Reverse Time Migration Reverse Time Migration. Outline Outline Finding a Rock Splash at Liberty Park...

Reverse Time Migration Reverse Time Migration

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• 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

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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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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

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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

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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


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Note: Note: tt < t < tss

t=0t=0

t=0t=0



FourierFourier



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Note: Note: tt < t < tss

Backward reconstructionBackward reconstructionof half circlesof half circles

t=0t=0

t=0t=0



FourierFourier


StationarityStationarityNote: Note: tt < t < tss

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LetLet t tss = = --ttss

----Note: Note: tt > t > tss

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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

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Numerical ExamplesNumerical Examples

3D Synthetic Data3D Synthetic Data

3D SEG/EAGE Salt Model3D SEG/EAGE Salt Model

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Cross line Cross line 160160

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3.53.5Offset (km)Offset (km)00

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Kirchhoff Kirchhoff MigrationMigration

Redatum + KMRedatum + KM

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Kirchhoff MigrationKirchhoff Migration



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Kirchhoff Kirchhoff MigrationMigration


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•GOM DataGOM Data

•Prism Synthetic ExamplePrism Synthetic Example

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GOM KirchhoffGOM Kirchhoff

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GOM RTMGOM RTM


•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:

Reverse Time Migration Reverse Time Migration. Outline Outline Finding a Rock Splash at Liberty Park...

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