paul@sep.stanford.edu analytical image perturbations for wave-equation migration velocity analysis...
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paul@sep.stanford.edu
Analytical image perturbations for wave-equation
migration velocity analysis
Paul Sava & Biondo BiondiStanford University
paul@sep.stanford.edu
Wave-equation MVA (WEMVA)
• Wavefield-based MVA method
• Closely related to– Wave-equation migration– Wave-equation tomography
• Benefits– Finite-frequency– Multipathing– Hi resolution
paul@sep.stanford.edu
A tomography problem
sqs LΔminΔTraveltime
tomography/MVA
Wave-equation tomography
Wave-equation MVA
q t traveltime
d
data
Rimage
L ray field wavefield wavefield
paul@sep.stanford.edu
Outline
1. WEMVA review
2. Image perturbation
3. Field data example
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Δss1
Δss1eW fU
WEMVA: main idea 1eWΔW Δs
1 f
1s
1s1 eW fU
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Born approximation 1eWΔW Δs
1 f
ΔsWΔW 1 f
iei 1
ie
sR LΔ
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WEMVA: objective function
slowness perturbation
image perturbation
slownessperturbation(unknown)
Linear WEMVAoperator
imageperturbation
(known)
sRs LΔminΔ
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Slowness backprojection
slowness perturbation
image perturbation
slowness perturbation
image perturbation
Rs Δ*L
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MVA informationTraveltime MVA Wave-equation MVA
• Offset focusing (flat gathers) • Offset focusing (flat gathers)
• Spatial focusing
• Frequency redundancy
z
z
xx
paul@sep.stanford.edu
Outline
1. WEMVA review
2. Image perturbation
3. Field data example
paul@sep.stanford.edu
“Data” estimate
Traveltime
MVA
Wave-equation tomography
Wave-equation MVA
t d Rray
tracing
data
modeling
residual
migration
sRs LΔminΔ
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Prestack Stolt residual migration
• Background image R1
• Velocity ratio ),( 1 RSR
1RRR • Image perturbation
R
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Incorrect velocityCorrect velocity
Zero offset image
Angle gathers
Synthetic model
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Residual migration: the problem
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Differential image perturbation
1d
dRR
1RRR Image
difference
Image differential
Computed Measured
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Background image
Zero offset image
Angle gathers
Background image
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Differential image
Differential image
Zero offset image
Angle gathers
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Image to slowness perturbation
Slowness perturbation
Image perturbation
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Image comparison
Updated slownessCorrect slowness
Zero offset image
slowness
paul@sep.stanford.edu
Outline
1. WEMVA review
2. Image perturbation
3. Field data example
paul@sep.stanford.edu
Field data example
• North Sea– Salt environment
– One non-linear iteration• Migration (background image)
• Residual migration (image perturbation)
• Slowness inversion (slowness perturbation)
• Slowness update (updated slowness)
• Re-migration (updated image)
location
dep
th
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location
dep
thde
pth
Zero offset image
Angle gathers
Background slowness
Background image
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dep
th
velocity ratio velocity ratio
Semblance Angle-gathers
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1
1
1
location
dep
th
Zero offset image
Background image
location
“Ratio” map
1d
dRR
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location
dep
th
location
Zero offset image Zero offset image
Background image
Image perturbation
paul@sep.stanford.edu
location
dep
th
location
Zero offset image
Image perturbation
Slowness perturbation
sRs LΔminΔ
paul@sep.stanford.edu
location
dep
thde
pth
Zero offset image
Angle gathers
Background slowness
Background image
paul@sep.stanford.edu
location
dep
thde
pth
Zero offset image
Angle gathers
Updated slowness
Updated image
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dep
thde
pth
location
Angle gathers
“Correct” slowness
Zero offset image
“Correct” image
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Summary
• Wave-equation MVA– Finite frequency– Multipathing– Hi resolution– Image space objective function
• Image perturbation– From prestack Stolt residual migration– Differential method– Compliant with the Born approximation
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