Wavepath Migration versus Kirchhoff Migration: 3-D Prestack Examples

Wavepath Migration versus Wavepath Migration versus Kirchhoff Migration: 3-D Kirchhoff Migration: 3-D

Prestack ExamplesPrestack Examples

H. Sun and G. T. SchusterH. Sun and G. T. SchusterUniversity of UtahUniversity of Utah

OutlineOutline Problems in Kirchhoff MigrationProblems in Kirchhoff Migration• Wavepath Migration Wavepath Migration • Implementation of WMImplementation of WM• Numerical ResultsNumerical Results• ConclusionsConclusions

Forward ModelingForward Modeling

( Xg, 0 )( Xg, 0 ) ( Xs, 0 )( Xs, 0 )

Specular RaySpecular Ray

3D Kirchhoff Migration3D Kirchhoff Migration

( Xg, 0 )( Xg, 0 ) ( Xs, 0 )( Xs, 0 )

3D Fat Ellipsoid3D Fat Ellipsoid

3-D KM of a Single Trace3-D KM of a Single Trace

RR SSAA

AA

BB

BB

CC

CC

Problems in Kirchhoff MigrationProblems in Kirchhoff Migration

Traveltime InformationTraveltime Information

Where Was Wave Reflected ?Where Was Wave Reflected ?

The Whole Fat Ellipsoid !The Whole Fat Ellipsoid !

Problem 1Problem 1

Strong Far-FieldStrong Far-FieldMigration ArtifactMigration Artifact

Problem 2Problem 2

Slow for 3-D IterativeSlow for 3-D IterativeVelocity AnalysisVelocity Analysis

OutlineOutline• Problems in Kirchhoff MigrationProblems in Kirchhoff Migration Wavepath Migration Wavepath Migration • Implementation of WMImplementation of WM• Numerical ResultsNumerical Results• ConclusionsConclusions

3D Wavepath Migration3D Wavepath Migration

( Xg, 0 )( Xg, 0 )

Fat RayFat Ray

Fat Fat EllipsoidEllipsoid

KM : Fat Ellipsoid, O(N )KM : Fat Ellipsoid, O(N )WM: Hatching Area, O(N )WM: Hatching Area, O(N )

3 3

1.5 1.5

3-D WM of a Single Trace3-D WM of a Single Trace

RR SSAA

BBCC

AABB

CC

Traveltime + Ray DirectionTraveltime + Ray Direction

TrueReflection point

SmallMigration Aperture

FewerFewerArtifactsArtifacts

LessLessExpensiveExpensive

Wavepath MigrationWavepath Migration

• To Achieve Higher CPU EfficiencyTo Achieve Higher CPU Efficiency Compared to 3-D KMCompared to 3-D KM • To Generate Comparable or BetterTo Generate Comparable or Better Image Quality than 3-D KMImage Quality than 3-D KM

Key Goals of 3-D WMKey Goals of 3-D WM

Related ReferencesRelated References• Time-Map MigrationTime-Map Migration SherrifSherrif & & GeldhartGeldhart (1985) (1985)• Wave Equation TomographyWave Equation Tomography Woodward Woodward && Rocca Rocca (1988) (1988)• Gaussian Beam MigrationGaussian Beam Migration Ross HillRoss Hill (1990) (1990)• Kirchhoff Beam MigrationKirchhoff Beam Migration Yonghe SunYonghe Sun et al., (1999) et al., (1999)

OutlineOutline• Problems in Kirchhoff MigrationProblems in Kirchhoff Migration• Wavepath Migration Wavepath Migration Implementation of WMImplementation of WM• Numerical ResultsNumerical Results• ConclusionsConclusions

Key Steps in WMKey Steps in WM

RaypathRaypath

RR SS

RaypathRaypath Fresnel Zone MigrationFresnel Zone MigrationQuasi-ellipsoidQuasi-ellipsoid

Quasi-ellipsoidQuasi-ellipsoid

OutlineOutline• Problems in Kirchhoff MigrationProblems in Kirchhoff Migration• Wavepath Migration Wavepath Migration • Implementation of WMImplementation of WM Numerical ResultsNumerical Results 3-D Prestack Point Scatterer Data3-D Prestack Point Scatterer Data 3-D Prestack SEG/EAGE Salt Data3-D Prestack SEG/EAGE Salt Data 3-D Prestack West Texas Field Data3-D Prestack West Texas Field Data• ConclusionsConclusions

3-D Prestack KM Point Scatterer Response3-D Prestack KM Point Scatterer Response R

efle

ctiv

ity

Ref

lect

ivit

y

Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)

11

-0.5-0.5

00

11

Ref

lect

ivit

yR

efle

ctiv

ity


11

-0.01-0.01

00

0.020.02

Ref

lect

ivit

yR

efle

ctiv

ity


11

-0.05-0.05

00

0.10.1

Ref

lect

ivit

yR

efle

ctiv

ity


11

-0.2-0.2

00

0.40.4

11

1111

11

Z0Z0

Z0-1Z0-1Z0-9Z0-9

Z0+8Z0+8

Ref

lect

ivit

yR

efle

ctiv

ity


11

-0.5-0.5

00

11

Ref

lect

ivit

yR

efle

ctiv

ity


11

-0.01-0.01

00

0.020.02

Ref

lect

ivit

yR

efle

ctiv

ity


11

-0.05-0.05

00

0.10.1

Ref

lect

ivit

yR

efle

ctiv

ity


11

-0.2-0.2

00

0.40.4

11

1111

11

3-D Prestack WM Point Scatterer Response3-D Prestack WM Point Scatterer Response

Z0Z0

Z0-1Z0-1Z0-9Z0-9

Z0+8Z0+8

A Common Shot GatherA Common Shot GatherTrace NumberTrace Number11 390390

Tim

e (s

ec)

Tim

e (s

ec)

00

5.05.0

Inline Velocity ModelInline Velocity Model

Offset (km)Offset (km)00 9.29.2

Dep

th (

km)

Dep

th (

km)

00

3.83.8

SALTSALT

Inline KMInline KM ((CPU=1CPU=1)) Inline WMInline WM ((CPU=1/33CPU=1/33))


00

3.83.8

De

pth

(k

m)

De

pth

(k

m)




00

3.83.8

De

pth

(k

m)

De

pth

(k

m)


(subsample)(subsample)

Zoom Views of Inline Sections Zoom Views of Inline Sections

Offset: 3~6.5 km, Depth: 0.3~1.8 kmOffset: 3~6.5 km, Depth: 0.3~1.8 km

WMWM

ModelModel

KM KM

SubSubWMWM

Offset: 1.8~4 km, Depth: 0.6~2.1 kmOffset: 1.8~4 km, Depth: 0.6~2.1 km

WMWM

ModelModel

KM KM

SubSubWMWM

Zoom Views of Crossline Sections Zoom Views of Crossline Sections

Inline: 1.8~7.2 km, Crossline: 0~4 kmInline: 1.8~7.2 km, Crossline: 0~4 km

WMWM

ModelModel

KM KM

SubSubWMWM

Horizontal Slices (Depth=1.4 km) Horizontal Slices (Depth=1.4 km)

A Common Shot GatherA Common Shot GatherTrace NumberTrace Number5454 193193

Tim

e (s

ec)

Tim

e (s

ec)

00

3.43.4

Inline KM Inline KM ((CPU=1CPU=1)) Inline WMInline WM ((CPU=1/14CPU=1/14))

Offset (km)Offset (km)0.40.4 4.54.5

0.80.8

3.83.8

De

pth

(k

m)

De

pth

(k

m)




0.80.8

3.83.8

De

pth

(k

m)

De

pth

(k

m)


(subsample)(subsample)

Crossline KM Crossline KM ((CPU=1CPU=1)) Crossline WMCrossline WM ((CPU=1/14CPU=1/14))


0.80.8

3.33.3

De

pth

(k

m)

De

pth

(k

m)


Crossline KMCrossline KM ((CPU=1CPU=1)) Crossline WMCrossline WM ((CPU=1/50CPU=1/50))(subsample)(subsample)


0.80.8

3.33.3

De

pth

(k

m)

De

pth

(k

m)


Inline: 0~4.6 km, Crossline: 0~3.8Inline: 0~4.6 km, Crossline: 0~3.8

KM (KM (CPU=1CPU=1))

Horizontal Slices (Depth=2.5 km) Horizontal Slices (Depth=2.5 km)

WM (WM (CPU=1/14CPU=1/14)) WM (Sub, WM (Sub, CPU=1/50CPU=1/50))

OutlineOutline• Problems in Kirchhoff MigrationProblems in Kirchhoff Migration• Wavepath Migration Wavepath Migration • Implementation of WMImplementation of WM• Numerical ResultsNumerical Results ConclusionsConclusions

ConclusionsConclusions

SEG/EAGE Salt DataSEG/EAGE Salt Data• Fewer Migration ArtifactsFewer Migration Artifacts• Better for Complex Salt BoundaryBetter for Complex Salt Boundary• Higher Computational EfficiencyHigher Computational Efficiency

CPUCPU KM: KM: 11 WM: WM: 1/331/33 Subsampled WM: Subsampled WM: 1/1701/170

ConclusionsConclusions

West Texas Field DataWest Texas Field Data• Fewer Migration ArtifactsFewer Migration Artifacts• Similar Image QualitySimilar Image Quality• Higher Computational EfficiencyHigher Computational Efficiency

CPUCPU KM: KM: 11 WM: WM: 1/141/14 Subsampled WM: Subsampled WM: 1/501/50

AcknowledgementsAcknowledgements

We thank UTAM sponsorsWe thank UTAM sponsorsfor their financial supportfor their financial support

Wavepath Migration versus Kirchhoff Migration: 3-D Prestack Examples

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