wave equation wavefront migration
DESCRIPTION
Wave Equation Wavefront Migration. M. Zhou and G.T. Schuster. Geology and Geophysics Department University of Utah. Outline. Objective Theory Examples SEG salt model Point-scatterer model Conclusions. Problem : Reverse-time migration accurate but - PowerPoint PPT PresentationTRANSCRIPT
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
OutlineOutline• ObjectiveObjective• TheoryTheory• ExamplesExamples SEG salt modelSEG salt model Point-scatterer modelPoint-scatterer model
• ConclusionsConclusions
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
OutlineOutline• ObjectiveObjective• TheoryTheory• ExamplesExamples SEG salt modelSEG salt model Point-scatterer modelPoint-scatterer model
• ConclusionsConclusions
TheoryTheoryReverse-time migration:Reverse-time migration:
Source fieldSource field Reverse migrate dataReverse migrate data
imageimage
TheoryTheoryWWM:WWM:
Migration operator (focusing kernel)Migration operator (focusing kernel) DataData
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
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))
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
Standard FDStandard FD Wavefront FDWavefront FD
Wavefront FD ModelingWavefront FD Modeling
Standard FDStandard FD Wavefront FDWavefront FD
Wavefront FD ModelingWavefront FD Modeling
OutlineOutline• ObjectiveObjective• TheoryTheory• ExamplesExamples SEG salt modelSEG salt model Wavefront forward modelingWavefront forward modeling MigrationMigration
Point-scatterer modelPoint-scatterer model
• ConclusionsConclusions
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
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
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
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
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
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
OutlineOutline• ObjectiveObjective• TheoryTheory• ExamplesExamples SEG salt modelSEG salt model Wavefront forward modelingWavefront forward modeling MigrationMigration
Point-scatterer modelPoint-scatterer model
• ConclusionsConclusions
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
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
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
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
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
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
OutlineOutline• ObjectiveObjective• TheoryTheory• ExamplesExamples SEG salt modelSEG salt model Point-scatterer model Point-scatterer model
• ConclusionsConclusions
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
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
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
WWM + Incidence AngleWWM + Incidence Angle
CSG dataCSG data
image pointimage point
Focusing kernelFocusing kernel
shotshot geophonegeophone
Scatterer pointScatterer point
WWM + Incidence AngleWWM + Incidence Angle
CSG dataCSG data
image pointimage point
Focusing kernelFocusing kernel
shotshot geophonegeophone
Scatterer pointScatterer point
WWM + Incidence AngleWWM + Incidence Angle
CSG dataCSG data
image pointimage point
Focusing kernelFocusing kernel
shotshot geophonegeophone
Scatterer pointScatterer point
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
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;
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.