[email protected]
Migration velocity analysis by recursive wavefield
extrapolation
Paul Sava & Biondo BiondiStanford University
SEP
[email protected]
Motivation
[email protected]
Wave-equation MVA (WEMVA)
• Band-limited• Multi-pathing• Resolution
• Born approximation– small anomaly
• Rytov approximation– phase unwrapping
[email protected]
Wave-equation MVA (WEMVA)
• WE tomography– data space
• WE MVA– image space
[email protected]
Outline
1. WEMVA overview
2. Born image perturbation
3. Differential image perturbation
4. Example
[email protected]
A tomography problem
sqs LΔminΔTraveltime
MVA
Wave-equation tomography
Wave-equation MVA
q t traveltime
d
data
Rimage
L ray field wavefield wavefield
[email protected]
Δss0
sii 0seW U
WEMVA: main idea
0WWWΔ
0s
0s0 eW iU
[email protected]
Born approximation 1eWΔW Δs
0 i
ΔsWΔW 0 i
iei 1
ie
sR LΔ
[email protected]
WEMVA: objective function
slowness perturbation
image perturbation
slownessperturbation(unknown)
Linear WEMVAoperator
imageperturbation
(known)
sRs LΔminΔ
[email protected]
WEMVA: objective function
sRs LΔminΔ
Traveltime
MVA
Wave-equation tomography
Wave-equation MVA
t d R
[email protected]
Fat ray: GOM example
[email protected]
Outline
1. WEMVA overview
2. Born image perturbation
3. Differential image perturbation
4. Example
[email protected]
“Data” estimate
Traveltime
MVA
Wave-equation tomography
Wave-equation MVA
t d Rray
tracing
data
modeling
residual
migration
sRs LΔminΔ
[email protected]
Prestack Stolt residual migration
• Background image R0
• Velocity ratio 0RSR
RR0
[email protected]
Prestack Stolt residual migration
0RRR • Image perturbation
RR0
[email protected]
Born approximation
[email protected]
Residual migration: the problem
Correct velocity Incorrect velocity
Zero offset image
Angle gathers
Zero offset image
Angle gathers
[email protected]
Born approximation
[email protected]
Outline
1. WEMVA overview
2. Born image perturbation
3. Differential image perturbation
4. Example
[email protected]
Differential image perturbation
0
1
ˆ Rd
dSR
00 RRSR Image
difference
Image differential
Computed Measured
[email protected]
Differential image perturbation
R
R
0
1
ˆ Rd
dSR
00 RRSR
R
[email protected]
Phase perturbation
[email protected]
Differential image perturbation
[email protected]
Born approximation
[email protected]
Example: background image
Zero offset image
Angle gathers
Background image
[email protected]
Example: differential image
Zero offset image
Angle gathers
Differential image
[email protected]
Example: slowness inversion
Slowness perturbation
Image perturbation
[email protected]
Example: updated image
Updated slowness
Updated image
[email protected]
Example: correct image
Correct slowness
Correct image
[email protected]
Outline
1. WEMVA overview
2. Born image perturbation
3. Differential image perturbation
4. Example
[email protected]
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
[email protected]
location
dep
thde
pth
[email protected]
dep
th
velocity ratio velocity ratio
[email protected]
1
1
1
location
dep
thde
pth
[email protected]
location
dep
th
location
[email protected]
location
dep
th
location
[email protected]
location
dep
thde
pth
[email protected]
location
dep
thde
pth
[email protected]
Summary
• MVA– Wavefield extrapolation methods– Born linearization– Differential image perturbations
• Key points– Band-limited (sharp velocity contrasts)– Multi-pathing (complicated wavefields)– Resolution (frequency redundancy)
[email protected]
MVA information (a)Traveltime MVA Wave-equation MVA
• Offset focusing (flat ADCIG) • Offset focusing (flat ADCIG)
z
z
xx
[email protected]
MVA information (b)Traveltime MVA Wave-equation MVA
• Offset focusing (flat ADCIG) • Offset focusing (flat ADCIG)
• Spatial focusing
z
z
xx
[email protected]
MVA information (c)Traveltime MVA Wave-equation MVA
• Offset focusing (flat ADCIG) • Offset focusing (flat ADCIG)
• Spatial focusing
• Frequency redundancy
low high
[email protected]
low high
WEMVA cost reduction
• Full image– Offset focusing
– Spatial focusing
– Frequency
• Normal incidence image
– Spatial focusing
– “fat” rays
[email protected]
Another example
[email protected]
Example: correct model
Zero offset image
Angle gathers
[email protected]
Example: background model
Zero offset image
Angle gathers
[email protected]
Example: correct perturbation
Zero offset image
Angle gathers
[email protected]
Example: differential perturbation
Zero offset image
Angle gathers
1d
dRR
[email protected]
Example: perturbations comparison
Differential
Difference
Correct
[email protected]
Example: differential perturbation
Zero offset image
Angle gathers
[email protected]
Example: difference perturbation
Zero offset image
Angle gathers
[email protected]
Example: updated model
Zero offset image
Angle gathers
[email protected]
Example: correct model
Zero offset image
Angle gathers