Prestack Migration Prestack Migration DeconvolutionDeconvolution

Jianxing Hu and Gerard T. SchusterUniversity of Utah

OutlineOutline• MotivationMotivation

• MethodologyMethodology

• Numerical TestsNumerical Tests

• ConclusionsConclusions

Comparison of Poststack MD Depth SlicesComparison of Poststack MD Depth Slices

66

88

Y

(k

m)

Y (

km

)

X (km)X (km)44 88 66 1010

Kirchhoff Kirchhoff ImageImage

MD ImageMD Image

66

88

Y

(k

m)

Y (

km

)

X (km)X (km)44 88 66 1010

Comparison of Prestack Migration and MD ImagesComparison of Prestack Migration and MD Images X (km)X (km) 44 66 88 1010

11

44

D

e pth

(km

)D

epth

(km

)

X (km)X (km) 44 66 88 1010 11

44

D

e pth

(km

)D

epth

(km

)

Prestack Kirchhoff Prestack Kirchhoff Migration Image of Migration Image of

a North Sea Data Seta North Sea Data Set

MD Image

OutlineOutline• MotivationMotivation

• MethodologyMethodology

• Numerical TestsNumerical Tests

• ConclusionsConclusions

Modeling and MigrationModeling and Migration

oosoogsg rdSrRrrGrrGrrd

)()(),(),(),(

drdrdrrdrrGrrGSrm sgsgsg

),(),(),()()( ***

Seismic dataSeismic data ReflectivityReflectivityGreen’s FunctionGreen’s Function

Model SpaceModel Space

Migrated ImageMigrated Image

Data SpaceData Space

Seismic DataSeismic Data

Forward Modeling:Forward Modeling:

Migration:Migration:

WaveletWavelet

ooomig rdrRrrrm

)()()( Model SpaceModel Space

),(),()()()( *** sgomig rrGrrGSSrrWhere:Where:

)( omig rr

Denote Denote as the migration Green’s Functionas the migration Green’s Function

drdrdrrGrrG sgsoog

),(),(

Relation of Migrated Image and Relation of Migrated Image and Reflectivity DistributionReflectivity Distribution

Data SpaceData Space

Reflectivity Modulated Reflectivity Modulated by Migration Green’s Functionby Migration Green’s Function

ooomig rdrRrrrm

)()()(

)(rm

)( omig rr

)( orR

Model SpaceModel Space

Migration DeconvolutionMigration Deconvolution

),,,,( oppoomig zyxzyyxx

oooooo dzdydxzyxR ),,(Model Space

ooomig rdrRrrrm

)()()( Model SpaceModel Space

),( pp yx --- --- reference position of migration Green’s functionreference position of migration Green’s function

Lateral Velocity VariationLateral Velocity Variation

Multi-Reference migration Green’s functionMulti-Reference migration Green’s function

Subdivide the migration image area and use multi-reference migration Green’s function to account for lateral velocity variation and far-field artifacts

MethodologyMethodology

Calculate migration Green’s function Calculate migration Green’s function Recording geometry &Recording geometry &migrated image dimensionmigrated image dimension

Velocity ModelVelocity Model

++Traveltime TableTraveltime Table

Migration Migration Green’s functionGreen’s function

)( orrG

MethodologyMethodologyApply migration deconvolution Apply migration deconvolution filter to the stacked prestack filter to the stacked prestack migration imagemigration image

5

Offset(km)

651

2

3

Dep

th (

km)

RTM

)(1orrG

Migration ImageMigration Image

Deconvolved ImageDeconvolved Image

Pseudo-ConvolutionPseudo-Convolution

Offset(km)

651

2

3

Dep

th (

km)

RTM

Difference between Poststack MD Difference between Poststack MD and Prestack MDand Prestack MD

Zero-offset trace location &Zero-offset trace location &migrated image dimensionmigrated image dimension

Velocity ModelVelocity Model

Traveltime TableTraveltime Table

Poststack migration migration Green’s functionGreen’s function

)( orrG

++

Prestack migration migration Green’s functionGreen’s function

Recording Geometry &Recording Geometry &migrated image dimensionmigrated image dimension

++

OutlineOutline• MotivationMotivation

• MethodologyMethodology

• Numerical TestsNumerical Tests

• ConclusionsConclusions

Numerical TestsNumerical Tests• 3-D point scatterer model3-D point scatterer model

• 3-D meandering stream model3-D meandering stream model

• 2-D SEG/EAGE overthrust model2-D SEG/EAGE overthrust model

• 2-D Husky data set (Canadian 2-D Husky data set (Canadian Foothills)Foothills)

• 3-D SEG/EAGE salt model 3-D SEG/EAGE salt model

• 3-D West Texas data set3-D West Texas data set

5 X 5 Sources; 21 X 21 Receivers5 X 5 Sources; 21 X 21 Receivers

(0, 0)(0, 0)

(1km, 0)(1km, 0)

(1km, 1km)(1km, 1km)

(0, 1km)(0, 1km)

Point scattererPoint scatterer

Recording Geometry

kmzyx ooo )7.0,5.0,5.0(

Wavelet frequency 50 Hz

Prestack KM vs. Prestack MDPrestack KM vs. Prestack MD

ozz ozz

dzzz o dzzz o

Y

X

Y

X

Y

X

Y

X

Prestack KM vs. Poststack MDPrestack KM vs. Poststack MD

ozz

dzzz o

Y

X

Y

X

ozz

dzzz o Y

X

Y

X

Numerical TestsNumerical Tests• 3-D point scatterer model3-D point scatterer model

• 3-D meandering stream model3-D meandering stream model

• 2-D SEG/EAGE overthrust model2-D SEG/EAGE overthrust model

• 2-D Husky data set (Canadian 2-D Husky data set (Canadian Foothills)Foothills)

• 3-D SEG/EAGE salt model 3-D SEG/EAGE salt model

• 3-D West Texas data set3-D West Texas data set

(0, 0)(0, 0)

(1 km, 0)(1 km, 0)

(1 km,1 km)(1 km,1 km)

(0, 1 km)(0, 1 km)

A river channelA river channel

Recording Geometry5 X 5 Sources; 21 X 21 Receivers5 X 5 Sources; 21 X 21 ReceiversWavelet frequency 50 Hz

Meandering River ModelMeandering River Model00 10001000

X (m)X (m)00

10001000

Y (

m)

Y (

m)

Kirchhoff Migration ImageKirchhoff Migration Image00 10001000

X (m)X (m)00

10001000

Y (

m)

Y (

m)

MD ImageMD Image00 10001000

X (m)X (m)00

10001000

Y (

m)

Y (

m)

Numerical TestsNumerical Tests• 3-D point scatterer model3-D point scatterer model

• 3-D meandering stream model3-D meandering stream model

• 2-D SEG/EAGE overthrust model2-D SEG/EAGE overthrust model

• 2-D Husky data set (Canadian 2-D Husky data set (Canadian Foothills)Foothills)

• 3-D SEG/EAGE salt model 3-D SEG/EAGE salt model

• 3-D West Texas data set3-D West Texas data set

Prestack Migration ImagePrestack Migration Image

Deconvolved Migration ImageDeconvolved Migration Image

0 km0 km 20 km20 km0 km0 km

4 km4 km

20 km20 km 0 km0 km0 km0 km

4 km4 km

X(km)

X(km)

Dep

th (

km

)D

epth

(k

m)

Zoom View of KM and MDZoom View of KM and MD

Prestack KMPrestack KM

Prestack MDPrestack MD

22

44

33

Dep

th (

km

)D

epth

(k

m)

33 77X (km)X (km)

22

44

33

Dep

th (

km

)D

epth

(k

m)

33 77X (km)X (km)

Numerical TestsNumerical Tests• 3-D point scatterer model3-D point scatterer model

• 3-D meandering stream model3-D meandering stream model

• 2-D SEG/EAGE overthrust model2-D SEG/EAGE overthrust model

• 2-D Husky data set (Canadian 2-D Husky data set (Canadian Foothills)Foothills)

• 3-D SEG/EAGE salt model 3-D SEG/EAGE salt model

• 3-D West Texas data set3-D West Texas data set

Husky Prestack Migration ImageHusky Prestack Migration Image

44

66

X(km)X(km)00

00 101055

22

Dep

th (

km

)D

epth

(k

m)

Velocity Model for Husky DataVelocity Model for Husky Data

66

X(km)X(km)00

00 101055

22

Dep

th (

km

)D

epth

(k

m)

70007000

32003200

Vel

ocit

y (m

/s)

MD with 20 reference positionsMD with 20 reference positions

66

X(km)X(km)00

00 101055

22

Dep

th (

km

)D

epth

(k

m)

AA

KMKM

X(km) 951

3

Dep

th (

km

)

MDMD

X(km) 951

3

Dep

th (

km

)

MD with 20 reference positionsMD with 20 reference positions

66

X(km)X(km)00

00 101055

22

Dep

th (

km

)D

epth

(k

m)

BB

KMKM

X(km) 1411

1

3

Dep

th (

km

)

MDMD

X(km) 1411

1

3

Dep

th (

km

)

MD with 20 reference positionsMD with 20 reference positions

66

X(km)X(km)00

00 101055

22

Dep

th (

km

)D

epth

(k

m)

CC

KMKM

X(km) 14102

5

Dep

th (

km

)

MDMD

X(km) 14102

5

Dep

th (

km

)

Numerical TestsNumerical Tests• 3-D point scatterer model3-D point scatterer model

• 3-D meandering stream model3-D meandering stream model

• 2-D SEG/EAGE overthrust model2-D SEG/EAGE overthrust model

• 2-D Husky data set2-D Husky data set

• 3-D SEG/EAGE salt model 3-D SEG/EAGE salt model

• 3-D West Texas data set3-D West Texas data set

KM Inline (97,Y) SectionKM Inline (97,Y) Section MD Inline (97,Y) SectionMD Inline (97,Y) Section

55 88Y (km)Y (km) 55 88Y (km)Y (km)00

44

22

00

44

22

Dep

th (

km

)D

epth

(k

m)

KM Crossline (X,97) SectionKM Crossline (X,97) Section MD Crossline (X,97) SectionMD Crossline (X,97) Section

00

44

22

Dep

th (

km

)D

epth

(k

m)118

X (km)118

X (km)

00

44

22

Numerical TestsNumerical Tests• 3-D point scatterer model3-D point scatterer model

• 3-D meandering stream model3-D meandering stream model

• 2-D SEG/EAGE overthrust model2-D SEG/EAGE overthrust model

• 2-D Husky data set2-D Husky data set

• 3-D SEG/EAGE salt model 3-D SEG/EAGE salt model

• 3-D West Texas data set3-D West Texas data set

KMKM MDMD00 33X(kft)

44

66

88

Dep

th (

kft

)D

epth

(k

ft) 44

66

88

00 33X(kft)

44

66

88

Dep

th (

kft

)D

epth

(k

ft)

KMKM MDMD

44

66

88

X(kft)22 44X(kft)22 44

OutlineOutline• MotivationMotivation

• MethodologyMethodology

• Numerical TestsNumerical Tests

• ConclusionsConclusions

ConclusionsConclusionsWorks well on 2-D land and 3-D Works well on 2-D land and 3-D synthetic marine prestack data synthetic marine prestack data

More work is needed to remedy More work is needed to remedy the problems in MD for 3-D the problems in MD for 3-D land prestack dataland prestack data

Standard post-migration processing procedure ?

AcknowledgementAcknowledgement• Thank 1999 UTAM sponsors for Thank 1999 UTAM sponsors for

their financial supporttheir financial support