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Wave-equation tomography using image-space phase-encoded data. Claudio Guerra*, Yaxun Tang and Biondo Biondi. SEG Houston – 2009. Motivation. Velocity determination is a difficult task, especially in areas of complex geology. Motivation. - PowerPoint PPT Presentation
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Wave-equation tomography using image-space
phase-encoded data
Claudio Guerra*, Yaxun Tang and Biondo Biondi
SEG Houston – 2009
2
• Velocity determination is a difficult task, especially in areas of complex geology
Motivation
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• Velocity determination is a difficult task, especially in areas of complex geology
• Wave-equation tomography (WETom) is a robust method to estimate the slowness model– uses wavefields as carriers of information– insensitive to multi-pathing
Motivation
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• Velocity determination is a difficult task, especially in areas of complex geology
• Wave-equation tomography (WETom) is a robust method to estimate the slowness model– uses wavefields as carriers of information– insensitive to multi-pathing
– computationally expensive
Motivation
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• WETom can be accelerated by– solving in a target-oriented way
Motivation
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• WETom can be accelerated by– solving in a target-oriented way
– using generalized sources • Shen and Symes (2008) – image-space WETom• Vigh and Starr (2008) – data-space WETom
Motivation
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• Image-space generalized sources– The prestack exploding-reflector modeling (Biondi,
2006) synthesizes areal data from a prestack image obtained with wave-equation methods
Motivation
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• Image-space generalized sources– The prestack exploding-reflector modeling (Biondi,
2006) synthesizes areal data from a prestack image obtained with wave-equation methods
– Wavefields are upward propagated to the top of the target saving computer time
Motivation
? ? ?
z
x
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• Image-space generalized sources– The prestack exploding-reflector modeling (Biondi,
2006) synthesizes areal data from a prestack image obtained with wave-equation methods
– Wavefields are upward propagated to the top of the target saving computer time
– Additional savings when combining modeling experiments
Motivation
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z
x
z
Optimized
Background True x
Motivation – reduce costs in WETom
5% cost
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• Introduction• Prestack exploding-reflector modeling• Image-space phase-encoded wavefields
(ISPEW)
• Image-space WETom using ISPEW
• Numerical example
• Conclusions
Agenda
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• The exploding reflector assumes all energy focused at zero-subsurface offset
• Generalizes the exploding reflector concept
Prestack exploding–reflector modeling
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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• Generalizes the exploding reflector concept• Uses a partially focused wave-equation prestack
image as initial condition
Prestack exploding–reflector modeling
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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• Generalizes the exploding reflector concept• Uses a partially focused wave-equation prestack
image as initial condition• Models areal source and receiver wavefields
suitable for MVA
Prestack exploding–reflector modeling
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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• The exploding–reflector assumes zero–subsurface offset reflectivity– Slowness inaccuracy spreads energy to nonzero-offsets
• Generalizes the exploding reflector concept• Uses a partially focused wave-equation prestack
image as initial condition• Models areal source and receiver wavefields
suitable for MVA• Can be used in a target–oriented way since the
wavefields can be collected at any depth
Prestack exploding–reflector modeling
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
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Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
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Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
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Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
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Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
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Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
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Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
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Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
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x h
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
angle
OriginalADCIG
PermADCIG
z
angle
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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• Combination of modeling experiments– reduces the data size
Prestack exploding–reflector modeling
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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• Combination of modeling experiments– reduces the data size
– generates crosstalk
Prestack exploding–reflector modeling
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
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x h
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
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Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
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Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
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Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
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Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
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Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
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x h
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
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x h
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Prestack exploding–reflector modeling
z
x h x h
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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• Phase-encode the modeling experiments– reduces the data size
Image-space phase-encoded wavefields
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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• Phase-encode the modeling experiments– reduces the data size
– attenuates crosstalk
Image-space phase-encoded wavefields
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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• Phase-encode the modeling experiments– reduces the data size
– attenuates crosstalk
– keeps the kinematic information
Image-space phase-encoded wavefields
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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• Phase-encode the modeling experiments– reduces the data size
– attenuates crosstalk
– keeps the kinematic information
– requires picking the prestack image
Image-space phase-encoded wavefields
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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• Phase-encode the modeling experiments– reduces the data size
– attenuates crosstalk
– keeps the kinematic information
– requires picking the prestack image
– allows selecting key reflectors
Image-space phase-encoded wavefields
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space phase-encoded wavefields
Source wavefield
Receiver wavefield
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space phase-encoded wavefields
Source wavefield initial condition
Receiver wavefield initial condition
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space phase-encoded wavefields
z
x h
z
x
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space phase-encoded wavefields
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x h
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x
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space phase-encoded wavefields
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x h
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Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space phase-encoded wavefields
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x h
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Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space phase-encoded wavefields
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Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space phase-encoded wavefields
z
x h
z
x
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space phase encoded wavefields
x
x
t
Source wavefield
Receiver wavefield
t
0
0
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space phase-encoded wavefields
z
x h x h
No phase-encoding Random phase-encoding
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space WETom with ISPEW
DownwardPropagation
Adjoint imaging
Adjoint scattering
Backgroundwavefields
Perturbedwavefields
Slownessperturbation
Scattering
Imaging
Scatteredwavefields
Perturbedimage
Slownessperturbation
DownProp
Perturbedwavefields
Perturbedimage
UpProp
Scatteredwavefields
Forward
Adjoint
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space WETom with ISPEW
Scattering
Imaging
Scatteredwavefields
Perturbedimage
Slownessperturbation
DownProp
Perturbedwavefields
Forward
Backgroundwavefields
DownwardPropagation
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space WETom with ISPEW
Imaging
Scatteredwavefields
Perturbedimage
DownProp
Perturbedwavefields
Forward
Backgroundwavefields
DownwardPropagation
ScatteringSlowness
perturbation
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space WETom with ISPEW
Imaging
Perturbedimage
Perturbedwavefields
Forward
Backgroundwavefields
DownwardPropagation
ScatteringSlowness
perturbation
Scatteredwavefields
DownProp
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space WETom with ISPEW
Forward
Backgroundwavefields
DownwardPropagation
ScatteringSlowness
perturbation
Scatteredwavefields
DownProp
Imaging
Perturbedimage
Perturbedwavefields
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space WETom with ISPEW
Adjoint imaging
Adjoint scattering
Perturbedwavefields
Slownessperturbation
Perturbedimage
UpProp
Scatteredwavefields
Adjoint
Backgroundwavefields
DownwardPropagation
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space WETom with ISPEW
Adjoint scattering
Perturbedwavefields
Slownessperturbation
UpProp
Scatteredwavefields
Adjoint
Backgroundwavefields
DownwardPropagation
Adjoint imaging
Perturbedimage
z
x hz
x
z
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space WETom with ISPEW
Adjoint scattering
Perturbedwavefields
Slownessperturbation
Adjoint
Backgroundwavefields
DownwardPropagation
Adjoint imaging
Perturbedimage
UpProp
Scatteredwavefields
z
x
z
x
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space WETom with ISPEW
Perturbedwavefields
Adjoint
Backgroundwavefields
DownwardPropagation
Adjoint imaging
Perturbedimage
UpProp
Scatteredwavefields
Adjoint scattering
Slownessperturbation
z
x0.0
-0.02
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space WETom with ISPEW
DownwardPropagation
Adjoint imaging
Adjoint scattering
Backgroundwavefields
Perturbedwavefields
Slownessperturbation
Scattering
Imaging
Scatteredwavefields
Perturbedimage
Slownessperturbation
DownProp
Perturbedwavefields
Perturbedimage
UpProp
Scatteredwavefields
Adjoint
Forward
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space WETom with ISPEW
Z
X X
Background image True slowness
401
sh
ot p
rofil
es
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Image-space WETom with ISPEW
z
x x x
z
Background image Perturbed image Slowness perturbation
401
sh
ot p
rofil
es1
1 im
ag
e-sp
ace
are
al s
ho
ts
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• Solves for the slowness model that minimizes the nonlinear objective function
Image-space WETom – optimization
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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• Solves for the slowness model that minimizes the nonlinear objective function
• WEMVA (Sava, 2004 and Sava and Biondi, 2004)
• DSVA (Shen 2004 and Shen and Symes, 2008)
Image-space WETom – optimization
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space WETom – optimization
Backgroundwavefields
Slownessperturbation
Perturbedimage
DownwardPropagation
Slownessupdate
Imaging
Focusingoperator
FocusedImage?
No
Yes
End
Backgroundimage
Adjoint
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Numerical example
• Marmousi slowness model
True slowness Background slowness
z
x x0.66
0.22
slo
wn
ess(
s/km
)
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Numerical example
1.2
1.0
0.8
z
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
• Marmousi slowness model
True slowness Background slowness
z
x x0.66
0.22
slo
wn
ess(
s/km
)
Slowness ratio
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Numerical example
• Two-way data 376 shots max.offset=6000m
• Background imageh
z
x
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Numerical example
h
z
x
• Image-space phase-encoded wavefields 12 reflectors
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Numerical example
• Image-space phase-encoded wavefields 12 reflectors
h
z
x
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Numerical example
• Marmousi slowness model
True slowness
z
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
x0.66
0.22
slo
wn
ess(
s/km
)
Optimized slowness
x
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Numerical example
• Marmousi slowness model
Smooth true slowness
z
x0.66
0.22
slo
wn
ess(
s/km
)
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
Optimized slowness
x
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Numerical example
• Marmousi slowness model
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Numerical example
z
x
x
Background
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
Optimized
z
Truex
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True
x Optimized
z
x
x
Background
Optimized
z
True
Numerical example
z
xBackground
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
Truex
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Conclusions
• We extended the theory of image-space WETom to the generalized source domain
Introduction ISPEW WETom using ISPEW Example Conclusion
77
Conclusions
• We extended the theory of image-space WETom to the generalized source domain
• ISPEW yields an accurate slowness model
Introduction ISPEW WETom using ISPEW Example Conclusion
78
Conclusions
• We extended the theory of image-space WETom to the generalized source domain
• ISPEW yields reasonable slowness model
• ISPEW drastically decreases the cost of image-space WETom– Reducing data size
– A target-oriented strategy is easily incorporated
Introduction ISPEW WETom using ISPEW Example Conclusion
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• We would like to acknowledge the sponsors of
Acknowledgements
80
Thanks
81
Image-space phase-encoded wavefields
Introduction ISPEW WETom using ISPEW Example Conclusion
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Image-space phase-encoded wavefields
Introduction ISPEW WETom using ISPEW Example Conclusion
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Image-space WETom – velocity optimization
Backgroundwavefields
Slownessperturbation
Perturbedimage
DownwardPropagation
Slownessupdate
Imaging
FocusedImage?
No
Yes
End
Backgroundimage
Adjoint
Focusingoperator
DSO:
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Image-space WETom – velocity optimization
Backgroundwavefields
Slownessperturbation
Perturbedimage
DownwardPropagation
Slownessupdate
Imaging
Focusingoperator
FocusedImage?
No
Yes
End
Backgroundimage
Adjoint
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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Numerical example – slowness perturbation
Introduction ISPEW WETom using ISPEW Example Conclusion
11 ISPEW
Fin
al g
rad
ien
t
z
x x
z
Init
ial g
rad
ien
t 8.0
0.0
70 ISPEW
8.0
0.0
86
Numerical example – slowness perturbation
Introduction ISPEW WETom using ISPEW Example Conclusion
11 ISPEW 70 ISPEW
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Numerical example
• Image-space phase-encoded wavefields 12 reflectors
h
z
x
Introduction PERM ISPEW WETom using ISPEW Example Conclusion
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