[email protected] wave-equation mva by inversion of differential image perturbations paul sava...
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![Page 1: Paul@sep.stanford.edu Wave-equation MVA by inversion of differential image perturbations Paul Sava & Biondo Biondi Stanford University SEP](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d4a5503460f94a26f4c/html5/thumbnails/1.jpg)
Wave-equation MVA by inversion of differential
image perturbations
Paul Sava & Biondo BiondiStanford University
SEP
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Wave-equation MVA (WEMVA)
• Band-limited• Multi-pathing• Resolution
• Born approximation– small anomaly
• Rytov approximation– phase unwrapping
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Outline
1. WEMVA overview
2. Born image perturbation
3. Differential image perturbation
4. Example
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A tomography problem
sqs LΔminΔTraveltime
MVA
Wave-equation tomography
Wave-equation MVA
q t traveltime
d
data
Rimage
L ray field wavefield wavefield
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WEMVA: objective function
slowness perturbation
image perturbation
slownessperturbation(unknown)
Linear WEMVAoperator
imageperturbation
(known)
sRs LΔminΔ
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WEMVA: objective function
sRs LΔminΔ
Traveltime
MVA
Wave-equation tomography
Wave-equation MVA
t d R
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Outline
1. WEMVA overview
2. Born image perturbation
3. Differential image perturbation
4. Example
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“Data” estimate
Traveltime
MVA
Wave-equation tomography
Wave-equation MVA
t d Rray
tracing
data
modeling
residual
migration
sRs LΔminΔ
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Residual migration: the problem
Correct velocity Incorrect velocity
Zero offset image
Angle gathers
Zero offset image
Angle gathers
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Outline
1. WEMVA overview
2. Born image perturbation
3. Differential image perturbation
4. Example
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Differential image perturbation
0
1
ˆ Rd
dSR
00 RRSR Image
difference
Image differential
Computed Measured
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Outline
1. WEMVA overview
2. Born image perturbation
3. Differential image perturbation
4. Example
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Field data example
• North Sea– Salt environment– Subset
– 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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Summary
• MVA– Wavefield extrapolation methods– Born linearization– Differential image perturbations
• Key points– Band-limited (sharp velocity contrasts)– Multi-pathing (complicated wavefields)– Resolution (frequency redundancy)
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MVA information (a)Traveltime MVA Wave-equation MVA
• Offset focusing (flat ADCIG) • Offset focusing (flat ADCIG)
z
z
xx
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MVA information (b)Traveltime MVA Wave-equation MVA
• Offset focusing (flat ADCIG) • Offset focusing (flat ADCIG)
• Spatial focusing
z
z
xx
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MVA information (c)Traveltime MVA Wave-equation MVA
• Offset focusing (flat ADCIG) • Offset focusing (flat ADCIG)
• Spatial focusing
• Frequency redundancy
low high
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low high
WEMVA cost reduction
• Full image– Offset focusing
– Spatial focusing
– Frequency
• Normal incidence image
– Spatial focusing
– “fat” rays