Wave Equation Wavefront Migration
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Transcript of Wave Equation Wavefront Migration
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Wave Equation Wavefront Migration
M. Zhou and G.T. SchusterM. Zhou and G.T. Schuster
Geology and Geophysics Department Geology and Geophysics Department University of UtahUniversity of Utah
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OutlineOutline• ObjectiveObjective• TheoryTheory• ExamplesExamples SEG salt modelSEG salt model Point-scatterer modelPoint-scatterer model
• ConclusionsConclusions
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ProblemProblem:: Reverse-time migration accurate butReverse-time migration accurate but expensiveexpensive
ObjectiveObjective:: Full-wave equation migration that isFull-wave equation migration that is accurate but relatively efficientaccurate but relatively efficient
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OutlineOutline• ObjectiveObjective• TheoryTheory• ExamplesExamples SEG salt modelSEG salt model Point-scatterer modelPoint-scatterer model
• ConclusionsConclusions
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TheoryTheoryReverse-time migration:Reverse-time migration:
Source fieldSource field Reverse migrate dataReverse migrate data
imageimage
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TheoryTheoryWWM:WWM:
Migration operator (focusing kernel)Migration operator (focusing kernel) DataData
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g (r’ | rg (r’ | rss))
Focusing kernel F(rFocusing kernel F(rss, r’, r, r’, rgg) =) = g (r’ | rg (r’ | rss)) g (rg (rgg | r’) | r’)
Scatterer point r’Scatterer point r’
shotshot geophonegeophone
g (rg (rgg | r’) | r’)
TheoryTheory
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Focusing kernel F(rFocusing kernel F(rss, r’, r, r’, rgg) =) = g (r’ | rg (r’ | rss)) g (rg (rgg | r’) | r’)
Scatterer point r’Scatterer point r’
shotshot geophonegeophone
1. Compute 1. Compute FocusingFocusing Kernel by Src at RecsKernel by Src at Recs
g (rg (rgg | r’) | r’) ReciprocityReciprocityg (r’ | rg (r’ | rgg))g (r’ | rg (r’ | rss))
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g (rg (rgg | r’) | r’)g (rg (rss | r’) | r’)
Focusing kernel F(rFocusing kernel F(rss, r’, r, r’, rgg) =) = g (r’ | rg (r’ | rss)) g (rg (rgg | r’) | r’)
Scatterer point r’Scatterer point r’
shotshot geophonegeophone
2. Compute 2. Compute Focusing Kernel by Src at DepthFocusing Kernel by Src at Depth
g (r’ | rg (r’ | rss))ReciprocityReciprocity
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Standard FDStandard FD Wavefront FDWavefront FD
Wavefront FD ModelingWavefront FD Modeling
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Standard FDStandard FD Wavefront FDWavefront FD
Wavefront FD ModelingWavefront FD Modeling
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OutlineOutline• ObjectiveObjective• TheoryTheory• ExamplesExamples SEG salt modelSEG salt model Wavefront forward modelingWavefront forward modeling MigrationMigration
Point-scatterer modelPoint-scatterer model
• ConclusionsConclusions
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Wavefront FD ModelingWavefront FD Modeling
X (km)X (km) X (km)X (km)
Dep
th (
km)
Dep
th (
km)
00 0000
1010 1010
WavefrontWavefrontStandardStandard
Time = 0.4Time = 0.4
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X (km)X (km) X (km)X (km)
Dep
th (
km)
Dep
th (
km)
00 0000
1010 1010
WavefrontWavefrontStandardStandard
Time = 2 secTime = 2 sec
Wavefront FD ModelingWavefront FD Modeling
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X (km)X (km) X (km)X (km)
Dep
th (
km)
Dep
th (
km)
00 0000
1010 1010
WavefrontWavefrontStandardStandard
Time = 4 sTime = 4 s
Wavefront FD ModelingWavefront FD Modeling
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X (km)X (km) X (km)X (km)
Tim
e (s
)T
ime
(s)
6600
88
Standard Wave Equation FDStandard Wave Equation FD Wavefront (save 35% CPU time)Wavefront (save 35% CPU time)
55
66 88
Wavefront FD ModelingWavefront FD Modeling
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X (km)X (km) X (km)X (km)
Tim
e (s
)T
ime
(s)
6600
88
Standard Wave Equation FDStandard Wave Equation FDData CSG200Data CSG200
55
66 88
Wavefront FD ModelingWavefront FD Modeling
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X (km)X (km) X (km)X (km)
Tim
e (s
)T
ime
(s)
6600
88
WavefrontWavefrontData CSG200Data CSG200
55
66 88
Wavefront FD ModelingWavefront FD Modeling
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OutlineOutline• ObjectiveObjective• TheoryTheory• ExamplesExamples SEG salt modelSEG salt model Wavefront forward modelingWavefront forward modeling MigrationMigration
Point-scatterer modelPoint-scatterer model
• ConclusionsConclusions
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Reverse-time ImagesReverse-time ImagesX (km)X (km)
Dep
th (
km)
Dep
th (
km)
2.02.0
Standard RTM ImageStandard RTM Image
Wavefront RTM Image Wavefront RTM Image (save 20% CPU time)(save 20% CPU time)
5500 1010 1515
2.52.5
3.03.0
3.53.5
Dep
th (
km)
Dep
th (
km)
2.02.0
2.52.5
3.03.0
3.53.5
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Standard RT ImageStandard RT Image
Synthetic ModelSynthetic Model
Reverse-time ImagesReverse-time ImagesX (km)X (km)
Dep
th (
km)
Dep
th (
km)
2.02.0
5500 1010 1515
2.52.5
3.03.0
3.53.5
Dep
th (
km)
Dep
th (
km)
2.02.0
2.52.5
3.03.0
3.53.5
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Synthetic ModelSynthetic Model
Reverse-time ImagesReverse-time ImagesX (km)X (km)
Dep
th (
km)
Dep
th (
km)
2.02.0
5500 1010 1515
2.52.5
3.03.0
3.53.5
Dep
th (
km)
Dep
th (
km)
2.02.0
2.52.5
3.03.0
3.53.5
Wavefront RT ImageWavefront RT Image
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Reverse-time ImagesReverse-time ImagesX (km)X (km)
Dep
th (
km)
Dep
th (
km)
2.02.0
Standard RTM ImageStandard RTM Image
WWM ImageWWM Image
8866 1010 1212
2.52.5
3.03.0
3.53.5
Dep
th (
km)
Dep
th (
km)
2.02.0
2.52.5
3.03.0
3.53.5
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Reverse-time ImagesReverse-time ImagesX (km)X (km)
Dep
th (
km)
Dep
th (
km)
2.02.0
WWM ImageWWM Image
8866 1010 1212
2.52.5
3.03.0
3.53.5
Dep
th (
km)
Dep
th (
km)
2.02.0
2.52.5
3.03.0
3.53.5
Synthetic ModelSynthetic Model
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Reverse-time ImagesReverse-time ImagesX (km)X (km)
Dep
th (
km)
Dep
th (
km)
2.02.0
Standard RTM ImageStandard RTM Image
8866 1010 1212
2.52.5
3.03.0
3.53.5
Dep
th (
km)
Dep
th (
km)
2.02.0
2.52.5
3.03.0
3.53.5
Synthetic ModelSynthetic Model
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OutlineOutline• ObjectiveObjective• TheoryTheory• ExamplesExamples SEG salt modelSEG salt model Point-scatterer model Point-scatterer model
• ConclusionsConclusions
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WWM + Incidence AngleWWM + Incidence Angle
X (km)X (km)
00 1.21.20.60.6
Dep
th (
km)
Dep
th (
km)
00
0.60.6
0.30.3 scattererscatterer
shotshot geophonegeophone
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WWM + Incidence AngleWWM + Incidence Angle
X (km)X (km)
00 1.21.20.60.6
Dep
th (
km)
Dep
th (
km)
00
0.60.6
0.30.3
shotshot
scattererscatterer
geophonegeophonett00
2t2t00
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WWM + Incidence AngleWWM + Incidence Angle
X (km)X (km)T
ime
(s)
Tim
e (s
)
0.250.2500
CSG gatherCSG gather
0.050.05
0.150.15
1.21.20.60.6
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WWM + Incidence AngleWWM + Incidence Angle
CSG dataCSG data
image pointimage point
Focusing kernelFocusing kernel
shotshot geophonegeophone
Scatterer pointScatterer point
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WWM + Incidence AngleWWM + Incidence Angle
CSG dataCSG data
image pointimage point
Focusing kernelFocusing kernel
shotshot geophonegeophone
Scatterer pointScatterer point
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WWM + Incidence AngleWWM + Incidence Angle
CSG dataCSG data
image pointimage point
Focusing kernelFocusing kernel
shotshot geophonegeophone
Scatterer pointScatterer point
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WWM + Incidence angleWWM + Incidence angleX (km)X (km)
00 1.21.20.60.6D
epth
(km
)D
epth
(km
)D
epth
(km
)D
epth
(km
)00
0.60.6
0.30.3
00
0.60.6
0.30.3
Standard Reverse-time MigrationStandard Reverse-time Migration
WWM + incidence angleWWM + incidence angle
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ConclusionsConclusions
• reduce artifacts;reduce artifacts;
• reduce migration artifacts;reduce migration artifacts;WWM + filtering constraintsWWM + filtering constraints
WWM by first arrivalsWWM by first arrivals
• high costs on I/O.high costs on I/O.
Wavefront forward modelingWavefront forward modeling• relatively efficient + accurate;relatively efficient + accurate;
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AcknowledgementsAcknowledgements I am grateful for the financial I am grateful for the financial support from the members of support from the members of the 2001 UTAM consortium.the 2001 UTAM consortium.
I am grateful for Yi Luo’s idea I am grateful for Yi Luo’s idea on target-oriented wave equationon target-oriented wave equation migration.migration.