LEAST SQUARES WAVEPATH MIGRATION
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LEAST SQUARES WAVEPATH LEAST SQUARES WAVEPATH MIGRATIONMIGRATION
Y. Liu and H. SunY. Liu and H. Sun
Geology and Geophysics Department Geology and Geophysics Department University of UtahUniversity of Utah
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OutlineOutline. . Objective Objective . Wavepath Migration. Wavepath Migration. Least Squares Wavepath Migration. Least Squares Wavepath Migration. Numerical Results. Numerical Results. Field Data Results . Field Data Results . Conclusions. Conclusions
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ObjectiveObjective Least-Squares MigrationLeast-Squares Migration a. Advantages:a. Advantages:• Apply to Incomplete dataApply to Incomplete data• Reduce acquisition footprintReduce acquisition footprint• Improve Image resolutionImprove Image resolution b. Disadvantage:b. Disadvantage:• Need more calculation timeNeed more calculation time
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• Forward Modeling: fastForward Modeling: fast
• Migration: slowMigration: slow
ObjectiveObjective
Least Squares Migration:Least Squares Migration:
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• Save calculation timeSave calculation time• Suppress artifactsSuppress artifacts
Wavepath MigrationWavepath Migration::
ObjectiveObjective
Advantages:Advantages:
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Least-Squares Wavepath Migration:Least-Squares Wavepath Migration:
ObjectiveObjective
Advantages:Advantages:• Apply to Incomplete dataApply to Incomplete data• Reduce acquisition footprintReduce acquisition footprint• Improve resolutionImprove resolution• Save calculation timeSave calculation time
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OutlineOutline. . Objective Objective . Wavepath Migration. Wavepath Migration. Least Squares Wavepath Migration. Least Squares Wavepath Migration. Numerical Results. Numerical Results. Field Data Results . Field Data Results . Conclusions. Conclusions
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Wavepath MigrationWavepath Migration
KM : Fat Ellipsoid, 3-D CPUKM : Fat Ellipsoid, 3-D CPUWM: Hatched Area, 1.5-D CPUWM: Hatched Area, 1.5-D CPU
( ( Xg, 0 )Xg, 0 )
Fat Fat EllipsoidEllipsoid
Fat RayFat Ray
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Traveltime + Ray DirectionTraveltime + Ray Direction
TrueReflection point
SmallMigration Aperture
FewerFewerArtifactsArtifacts
LessLessExpensiveExpensive
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SEG Overthrust Model ResultsSEG Overthrust Model Results
Offset (km)Offset (km)00 1818
00
44
De
pth
(k
m)
De
pth
(k
m)
KM Image (CPU: KM Image (CPU: 1.01.0)) WM Image (CPU: WM Image (CPU: 0.780.78))
Offset (km)Offset (km)00 1818
00
De
pth
(k
m)
De
pth
(k
m)
44
BBAA
BBAA
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SEG/EAGE Salt DataSEG/EAGE Salt Data
KM: KM: 11 WM: WM: 1/331/33
CPU Comparison in 3-DCPU Comparison in 3-D
West Texas Field DataWest Texas Field Data
KM: KM: 11 WM: WM: 1/141/14
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OutlineOutline. . Objective Objective . Wavepath Migration. Wavepath Migration. Least Squares Wavepath Migration. Least Squares Wavepath Migration. Numerical Results. Numerical Results. Field Data Results . Field Data Results . Conclusions. Conclusions
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ForwardForward : : d=Lm d=Lm (1)(1) Migration:Migration: m mstst=L d =L d (2)(2) Objective Function:Objective Function:
P(m)=|| Lm-d ||P(m)=|| Lm-d || (3)(3)
LSWM:LSWM: mmstst==[[LLLL]] Ld Ld (4)(4)
Least Square Wavepath MigrationLeast Square Wavepath Migration
TT
TT
TT-1-1
22
00
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Least Square Wavepath MigrationLeast Square Wavepath Migration
Field DataField Data
Wavepath MigrationWavepath Migration
ForwardForward
Wavepath MigrationWavepath Migration
Y/NY/N
Iteration process:Iteration process:
Synthetic DataSynthetic Data Stop Stop CriteriaCriteria
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OutlineOutline. . Objective Objective . Wavepath Migration. Wavepath Migration. Least Squares Wavepath Migration. Least Squares Wavepath Migration. Numerical Results. Numerical Results. Field Data Results . Field Data Results . Conclusions. Conclusions
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Point Scatterer modelPoint Scatterer model
X(km)X(km)00
Tim
e (s
)T
ime
(s)
2.52.544
00 44X (km)X (km)
Dep
th(k
m)
Dep
th(k
m)
0044
..
00
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Scatterer ImageScatterer Image
KM image KM image WM image WM image LSWM imageLSWM image
..
00 44X (km)X (km) 00 44X (km)X (km) 00 44X (km)X (km)00
44
Dep
th(k
m)
Dep
th(k
m)
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OutlineOutline. . Objective Objective . Wavepath Migration. Wavepath Migration. Least Squares Wavepath Migration. Least Squares Wavepath Migration. Numerical Results. Numerical Results. Field Data Results . Field Data Results . Conclusions. Conclusions
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CSG for Mobil DataCSG for Mobil Data
GEOMETRYGEOMETRY
Shots: 668Shots: 668Trace: 120Trace: 120Total: 80160Total: 80160Ns=1500Ns=1500Dt=4msDt=4msDs=25mDs=25mDg=25mDg=25mMin/Offset=262mMin/Offset=262m
TraceTrace11 120120
Tim
e(s)
Tim
e(s)
00
55
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Velocity ModelVelocity Model
Dx=12.5Dx=12.5Dz=12.5Dz=12.5Nx=1594Nx=1594Nz=281Nz=281CDP=12.5CDP=12.5 D
epth
(km
)D
epth
(km
)00
3.53.5
00 19.919.9CDP NumberCDP Number
1.51.5
3.53.5
(Km
/s)
(Km
/s)
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WM vs. LSWMWM vs. LSWMX(Km)X(Km)
Dep
th(K
m)
Dep
th(K
m)
X(Km)X(Km)4.84.8
3.43.4
19.019.0 19.019.0
After 15 iternationsAfter 15 iternations
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X(m)X(m)
Dep
th(m
)D
epth
(m)
WM Image for Mobil DataWM Image for Mobil Data
LSWM image (15)LSWM image (15)
WM image (0)WM image (0)
12.012.0 18.018.0
12.012.0 18.018.0
2.82.8
2.82.8
Dep
th(m
)D
epth
(m)
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OutlineOutline. . Objective Objective . Wavepath Migration. Wavepath Migration. Least Squares Wavepath Migration. Least Squares Wavepath Migration. Numerical Results. Numerical Results. Field Data Results . Field Data Results . Conclusions. Conclusions
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ConclusionsConclusions • Suppress artifactsSuppress artifacts• Improve ResolutionImprove Resolution
• Computation time (Mobil Data) Computation time (Mobil Data) WM CPU 1.0WM CPU 1.0 LSWM CPU (15): LSWM CPU (15): 8.58.5
• Slightly sensitive to velocitySlightly sensitive to velocity
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AcknowledgementsAcknowledgements
We thank 2001 UTAM We thank 2001 UTAM sponsors for their financial sponsors for their financial
supportssupports