Reverse Time Migration Reverse Time Migration. Outline Outline Finding a Rock Splash at Liberty Park Finding a Rock Splash at Liberty Park ZO Reverse.
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Reverse Time Migration Reverse Time Migration
Outline Outline
• Finding a Rock Splash at Liberty ParkFinding a Rock Splash at Liberty Park
• ZO Reverse Time Migration (backwd in time)ZO Reverse Time Migration (backwd in time)
• ZO Reverse Time Migration (forwd in time)ZO Reverse Time Migration (forwd in time)
• ZO Reverse Time Migration CodeZO Reverse Time Migration Code
• ExamplesExamples
Liberty Park Lake Liberty Park Lake Rolls of Toilet PaperRolls of Toilet Paper
TimeTime
Find Location of Rock Find Location of Rock Rolls of Toilet PaperRolls of Toilet Paper
TimeTime
Find Location of Rock Find Location of Rock Rolls of Toilet PaperRolls of Toilet Paper
TimeTime
Find Location of Rock Find Location of Rock Rolls of Toilet PaperRolls of Toilet Paper
TimeTime
Find Location of Rock Find Location of Rock Rolls of Toilet PaperRolls of Toilet Paper
TimeTime
Find Location of Rock Find Location of Rock Rolls of Toilet PaperRolls of Toilet Paper
TimeTime
Find Location of Rock Find Location of Rock Rolls of Toilet PaperRolls of Toilet Paper
TimeTime
Outline Outline
• Finding a Rock Splash at Liberty ParkFinding a Rock Splash at Liberty Park
• ZO Reverse Time Migration (backwd in time)ZO Reverse Time Migration (backwd in time)
• ZO Reverse Time Migration (forwd in time)ZO Reverse Time Migration (forwd in time)
• ZO Reverse Time Migration CodeZO Reverse Time Migration Code
• ExamplesExamples
ZO ModelingZO Modeling
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Reverse Order Traces in TimeReverse Order Traces in Time
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Reverse Time Migration Reverse Time Migration (Go Backwards in Time)(Go Backwards in Time)
T=0 Focuses at Hand GrenadesT=0 Focuses at Hand Grenades
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Outline Outline
• Finding a Rock Splash at Liberty ParkFinding a Rock Splash at Liberty Park
• ZO Reverse Time Migration (backwd in time)ZO Reverse Time Migration (backwd in time)
• ZO Reverse Time Migration (forwd in time)ZO Reverse Time Migration (forwd in time)
• ZO Reverse Time Migration CodeZO Reverse Time Migration Code
• ExamplesExamples
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Reverse Time MigrationReverse Time Migration(Reverse Traces Go Forward in Time)(Reverse Traces Go Forward in Time)
T=0 Focuses at Hand GrenadesT=0 Focuses at Hand Grenades
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Poststack RTMPoststack RTM
1. Reverse Time Order of Traces1. Reverse Time Order of Traces55
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2. Reversed Traces are Wavelets of 2. Reversed Traces are Wavelets of loudspeakersloudspeakers
Outline Outline
• Finding a Rock Splash at Liberty ParkFinding a Rock Splash at Liberty Park
• ZO Reverse Time Migration (backwd in time)ZO Reverse Time Migration (backwd in time)
• ZO Reverse Time Migration (forwd in time)ZO Reverse Time Migration (forwd in time)
• ZO Reverse Time Migration CodeZO Reverse Time Migration Code
• ExamplesExamples
Forward ModelingForward Modeling
for it=1:1:nt p2 = 2*p1 - p0 + cns.*del2(p1); p2(xs,zs) = p2(xs,zs) + RICKER(it); % Add bodypoint src term p0=p1;p1=p2; end
for it=nt:-1:1 p2 = 2*p1 - p0 + cns.*del2(p1); p2(1:nx,2) = p2(1:nx,2) + data(1:nx,it); % Add bodypoint src term p0=p1;p1=p2; end
Reverse Time ModelingReverse Time Modeling
Recall Forward ModelingRecall Forward Modeling
d=Lm d(x) = G(x|d=Lm d(x) = G(x|x’x’)m()m(x’x’)d)dx’x’~~ ~~ ~~ ~~ ~~ ~~
FourierFourier
d(x,t) = G(x,t-d(x,t) = G(x,t-ttss||x’,0x’,0)m()m(x’,tx’,tss)d)dx’dtx’dtss= G(x,t|= G(x,t|x’,tx’,tss)m()m(x’,tx’,tss)d)dx’dtx’dts s
StationarityStationarity
xx
zz
tt
srcsrcForward reconstructionForward reconstructionof half circlesof half circles
Migration = Adjoint of DataMigration = Adjoint of Data
d=Lm d(x) = G(x|d=Lm d(x) = G(x|x’x’)m()m(x’x’)d)dx’x’m=L d m(m=L d m(x’x’) = G(x|) = G(x|x’x’)*d(x)dx)*d(x)dxTT
FourierFourier
m(x) = G(x,-t+m(x) = G(x,-t+ttss||x’,0x’,0)d()d(x’,tx’,tss)d)dx’dtx’dtss= G(x, = G(x, ttss||x’,x’,t)d(t)d(x’,tx’,tss)d)dx’dtx’dtss
StationarityStationarity
xx
zz
tt
Note: Note: tt < t < tss
t=0t=0
t=0t=0
Migration = Adjoint of DataMigration = Adjoint of Data
d=Lm d(x) = G(x|d=Lm d(x) = G(x|x’x’)m()m(x’x’)d)dx’x’m=L d m(m=L d m(x’x’) = G(x|) = G(x|x’x’)*d(x)dx)*d(x)dxTT
FourierFourier
m(x) = G(x,-t+m(x) = G(x,-t+ttss||x’,0x’,0)d()d(x’,tx’,tss)d)dx’dtx’dtss= G(x, = G(x, ttss||x’,x’,t)d(t)d(x’,tx’,tss)d)dx’dtx’dtss
StationarityStationarity
xx
zz
tt
Note: Note: tt < t < tss
t=0t=0
t=0t=0
Migration = Adjoint of DataMigration = Adjoint of Data
d=Lm d(x) = G(x|d=Lm d(x) = G(x|x’x’)m()m(x’x’)d)dx’x’m=L d m(m=L d m(x’x’) = G(x|) = G(x|x’x’)*d(x)dx)*d(x)dxTT
FourierFourier
m(x) = G(x,-t+m(x) = G(x,-t+ttss||x’,0x’,0)d()d(x’,tx’,tss)d)dx’dtx’dtss= G(x, = G(x, ttss||x’,x’,t)d(t)d(x’,tx’,tss)d)dx’dtx’dtss
StationarityStationarity
xx
zz
tt
Note: Note: tt < t < tss
t=0t=0
t=0t=0
Migration = Adjoint of DataMigration = Adjoint of Data
d=Lm d(x) = G(x|d=Lm d(x) = G(x|x’x’)m()m(x’x’)d)dx’x’m=L d m(m=L d m(x’x’) = G(x|) = G(x|x’x’)*d(x)dx)*d(x)dxTT
FourierFourier
m(x) = G(x,-t+m(x) = G(x,-t+ttss||x’,0x’,0)d()d(x’,tx’,tss)d)dx’dtx’dtss= G(x, = G(x, ttss||x’,x’,t)d(t)d(x’,tx’,tss)d)dx’dtx’dtss
StationarityStationarity
xx
zz
tt
Note: Note: tt < t < tss
t=0t=0
t=0t=0
Migration = Adjoint of DataMigration = Adjoint of Data
d=Lm d(x) = G(x|d=Lm d(x) = G(x|x’x’)m()m(x’x’)d)dx’x’m=L d m(m=L d m(x’x’) = G(x|) = G(x|x’x’)*d(x)dx)*d(x)dxTT
FourierFourier
m(x) = G(x,-t+m(x) = G(x,-t+ttss||x’,0x’,0)d()d(x’,tx’,tss)d)dx’dtx’dtss= G(x, = G(x, ttss||x’,x’,t)d(t)d(x’,tx’,tss)d)dx’dtx’dtss
StationarityStationarity
xx
zz
tt
Note: Note: tt < t < tss
Backward reconstructionBackward reconstructionof half circlesof half circles
t=0t=0
t=0t=0
Migration = Adjoint of DataMigration = Adjoint of Data
d=Lm d(x) = G(x|d=Lm d(x) = G(x|x’x’)m()m(x’x’)d)dx’x’m=L d m(m=L d m(x’x’) = G(x|) = G(x|x’x’)*d(x)dx)*d(x)dxTT
FourierFourier
m(x) = G(x,-t+m(x) = G(x,-t+ttss||x’,0x’,0)d()d(x’,tx’,tss)d)dx’dtx’dtss= G(x, = G(x, ttss||x’,x’,t)d(t)d(x’,tx’,tss)d)dx’dtx’dtss
StationarityStationarityNote: Note: tt < t < tss
xx
zz
tt
Backward reconstructionBackward reconstructionof half circlesof half circles
LetLet t tss = = --ttss
----Note: Note: tt > t > tss
xx
zz
tt
Backward reconstructionBackward reconstructionof half circlesof half circles
zz
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tt
Forward prop. Of Forward prop. Of reverse time datareverse time data
t=0t=0
t=0t=0
Advantages of Advantages of m(x’+dx) = d(m(x’+dx) = d(xx) G() G(xx||x’+dx)* x’+dx)*
timetime timetime
MultiplesMultiples
PrimaryPrimaryPrimaryPrimary
Kirchhoff Mig. vs Full Trace Migration Kirchhoff Mig. vs Full Trace Migration
1. Low-Fold Stack vs Superstack 1. Low-Fold Stack vs Superstack
2. Poor Resolution vs Superresolution 2. Poor Resolution vs Superresolution
MultiplesMultiples
xx
Outline Outline
• Finding a Rock Splash at Liberty ParkFinding a Rock Splash at Liberty Park
• ZO Reverse Time Migration (backwd in time)ZO Reverse Time Migration (backwd in time)
• ZO Reverse Time Migration (forwd in time)ZO Reverse Time Migration (forwd in time)
• ZO Reverse Time Migration CodeZO Reverse Time Migration Code
• ExamplesExamples
Numerical ExamplesNumerical Examples
3D Synthetic Data3D Synthetic Data
3D SEG/EAGE Salt Model3D SEG/EAGE Salt Model
Z
Z 2
2 .0.0
Km
Km
X X 3.5 Km3.5 Km
Y Y 3.5 Km3.5 Km
44
Cross line Cross line 160160
Dep
th (
Km
)D
epth
(K
m)
00WW EE
3D Synthetic Data3D Synthetic Data
3.53.5Offset (km)Offset (km)00
22.0.0
33.5.5Offset (km)Offset (km)00
Kirchhoff Kirchhoff MigrationMigration
Redatum + KMRedatum + KM
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Cross line Cross line 180180
Dep
th (
Km
)D
epth
(K
m)
00WW EE
3.53.5Offset (km)Offset (km)00
22.0.0
33.5.5Offset (km)Offset (km)00
Kirchhoff MigrationKirchhoff Migration
Redatum + KMRedatum + KM
3D Synthetic Data3D Synthetic Data
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3D Synthetic Data3D Synthetic Data
Cross line Cross line 200200
Dep
th (
Km
)D
epth
(K
m)
00WW EE
3.53.5Offset (km)Offset (km)00
22.0.0
33.5.5Offset (km)Offset (km)00
Kirchhoff Kirchhoff MigrationMigration
Redatum + KMRedatum + KM
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Numerical ExamplesNumerical Examples
•GOM DataGOM Data
•Prism Synthetic ExamplePrism Synthetic Example
??
GOM KirchhoffGOM Kirchhoff
??
GOM RTMGOM RTM
??
Numerical ExamplesNumerical Examples
•GOM DataGOM Data
•Prism Synthetic ExamplePrism Synthetic Example
Prism Wave MigrationPrism Wave MigrationOne Way Migration of Prestack DataOne Way Migration of Prestack Data RTM of Prestack DataRTM of Prestack Data
Courtesy TLE: Farmer et al. (2006)Courtesy TLE: Farmer et al. (2006)
SummarySummary1.1. RTM much more expensive than Kirchhoff Mig. RTM much more expensive than Kirchhoff Mig.
2.2. If V(x,y,z) accurate then all multiples If V(x,y,z) accurate then all multiples Included so better S/N ration and better Included so better S/N ration and better Resolution.Resolution.
3.3. If V(x,y,z) not accurate then smooth velocity If V(x,y,z) not accurate then smooth velocityModel seems to work better. Free surface multiples Model seems to work better. Free surface multiples included.included.
4.4. RTM worth it for salt models, not layered V(x,y,z). RTM worth it for salt models, not layered V(x,y,z).
5.5. RTM is State of art for GOM and Salt Structures. RTM is State of art for GOM and Salt Structures.
SolutionSolution• Claim:Claim: Image both Primaries and Multiples Image both Primaries and Multiples
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AA DD
• Methods:Methods: RTM RTM
Piecemeal MethodsPiecemeal Methods
• Assume Knowledge of Important MirrorAssume Knowledge of Important Mirror
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AA DD
• Reverse Time MigrationReverse Time Migration
2-Way Mirror Wave Migration:2-Way Mirror Wave Migration:
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