[email protected]. edu Migration velocity analysis by recursive wavefield extrapolation Paul Sava & Biondo Biondi Stanford University SEP
Jan 02, 2016
Migration velocity analysis by recursive wavefield
extrapolation
Paul Sava & Biondo BiondiStanford University
SEP
Wave-equation MVA (WEMVA)
• Band-limited• Multi-pathing• Resolution
• Born approximation– small anomaly
• Rytov approximation– phase unwrapping
Outline
1. WEMVA overview
2. Born image perturbation
3. Differential image perturbation
4. Example
A tomography problem
sqs LΔminΔTraveltime
MVA
Wave-equation tomography
Wave-equation MVA
q t traveltime
d
data
Rimage
L ray field wavefield wavefield
WEMVA: objective function
slowness perturbation
image perturbation
slownessperturbation(unknown)
Linear WEMVAoperator
imageperturbation
(known)
sRs LΔminΔ
WEMVA: objective function
sRs LΔminΔ
Traveltime
MVA
Wave-equation tomography
Wave-equation MVA
t d R
Outline
1. WEMVA overview
2. Born image perturbation
3. Differential image perturbation
4. Example
“Data” estimate
Traveltime
MVA
Wave-equation tomography
Wave-equation MVA
t d Rray
tracing
data
modeling
residual
migration
sRs LΔminΔ
Residual migration: the problem
Correct velocity Incorrect velocity
Zero offset image
Angle gathers
Zero offset image
Angle gathers
Outline
1. WEMVA overview
2. Born image perturbation
3. Differential image perturbation
4. Example
Differential image perturbation
0
1
ˆ Rd
dSR
00 RRSR Image
difference
Image differential
Computed Measured
Outline
1. WEMVA overview
2. Born image perturbation
3. Differential image perturbation
4. Example
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
Summary
• MVA– Wavefield extrapolation methods– Born linearization– Differential image perturbations
• Key points– Band-limited (sharp velocity contrasts)– Multi-pathing (complicated wavefields)– Resolution (frequency redundancy)
MVA information (a)Traveltime MVA Wave-equation MVA
• Offset focusing (flat ADCIG) • Offset focusing (flat ADCIG)
z
z
xx
MVA information (b)Traveltime MVA Wave-equation MVA
• Offset focusing (flat ADCIG) • Offset focusing (flat ADCIG)
• Spatial focusing
z
z
xx
MVA information (c)Traveltime MVA Wave-equation MVA
• Offset focusing (flat ADCIG) • Offset focusing (flat ADCIG)
• Spatial focusing
• Frequency redundancy
low high
low high
WEMVA cost reduction
• Full image– Offset focusing
– Spatial focusing
– Frequency
• Normal incidence image
– Spatial focusing
– “fat” rays