : receiver wavefield
![Page 26: Yuting Duan , Antoine Guitton, and Paul Sava Center for Wave …newton.mines.edu/paul/talks/2017_CWP_ElasticLSRTM.pdf · Elastic least-squares migration Yuting Duan , Antoine Guitton,](https://reader031.vdocuments.pub/reader031/viewer/2022022001/5c695d5e09d3f29b758d1277/html5/thumbnails/26.jpg)
objective function
J =∑e
1
2‖W (KBFm− d) ‖2
I W (e, x, t): data weighting
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objective function
J =∑e
1
2‖W (KPBm− d) ‖2
I W (e, x, t): data weighting
![Page 28: Yuting Duan , Antoine Guitton, and Paul Sava Center for Wave …newton.mines.edu/paul/talks/2017_CWP_ElasticLSRTM.pdf · Elastic least-squares migration Yuting Duan , Antoine Guitton,](https://reader031.vdocuments.pub/reader031/viewer/2022022001/5c695d5e09d3f29b758d1277/html5/thumbnails/28.jpg)
objective function
J =∑e
1
2‖W (KPBm− d) ‖2
I W (e, x, t): data weighting
![Page 29: Yuting Duan , Antoine Guitton, and Paul Sava Center for Wave …newton.mines.edu/paul/talks/2017_CWP_ElasticLSRTM.pdf · Elastic least-squares migration Yuting Duan , Antoine Guitton,](https://reader031.vdocuments.pub/reader031/viewer/2022022001/5c695d5e09d3f29b758d1277/html5/thumbnails/29.jpg)
example
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Marmousi
α
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Marmousi
β
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δα
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δβ
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δα���
���
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δβ���
���
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recorded dz
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recorded dz
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δα���
���
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δβ���
���
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δβ���
���
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α β
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Volve data
I 240 receivers
I 242 shots
I Models: Vp, Vs , δ, ε
I frequency: 0− 15Hz
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Volve data
I 240 receivers
I 242 shots
I Models: Vp, Vs , δ, ε
I frequency: 0− 15Hz
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Volve data
I 240 receivers
I 242 shots
I Models: α, β, δ, ε
I frequency: 0− 15Hz
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α model
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β model
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bandpass
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3D to 2D compensation
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data weighting
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data
@@@R
@@@R
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α elastic RTM image
@@@R
@@@R
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α elastic LSRTM image
@@@R
@@@R
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β elastic RTM image
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β elastic LSRTM image
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vertical component: observation
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vertical component: prediction with α & β image
@@@R
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vertical component: data misfit
@@@R
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summary
elastic imaging conditionelastic model perturbationno polarity reversal
elastic LSM methodhigher resolutionimproved amplitudes
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acknowledgement
d
Statoil ASA and the Volve license partnersExxonMobil E&P Norway ASBayerngas Norge AS
d
dd • Disclaimer: The views expressed in this presentation are the views of the authors anddo not necessarily reflect the views of Statoil ASA and the Volve field license partners.
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vertical component: prediction with α image
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vertical component: prediction with β image