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![Page 1: V.2 Wavepath Migration Overview Overview Kirchhoff migration smears a reflection along a fat ellipsoid, so that most of the reflection energy is placed.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649e7f5503460f94b83348/html5/thumbnails/1.jpg)
V.2 V.2 Wavepath MigrationWavepath Migration OverviewOverview
Kirchhoff migration smears a reflection along a fat Kirchhoff migration smears a reflection along a fat ellipsoid, so that most of the reflection energy is placed in ellipsoid, so that most of the reflection energy is placed in regions far from the actual specular reflection point. This is regions far from the actual specular reflection point. This is both inefficient and artifact-prone. To place the reflection both inefficient and artifact-prone. To place the reflection energy at or near its specular reflection point we first perform energy at or near its specular reflection point we first perform a local slant stack on the trace, and propagate it along its a local slant stack on the trace, and propagate it along its associated wavepath cosnistent with the incident angle of the associated wavepath cosnistent with the incident angle of the arrival. The reflection is now smeared along the portion of the arrival. The reflection is now smeared along the portion of the wavepath centered about the specular reflection point. Thus wavepath centered about the specular reflection point. Thus wavepath migration smears the reflection energy along a small wavepath migration smears the reflection energy along a small portion of a wavepath, which reduces both cost and aliasing portion of a wavepath, which reduces both cost and aliasing artifacts. The drawback is the sensitivity of the incidence angle artifacts. The drawback is the sensitivity of the incidence angle calculation due to noise or inaccurate migration velocities.calculation due to noise or inaccurate migration velocities.
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• Problem & MotivationProblem & Motivation
• TheoryTheory
• Synthetic Numerical ExamplesSynthetic Numerical Examples
• Field Data Numerical ExamplesField Data Numerical Examples
• ConclusionsConclusions
OutlineOutline
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ExpenseExpense
Acc
ura
cyA
ccu
rac y
Full-WaveFull-Wave
Ray-BeamRay-BeamKirchhoffKirchhoff
Migration Accuracy vs $$$Migration Accuracy vs $$$
Target RTMTarget RTM
No Approx.No Approx.
Multiple ArrivMultiple Arriv
Anti-aliasingAnti-aliasingPhase-ShiftPhase-Shift
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3-D KM of a Single Trace3-D KM of a Single Trace
RR SSAA
AA
BB
BB
CC
CC
ProblemProblem
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Problem & SolutionProblem & Solution ProblemProblem:: Kirchhoff Migration Expensive; Kirchhoff Migration Expensive; O(N ) per TraceO(N ) per Trace Reflection Energy Smeared Reflection Energy Smeared AllAll Along EllipseAlong Ellipse
SolutionSolution: Wavepath Migration. Smear: Wavepath Migration. Smear Energy along Wavepaths notEnergy along Wavepaths not Ellipses; O(N )per TraceEllipses; O(N )per Trace
33
1.51.5
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SS RR
ImageImagePointPoint
Fresnel ZoneFresnel Zone
Smear Reflection along WavepathSmear Reflection along Wavepath
Inc. AngleInc. Angleby Slant Stackby Slant Stack
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MVA ObjectivesMVA Objectives
• Can WMVA effectively improve theCan WMVA effectively improve the migration velocity?migration velocity?
• Whether the WMVA updated velocity Whether the WMVA updated velocity differs much from the KMVA updateddiffers much from the KMVA updated velocity?velocity?
• Can WMVA be much faster than Can WMVA be much faster than KMVA?KMVA?
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RR SSAA
BBCC
AABB
CC
3-D WM of a Single 3-D WM of a Single TraceTrace
SolutionSolution
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Problem & SolutionProblem & Solution ProblemProblem:: Kirchhoff Migration Expensive; Kirchhoff Migration Expensive; O(N ) per TraceO(N ) per Trace Reflection Energy Smeared Reflection Energy Smeared AllAll Along EllipseAlong Ellipse
SolutionSolution: Wavepath Migration. Smear: Wavepath Migration. Smear Energy along Wavepaths notEnergy along Wavepaths not Ellipses; O(N )per TraceEllipses; O(N )per Trace
33
1.51.5
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Numerical TestsNumerical Tests
• 3-D Pt. Scatterer Model3-D Pt. Scatterer Model
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3-D Prestack KM Point Scatterer Response3-D Prestack KM Point Scatterer Response R
efle
ctiv
ity
Ref
lect
ivit
y
Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)
11
-0.5-0.5
00
11
Ref
lect
ivit
yR
efle
ctiv
ity
Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)
11
-0.01-0.01
00
0.020.02
Ref
lect
ivit
yR
efle
ctiv
ity
Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)
11
-0.05-0.05
00
0.10.1
Ref
lect
ivit
yR
efle
ctiv
ity
Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)
11
-0.2-0.2
00
0.40.4
11
1111
11
Z0Z0
Z0-1Z0-1Z0-9Z0-9
Z0+8Z0+8
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Ref
lect
ivit
yR
efle
ctiv
ity
Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)
11
-0.5-0.5
00
11
Ref
lect
ivit
yR
efle
ctiv
ity
Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)
11
-0.01-0.01
00
0.020.02
Ref
lect
ivit
yR
efle
ctiv
ity
Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)
11
-0.05-0.05
00
0.10.1
Ref
lect
ivit
yR
efle
ctiv
ity
Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)
11
-0.2-0.2
00
0.40.4
11
1111
11
3-D Prestack WM Point Scatterer Response3-D Prestack WM Point Scatterer Response
Z0Z0
Z0-1Z0-1Z0-9Z0-9
Z0+8Z0+8
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Numerical TestsNumerical Tests
• 3-D Pt. Scatterer Model3-D Pt. Scatterer Model
• 2-D SEG/EAGE overthrust 2-D SEG/EAGE overthrust modelmodel
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Velocity ModelVelocity Model 0km0km 15km15km10km10km5km5km
00
15015000
45004500
30003000Dep
th (
m)
Dep
th (
m)
60006000
25025000
Velocity (m
/sec)V
elocity (m/sec)
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Wavepath vs Kirchhoff Migration
Offset (km)4 10
Dep
th (
km)
0.5
2.5
4 Offset (km) 10 4 Offset (km) 10
WM Image (CPU: 0.088) KM Image (CPU: 1.0)Structure(Slant Stack)
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Numerical TestsNumerical Tests
• 3-D Pt. Scatterer Model3-D Pt. Scatterer Model
• 2-D SEG/EAGE overthrust model2-D SEG/EAGE overthrust model• 2-D Canadian Land Data2-D Canadian Land Data
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A Raw CSG of Husky Field DataA Raw CSG of Husky Field Data
Trace NumberTrace Number11 300300
Tim
e (s
ec)
Tim
e (s
ec)
00
3.03.0
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Husky Field Data ResultsHusky Field Data Results
Offset (km)Offset (km)00 141400
77
Dep
th (
km)
Dep
th (
km)
KM KM (CPU:(CPU:1.01.0))
AA
BB
WM WM (CPU: (CPU: 2.232.23))
Offset (km)Offset (km)00 1414
AA
BB
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Husky Field Data ResultsHusky Field Data Results
Offset (km)Offset (km)2.52.5 5.55.5
2.52.5
5.05.0
Dep
th (
km)
Dep
th (
km)
KM Image (Box A)KM Image (Box A) WM Image (Box A)WM Image (Box A)
Offset (km)Offset (km)2.52.5 5.55.5
2.52.5
Dep
th (
km)
Dep
th (
km)
5.05.0
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Husky Field Data ResultsHusky Field Data Results
Offset (km)Offset (km)00 141400
77
Dep
th (
km)
Dep
th (
km)
KM KM (CPU:(CPU:1.01.0))
AA
BB
WM WM (Slant Stack, CPU: (Slant Stack, CPU: 0.240.24))
Offset (km)Offset (km)00 1414
AA
BB
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Numerical TestsNumerical Tests
• 3-D Pt. Scatterer Model3-D Pt. Scatterer Model
• 2-D SEG/EAGE overthrust model2-D SEG/EAGE overthrust model
• 3-D SEG/EAGE Salt Model3-D SEG/EAGE Salt Model
• 2-D Canadian Land Data2-D Canadian Land Data
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Receiver DistributionReceiver DistributionC
ross
line
(m)
Cro
sslin
e (m
)
44804480
23202320
19201920
19201920 Inline (m)Inline (m)
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Inline Velocity ModelInline Velocity Model
Offset (km)Offset (km)00 9.29.2
Dep
th (
km)
Dep
th (
km)
00
3.83.8
SALTSALT
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Inline KMInline KM (CPU=1)(CPU=1) Inline WMInline WM (CPU=1/33)(CPU=1/33)
Offset (km)Offset (km)00 9.29.2
00
3.3.88
Dep
th (
km)
Dep
th (
km)
Offset (km)Offset (km)00 9.29.2
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Zoom Views of Inline Sections Zoom Views of Inline Sections
Offset: 3~6.5 km, Depth: 0.3~1.8 kmOffset: 3~6.5 km, Depth: 0.3~1.8 km
WMWM
ModelModel
KirchhoffKirchhoff
SubSubWMWM
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ModelModel
Migration of SEG Salt Data (Crossline Sections) Migration of SEG Salt Data (Crossline Sections)
Offset: 1.8~4 km, Depth: 0.6~2.1 kmOffset: 1.8~4 km, Depth: 0.6~2.1 km
WMWMKM KM
SubSubWMWM
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Inline: 1.8~7.2 km, Crossline: 0~4 kmInline: 1.8~7.2 km, Crossline: 0~4 km
WMWM
ModelModel
KM KM
SubSubWMWM
Migration of SEG Salt Data (Horizontal Slices) Migration of SEG Salt Data (Horizontal Slices)
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Numerical TestsNumerical Tests
• 3-D Pt. Scatterer Model3-D Pt. Scatterer Model
• 2-D SEG/EAGE Overthrust model2-D SEG/EAGE Overthrust model
• 3-D SEG/EAGE Salt Model3-D SEG/EAGE Salt Model
• 2-D Canadian Land Data2-D Canadian Land Data
• 3-D W. Texas Data3-D W. Texas Data
![Page 29: V.2 Wavepath Migration Overview Overview Kirchhoff migration smears a reflection along a fat ellipsoid, so that most of the reflection energy is placed.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649e7f5503460f94b83348/html5/thumbnails/29.jpg)
A Common Shot GatherA Common Shot Gather
Trace NumberTrace Number5454 193193
Tim
e (s
ec)
Tim
e (s
ec)
00
3.43.4
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Receiver DistributionReceiver DistributionC
ross
line
(km
)C
ross
line
(km
)
4.54.51.21.2
3.53.5
1.51.5 Inline (km)Inline (km)
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Receiver DistributionReceiver DistributionC
ross
line
(km
)C
ross
line
(km
)
4.54.51.21.2
3.53.5
1.51.5 Inline (km)Inline (km)
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Inline KM Inline KM (CPU=1)(CPU=1) Inline WMInline WM (CPU=1/14)(CPU=1/14)
Offset (km)Offset (km)0.40.4 4.54.5
0.80.8
3.83.8
Dep
th (
km)
Dep
th (
km)
Offset (km)Offset (km)0.40.4 4.54.5
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Inline KMInline KM (CPU=1)(CPU=1) Inline WMInline WM (CPU=1/50)(CPU=1/50)
Offset (km)Offset (km)0.40.4 4.54.5
0.80.8
3.83.8
Dep
th (
km)
Dep
th (
km)
Offset (km)Offset (km)0.40.4 4.54.5
(subsample)(subsample)
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Crossline KM Crossline KM (CPU=1)(CPU=1) Crossline WMCrossline WM (CPU=1/14)(CPU=1/14)
Offset (km)Offset (km)0.30.3 3.53.5
0.80.8
3.33.3
Dep
th (
km)
Dep
th (
km)
Offset (km)Offset (km)0.30.3 3.53.5
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Crossline KMCrossline KM (CPU=1)(CPU=1) Crossline WMCrossline WM (CPU=1/50)(CPU=1/50)(subsample)(subsample)
Offset (km)Offset (km)0.30.3 3.53.5
0.80.8
3.33.3
Dep
th (
km)
Dep
th (
km)
Offset (km)Offset (km)0.30.3 3.53.5
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Inline: 0~4.6 km, Crossline: 0~3.8Inline: 0~4.6 km, Crossline: 0~3.8
KM (CPU=1)KM (CPU=1)
Horizontal Slices (Depth=2.5 km) Horizontal Slices (Depth=2.5 km)
WM (CPU=1/14)WM (CPU=1/14) WM (Sub, CPU=1/50)WM (Sub, CPU=1/50)
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Numerical TestsNumerical Tests
• 3-D Pt. Scatterer Model3-D Pt. Scatterer Model
• 2-D SEG/EAGE Overthrust model2-D SEG/EAGE Overthrust model
• 3-D SEG/EAGE Salt Model3-D SEG/EAGE Salt Model
• 2-D Canadian Land Data2-D Canadian Land Data
• 3-D W. Texas Data3-D W. Texas Data• MVAMVA
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Initial Migration VelocityInitial Migration Velocity
0000
1818
1.51.5
Horizontal Distance (km)Horizontal Distance (km)
Dep
th (
km)
Dep
th (
km) 2.12.1
1.51.5
(km
/s)
(km
/s)
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KM Image with Initial VelocityKM Image with Initial Velocity0000
18 km18 km
1.51.5
Dep
th (
km)
Dep
th (
km)
00
1.51.5
Dep
th (
km)
Dep
th (
km)
KMVA Velocity Changes in the 1st IterationKMVA Velocity Changes in the 1st Iteration
5050
00
(m
/s)
(m /s
)
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KM Image with Initial VelocityKM Image with Initial Velocity
KM Image with Updated VelocityKM Image with Updated Velocity
9 km9 km
12601260
De
pth
(m
)D
ep
th (
m)
2 km2 km
10701070
12601260
De
pth
(m
)D
ep
th (
m)
10701070
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KMVA CIGs with Initial VelocityKMVA CIGs with Initial Velocity
00
1.51.5
Dep
th (
km)
Dep
th (
km)
KMVA CIGs with Updated VelocityKMVA CIGs with Updated Velocity
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0000
18 km18 km
1.51.5
Dep
th (
km)
Dep
th (
km)
00
1.51.5
Dep
th (
km)
Dep
th (
km)
KMVA Velocity Changes in the 1st Iteration (KMVA Velocity Changes in the 1st Iteration (CPU=6CPU=6))
5050
00
(m
/s)
(m /s
)
WMVA Velocity Changes in the 1st Iteration (WMVA Velocity Changes in the 1st Iteration (CPU=1CPU=1))
5050
00
(m
/s)
(m /s
)
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WM Image with Initial VelocityWM Image with Initial Velocity
WM Image with Updated VelocityWM Image with Updated Velocity
9 km9 km
12601260
De
pth
(m
)D
ep
th (
m)
2 km2 km
10701070
12601260
De
pth
(m
)D
ep
th (
m)
10701070
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WMVA CIGs with Initial VelocityWMVA CIGs with Initial Velocity
00
1.51.5
Dep
th (
km)
Dep
th (
km)
WMVA CIGs with Updated VelocityWMVA CIGs with Updated Velocity
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KM Image with Initial VelocityKM Image with Initial Velocity 9 km9 km
12601260
De
pth
(m
)D
ep
th (
m)
2 km2 km
10701070
KM Image with KMVA Updated VelocityKM Image with KMVA Updated Velocity
12601260
De
pth
(m
)D
ep
th (
m)
10701070
KM Image with WMVA Updated VelocityKM Image with WMVA Updated Velocity
12601260
De
pth
(m
)D
ep
th (
m)
10701070
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Numerical TestsNumerical Tests
• 3-D Pt. Scatterer Model3-D Pt. Scatterer Model
• 2-D SEG/EAGE Overthrust model2-D SEG/EAGE Overthrust model
• 3-D SEG/EAGE Salt Model3-D SEG/EAGE Salt Model
• 2-D Canadian Land Data2-D Canadian Land Data
• Crosswell DataCrosswell Data
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ModelModel
Crosswell Imaging of Synthetic Fault Data Crosswell Imaging of Synthetic Fault Data WMWMKM KM
00
210210
Dep
th (
m)
Dep
th (
m)
0 900 90
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ConclusionsConclusions
• Typically WM has fewer artifacts than Typically WM has fewer artifacts than KMKM
• Typically WM 2-50 times faster than than Typically WM 2-50 times faster than than KMKM• Tradeoff between quality and speedTradeoff between quality and speed
• Conflicting dip arrivals still an issueConflicting dip arrivals still an issue
• Slant stack traces essential for efficiency Slant stack traces essential for efficiency
• Fast velocity analysis toolFast velocity analysis tool
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ConclusionsConclusions
Subdivision method is able to account Subdivision method is able to account for lateral-velocity variations and for lateral-velocity variations and attenuate some far-field artifactsattenuate some far-field artifacts
A post-migration processing: Cost 2XA post-migration processing: Cost 2X
Works on synthetic and field Works on synthetic and field poststack time migration data, poststack time migration data, improve resolution, mitigate some improve resolution, mitigate some migration artifactsmigration artifacts
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ExpenseExpense
Acc
ura
cyA
ccu
rac y
Full-WaveFull-Wave
Ray-BeamRay-BeamKirchhoffKirchhoff
Migration Accuracy vs $$$Migration Accuracy vs $$$
Target RTMTarget RTM
No Approx.No Approx.
Multiple ArrivMultiple Arriv
Anti-aliasingAnti-aliasingPhase-ShiftPhase-Shift