Stabilization of Migration Deconvolution Jianxing Hu University of Utah.

Stabilization of Migration Deconvolution

Jianxing HuUniversity of Utah

OutlineOutline• MotivationMotivation

• MethodologyMethodology

• Numerical TestsNumerical Tests

• ConclusionsConclusions

KMKM MDMD2420

1.5

2.3

Tim

e (s

)

X(km)24201.5

2.3

Tim

e (s

)

X(km)

Comparison of RTM and MD ImagesComparison of RTM and MD Images 66

X(km)X(km)

55 11

22

33

D

epth

(k

m)

Dep

t h (

km

)

11 66

X(km)X(km)

55

22

33

D

epth

(k

m)

Dep

t h (

km

)

RTMRTM MDMD

MotivationMotivationInvestigate banding noise in the MD image and improve the stability of MD system.

Banding

X(km)0 150

4

Dep

th(k

m)

OutlineOutline• MotivationMotivation

• MethodologyMethodology

• Numerical TestsNumerical Tests

• ConclusionsConclusions

Migration Noise ProblemsMigration Noise Problems• AliasingAliasing

• Recording FootprintRecording Footprint

• Limited ResolutionLimited Resolution

• Amplitude DistortionAmplitude Distortion 0 km0 km 15 km15 km

Migration noise and artifacts

Footprint Amplitude distortion

0

2

Tim

e (s

)

Solution: Deconvolve the point Solution: Deconvolve the point scatterer response from the migrated scatterer response from the migrated imageimage

TTrr = ( = (L LL L ) m ) m

-1-1

Reflectivity MigratedReflectivity Migrated SectionSection

ReasonReason:: m = m = L dL dTT

MigratedMigratedSectionSection

DataData

butbut dd = L = L rrL rL r

Migration SectionMigration Section == Blured Blured Image ofImage of rr

= L LL LDefine T

as migration Green’sfunction

Depth Slices of Point ScatterersDepth Slices of Point Scatterers

Kirch.Kirch. MigrationMigration ImageImage MD ImageMD Image

00 X(km)X(km) 11

Y

(km

)Y

(km

)

00

11

00 X(km)X(km) 11

Y

(km

)Y

(km

)

00

11

m = m = L LL L rrTT rr = ( = (L LL L ) m ) mTT -1 -1

Migration DeconvolutionMigration Deconvolution

),,,,( oppoo zyxzyyxx

oooooo dzdydxzyxR ),,(Model Space

ooo rdrRrrrm

)()()( Model SpaceModel Space

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

)(~.

)(~

)(~

),~,(~

...,),,~,(~

),,~,(~...

),~,(~

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),~,(~

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),,~,(~

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.

)(~)(~

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12111

2

1

nnpnpnpn

nppp

nppp

n zkR

zkR

zkR

zxzkzxzkzxzk

zxzkzxzkzxzk

zxzkzxzkzxzk

zkm

zkm

zkm

MD System of Equations

where ),,(~

ipj zxzk represents the spectrum of

),,( ipj zxzx on the depth of with a scatterer

),( ip zxjz

located at

Migration Green’s Function Coefficient Matrix Structure

Diagonal element

Off-diagonal element

Coefficient matrix regularization

Artifacts in MDArtifacts in MD

Poststack Poststack

MD ImageMD Image

00

44

X (km)X (km) 1515

D

e pth

(km

)D

epth

(km

)

00

Banding Noise

Coefficient Matrix Condition Number v.s. Wavenumber

-0.02 0.02-0.01 0.010

Wavenumber (radian/m)

350

150

250

50

0

Stabilization of MD Stabilization of MD System EquationsSystem Equations

Monitor the condition number of MD Monitor the condition number of MD

system equation for each wavenumbersystem equation for each wavenumber

mRI ~~)

~(

If wavenumber <preset tolerance

mR ~~~ Otherwise

OutlineOutline• MotivationMotivation

• MethodologyMethodology

• Numerical TestsNumerical Tests

• ConclusionsConclusions

Numerical TestsNumerical Tests• 2-D SEG/EAGE overthrust model 2-D SEG/EAGE overthrust model

poststack MDpoststack MD

• 3-D SEG/EAGE salt model 3-D SEG/EAGE salt model poststack MDpoststack MD

• 2-D SEG/EAGE overthrust model 2-D SEG/EAGE overthrust model prestack MDprestack MD

Regularization of MD System EquationsRegularization of MD System Equations

Poststack Poststack MD ImageMD Image without without regularizationregularization

00

44

X (km)X (km) 1515

D

e pth

(km

)D

epth

(km

)

00

00

44

X (km)X (km) 1515

D

e pth

(km

)D

epth

(km

)

00

Poststack Poststack MD ImageMD Image with with regularizationregularization

Numerical TestsNumerical Tests• 2-D SEG/EAGE Overthrust Model 2-D SEG/EAGE Overthrust Model

Poststack MDPoststack MD

• 3-D SEG/EAGE Salt Model 3-D SEG/EAGE Salt Model Poststack MDPoststack MD

• 2-D SEG/EAGE Overthrust Model 2-D SEG/EAGE Overthrust Model Prestack MDPrestack MD

Kirchhoff Migration ImagesKirchhoff Migration Images

04 6 8

X (km)

Dep

t h (

km

)

4

3

2

1

Inline Section

Y (km)

04 6 8

Dep

th (

km

)

4

3

2

1

Crossline Section

MD Images no RegularizationMD Images no Regularization

04 6 8

X (km)

Dep

t h (

km

)

4

3

2

1

Inline Section

Y (km)

04 6 8

Dep

th (

km

)

4

3

2

1

Crossline Section

MD Images with RegularizationMD Images with Regularization

04 6 8

X (km)

Dep

t h (

km

)

4

3

2

1

Inline Section

Y (km)

04 6 8

Dep

th (

km

)

4

3

2

1

Crossline Section

Comparison of Migration and MD ImageComparison of Migration and MD Image

04 6 8

X (km)

Dep

t h (

km

)

4

3

2

1

Migration Inline Section

X (km)

04 6 8

Dep

th (

km

)

4

3

2

1

MD inline Section

Comparison of Migration and MD ImageComparison of Migration and MD Image

04 6 8

Y (km)

Dep

t h (

km

)

4

3

2

1

Migration Crossline Section

Y (km)

04 6 8

Dep

th (

km

)

4

3

2

1

MD Crossline Section

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• 2-D SEG/EAGE Overthrust Model 2-D SEG/EAGE Overthrust Model

Poststack MDPoststack MD

• 3-D SEG/EAGE Salt Model 3-D SEG/EAGE Salt Model Poststack MDPoststack MD

• 2-D SEG/EAGE Overthrust Model 2-D SEG/EAGE Overthrust Model Prestack MD in COGPrestack MD in COG

Regularization of MD System EquationsRegularization of MD System Equations

Prestack Prestack COGCOG Migration Migration ImageImage 0-450 m0-450 m withoutwithout regularizationregularization

00

44

X (km)X (km) 2020

D

e pth

(km

)D

epth

(km

)

00

00

44

X (km)X (km) 2020

D

e pth

(km

)D

epth

(km

)

00

Prestack Prestack COGCOG Migration Migration ImageImage 0-450 m0-450 m withwith regularizationregularization

ConclusionsConclusions

Worse condition number causes the Worse condition number causes the banding noise in MD resultsbanding noise in MD results

Condition number is related to the waveletfrequency, position of migration Green’sfunction and velocity medium

Regularization of the MD system equations enhances the stability of MD system

AcknowledgementAcknowledgement• Thanks to 2000 UTAM sponsors for their financial supportThanks to 2000 UTAM sponsors for their financial support• Thanks to Advanced Data Solutions for providing the SEG Thanks to Advanced Data Solutions for providing the SEG

salt model migration resultsalt model migration result

MotivationMotivationInvestigate Banding Noise in the MD image and improve the stability of MD system.