Wave Equation Wavefront Migration

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.