migration and attenuation of surface-related and interbed multiple reflections

Migration and Attenuation of Migration and Attenuation of Surface-Related and Interbed Surface-Related and Interbed

Multiple ReflectionsMultiple Reflections

Zhiyong JiangZhiyong Jiang

University of UtahUniversity of Utah

April 21, 2006April 21, 2006

OutlineOutline• OverviewOverview• Surface Multiple Migration Surface Multiple Migration • Interbed Multiple MigrationInterbed Multiple Migration• Multiple Attenuation inMultiple Attenuation in Multiple ImagingMultiple Imaging• ConclusionsConclusions

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PrimaryPrimary

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Surface MultipleSurface Multiple

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Interbed MultipleInterbed Multiple

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High-order MultipleHigh-order Multiple

• For the first time, I examine the imaging and For the first time, I examine the imaging and computational properties of three different surface computational properties of three different surface multiple imaging methods, and apply them to both multiple imaging methods, and apply them to both synthetic and field datasynthetic and field data

Technical ContributionsTechnical Contributions

• I develop two novel methods for imaging interbed I develop two novel methods for imaging interbed multiples, and apply them to field and synthetic datamultiples, and apply them to field and synthetic data

• I attenuate high-order multiples to solve a major I attenuate high-order multiples to solve a major problem in multiple imaging: the interference from problem in multiple imaging: the interference from other multiples. This strategy makes multiple other multiples. This strategy makes multiple imaging a more practical toolimaging a more practical tool

OutlineOutline• OverviewOverview• Surface Multiple Migration Surface Multiple Migration

• MotivationMotivation• Methodology Methodology • Numerical ResultsNumerical Results• Summary Summary

Why Migrate Surface Multiples?Why Migrate Surface Multiples?

Better FoldBetter Fold

Better Vert. Res.Better Vert. Res.

Wider CoverageWider Coverage

Shot radius

Z

3D VSP3D VSP SurveySurvey


• MotivationMotivation• MethodologyMethodology • Numerical ResultsNumerical Results• Summary Summary

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d(s,g)d(s,g)mult.mult. = m(x = m(x00 , , ωω) W() W(ωω))

exp[iexp[iωω ( (ττsxsx ++ττx gx g ++ττg gg g)] )] 00 00 0000

..~~ ~~ ~~

Modeling EquationModeling Equation

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g’g’00BB00

Method 1: Model-based Multiple ImagingMethod 1: Model-based Multiple Imaging

m(x, m(x, ωω) = ) = ∫∫ ∫∫ d(s, g)d(s, g)mult.mult.

exp[-iexp[-iωω ( (ττsx sx ++ττxg’xg’ ++ττg’gg’g)] )] ddssddg g 0000

..

ττsxsx ττxg’xg’00

ττg’gg’g00

ττxg’xg’ ++ττg’gg’g = = min min ((ττxg’xg’ ++ττg’gg’g))g’g’ BB00

00 00

g’g’

g’ : diffraction pointg’ : diffraction pointgg00’: specular point’: specular point

X : trial image pointX : trial image point

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ss

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g’g’00BB00

Method 2: Mig. with Semi-natural Green’s functionsMethod 2: Mig. with Semi-natural Green’s functions

m(x, m(x, ωω) = ) = ∫∫ ∫∫ d(s, g)d(s, g)mult.mult.


..


00 00

g’g’

g’ : diffraction pointg’ : diffraction pointgg00’: specular point’: specular point

X : trial image pointX : trial image point

~~

~~ ~~

ττsxsx ττxg’xg’

ττg’gg’g

00

~~

00

gg

ss

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BB00

Method 3: Interferometric ImagingMethod 3: Interferometric Imaging

m(x, m(x, ωω) = ) = ∫∫∫ ∫∫∫ d(s, g)d(s, g)mult.mult.

exp[-iexp[-iωω ( (ττsx sx ++ττxg’ xg’ ++ττg’gg’g)] )] ddssddggddg’ g’ ..

g’g’

g’ : diffraction pointg’ : diffraction pointX : trial image pointX : trial image point

~~

ττsxsx

MigrationMigration

MethodsMethods

Sensitivity Sensitivity to velocity to velocity errors errors

Receiver Receiver Statics in Statics in VSP case VSP case eliminated?eliminated?

Receiver Receiver geometry geometry needs to be needs to be known in known in VSP case?VSP case?

Coverage Coverage in VSP in VSP casecase

Applicablbe Applicablbe to to IVSPWD?IVSPWD?

Model-based Model-based multiple multiple MigrationMigration

High No Yes Wide No

Semi-natural Semi-natural Green’s Green’s functionsfunctions

Low Yes No Wide No

Interferomet-Interferomet-ric Imagingric Imaging

Low Yes No Wide Yes

Primary Primary MigrationMigration

Low No Yes Narrow No

Imaging Properties of Migration MethodsImaging Properties of Migration Methods


• MotivationMotivation• Methodology Methodology • Numerical ResultsNumerical Results• Summary Summary

Numerical ResultsNumerical Results

• 2-D Dipping Layer Model2-D Dipping Layer Model

• 3-D Real Data3-D Real Data

• 3-D Synthetic Data3-D Synthetic Data

Velocity ModelVelocity Model

00

13001300

92592500 X (m)X (m)

Dep

th (

m)

Dep

th (

m)

19001900

40004000V (m/s)V (m/s)

Shots: 92; Receivers: 91 (50m -950 m)Shots: 92; Receivers: 91 (50m -950 m)

WellWell

CSG 51CSG 51

5050 950m950m 950m950m5050

Tim

e (s

)T

ime

(s)

33

00Ghost ComponentGhost Component

SS

GG

XX

AAWellWell

CSG 51CSG 51

5050 950m950m 950m950m5050

Tim

e (s

)T

ime

(s)

33

00Primary ComponentPrimary Component

SS

GG

XX

AAWellWell

X (m)X (m)00 925925

00

13001300

Dep

th (

m)

Dep

th (

m)

X (m)X (m) 92592500

PrimaryPrimary 1st-order multiple 1st-order multiple 8 Receivers8 Receivers




• 3-D Synthetic Data3-D Synthetic Data




• 3-D Synthetic Data 3-D Synthetic Data

Y (m)Y (m)00 2000200000

X (

m)

X (

m)

20002000

1089 shots

111 receivers

WellWell

Sources/Wells LocationsSources/Wells Locations

CSG10 CSG10

11 111111 11111111

Tim

e (s

)T

ime

(s)

3.53.5

00

XX

CSG540CSG540

Receiver NumberReceiver Number Receiver NumberReceiver Number

100100

11001100

Dep

th (

m)

Dep

th (

m)

PrimaryPrimary


X=1000mX=1000m

Y (m)Y (m)00 20002000

100100

11001100

Dep

th (

m)

Dep

th (

m)

100100

11001100

Dep

th (

m)

Dep

th (

m)

11stst order ghost order ghost


X=1000mX=1000m

Y (m)Y (m)00 20002000

100100

11001100

Dep

th (

m)

Dep

th (

m)

100100

11001100

Dep

th (

m)

Dep

th (

m)

PrimaryPrimary


Y=1000mY=1000m

X (m)X (m)00 20002000

100100

11001100

Dep

th (

m)

Dep

th (

m)

100100

11001100

Dep

th (

m)

Dep

th (

m)

11stst order ghost order ghost


Y=1000mY=1000m

X (m)X (m)00 20002000

100100

11001100

Dep

th (

m)

Dep

th (

m)


• MotivationMotivation• Methodology Methodology • Numerical ResultsNumerical Results• SummarySummary

SummarySummary

Wider subsurface coverage can be achievedWider subsurface coverage can be achieved

by migrating multiplesby migrating multiples

Multiples illuminate areas invisible to primariesMultiples illuminate areas invisible to primaries

AdvantagesAdvantages

SummarySummary

Multiple is weakMultiple is weak

Interferences from primary and other events, Interferences from primary and other events,

such as high-order multiplessuch as high-order multiples

LimitationLimitation

OutlineOutline• OverviewOverview• Interbed Multiple Migration Interbed Multiple Migration

• MotivationMotivation• MethodsMethods• Numerical TestsNumerical Tests• Summary Summary

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What is below the salt?What is below the salt?

Challenge with VSP Surface Multiples: Challenge with VSP Surface Multiples: Long raypath, strong attenuation, Long raypath, strong attenuation, triple passage through salttriple passage through salt

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Challenge with CDP primary reflections:Challenge with CDP primary reflections:strong attenuation, strong attenuation, double passage through salt double passage through salt

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Can we try interbed multiples?Can we try interbed multiples?Advantages: short raypth, less Advantages: short raypth, less attenuation, single passage through saltattenuation, single passage through salt

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Modeling EquationModeling Equation

d(s,g)d(s,g)inter.inter. = m(x = m(x00 , , ωω) W() W(ωω))

exp[iexp[iωω ( (ττsx sx ++ττx gx g ++ττg gg g)] )] 00 00 0000

..~~ ~~ ~~

gg

ss

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g’g’00

BB00

BB11

Method 1: Fermat’s principleMethod 1: Fermat’s principle

m(x, m(x, ωω) = ) = ∫∫ ∫∫ d(s, g)d(s, g)inter.inter.


..

ττsxsx

ττxg’xg’00

ττg’gg’g00


00 00

g’g’

gg

ss

xx

BB00

BB11

g’g’

Method 2: Summation of all the diffraction energyMethod 2: Summation of all the diffraction energy

m(x, m(x, ωω) = ) = ∫∫∫ ∫∫∫ d(s, g)d(s, g)inter.inter.

exp[-iexp[-iωω ( (ττsx sx ++ττxg’ xg’ ++ττg’gg’g)] )] ddssddggddg’ g’ ..

ττsxsx

Numerical TestsNumerical Tests

• SEG/EAGE ModelSEG/EAGE Model• Large Salt ModelLarge Salt Model• Field Data TestField Data Test

00

20002000

Dep

th (

m)

Dep

th (

m)

30003000X (m)X (m)

Shots: 301; Receivers: 61 (1000m - 1600m)Shots: 301; Receivers: 61 (1000m - 1600m)


00

20002000

Dep

th (

m)

Dep

th (

m)

3000300000 X (m)X (m)

ss

Upper-salt-boundary Interbed MultipleUpper-salt-boundary Interbed Multiple

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g’g’00

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Interbed Multiple Interbed Multiple Migration ImageMigration Image

1200120000 X (m)X (m)

800800

20002000

Dep

th (

m)

Dep

th (

m)

1200120000 X (m)X (m)


00

20002000

Dep

th (

m)

Dep

th (

m)

3000300000 X (m)X (m)

ss

Lower-salt-boundary Interbed MultipleLower-salt-boundary Interbed Multiple

xx

g’g’00

gg

00

800800

20002000

Dep

th (

m)

Dep

th (

m)

12001200X (m)X (m) 00 12001200X (m)X (m)

Velocity ModelVelocity Model Interbed Multiple Interbed Multiple Migration ImageMigration Image

160001600000 X (m)X (m)00

1100011000

Dep

th (

m)

Dep

th (

m)Velocity ModelVelocity Model

Shots: 319; Receivers: 21Shots: 319; Receivers: 21

160001600000 X (m)X (m)

00

1100011000

Dep

th (

m)

Dep

th (

m)

Lower-salt-boundary Interbed MultipleLower-salt-boundary Interbed Multiple

ss

xxgg

g’g’00

00 12001200X (m)X (m)

62506250

72507250

Dep

th (

m)

Dep

th (

m)

00

62506250

72507250

Dep

th (

m)

Dep

th (

m)

12001200X (m)X (m)


Interbed Multiple Migration ImageInterbed Multiple Migration Image

00

1066810668

Dep

th (

m)

Dep

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m)

16000m16000m00

Shots: 102; Receivers: 12Shots: 102; Receivers: 12


00

1066810668

Dep

th (

m)

Dep

th (

m)

16000m16000m00

Sea-bed Interbed MultipleSea-bed Interbed Multiple

ss

gg

g’g’00

xx

4000400000 X (m)X (m)40004000

Dep

th (

m)

Dep

th (

m)

20002000

40004000

Dep

th (

m)

Dep

th (

m)

20002000Velocity ModelVelocity Model

Interbed Multiple Migration ImageInterbed Multiple Migration Image

• Interbed multiples are used to image saltInterbed multiples are used to image salt boundaries and subsalt structuresboundaries and subsalt structures

SummarySummary

• Challenge: Accuracy of the multipleChallenge: Accuracy of the multiple generating interface generating interface

• Challenge: Interference from other multiplesChallenge: Interference from other multiples

OutlineOutline• OverviewOverview• Multiple Attenuation inMultiple Attenuation in Multiple ImagingMultiple Imaging

• Motivation Motivation • Methodology Methodology • Numerical ExamplesNumerical Examples• SummarySummary

A major problem with multiple imaging:

high-order high-order multiplemultipleIncorrectly positioned as Incorrectly positioned as

low-order multiplelow-order multiple

interference from high-order multiple interference from high-order multiple

Step1: Prediction

second-order second-order multiplemultiple

SS

g’g’ gg

Physics Behind PredictionPhysics Behind Prediction

DD(g | s)(g | s) ==∫∫ GG(g | g’)(g | g’) DD(g’ | s)(g’ | s) ddg’g’

DD(g’|s):(g’|s): Downgoing componentDowngoing component

GG(g|g’):(g|g’): Green’s function for Green’s function for propagating the wavefield propagating the wavefield

DD(g|s):(g|s): Predicted high-order multiplesPredicted high-order multiplesSS

g’g’ gg

p(t)p(t) = = y(t)y(t) - - ffjj(t)(t)mmjj(t)(t)

Step2: SubtractionStep2: Subtraction

Predicted high-order Predicted high-order multiplemultiple

Original dataOriginal dataHigh-order multiple-High-order multiple-free datafree data

Numerical ExamplesNumerical Examples

• Synthetic Data TestSynthetic Data Test

• Field Data TestField Data Test

Density ModelDensity Model

00 14,00014,000X (m)X (m)

00

6,0006,000

Dep

th (

m)

Dep

th (

m)

20 receivers20 receivers6.25m spacing6.25m spacing

276 shots, 50m spacing276 shots, 50m spacing

CRG1: Different Order MultiplesCRG1: Different Order Multiples

direct wavedirect wave11stst order order

22ndnd order order

33rdrd order order

2.52.500 14,00014,000X (m)X (m)

0.40.4

Tim

e (s

ec)

Tim

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ec)

Before AttenuationBefore Attenuation

2.52.500 14,00014,000X (m)X (m)

0.40.4

Tim

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ec)

Tim

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PredictionPrediction

2.52.500 14,00014,000X (m)X (m)

0.40.4

Tim

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ec)

Tim

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ec)

After AttenuationAfter Attenuation

2.52.500 14,00014,000X (m)X (m)

0.40.4

Tim

e (s

ec)

Tim

e (s

ec)


Migration Image: Before AttenuationMigration Image: Before Attenuation

500500

Dep

th (

m)

Dep

th (

m)

6000600015001500 1250012500X (m)X (m)

Interference from high-Interference from high-order multipleorder multiple

Migration Image: After AttenuationMigration Image: After Attenuation

500500

Dep

th (

m)

Dep

th (

m)

6000600015001500 1250012500X (m)X (m)

Numerical ExamplesNumerical Examples

• Synthetic Data TestSynthetic Data Test

• Field Data TestField Data Test

Velocity Model

00 6000060000X (ft)X (ft)

Dep

th (ft)

Dep

th (ft)

00

4300043000

V (ft/s)V (ft/s)49104910

1430014300

652 shots652 shots

12 receivers12 receivers

Different Order MultiplesDifferent Order Multiples

direct direct wavewave

11stst order order

22ndnd order order


5.005.00

1.251.25T

ime

(sec

)T

ime

(sec

)

00 6000060000X (ft)X (ft)

22ndnd-order -order multiplemultiple

11stst-order -order multiplemultiple

Predicted MultiplePredicted Multiple

5.005.00

1.251.25T

ime

(sec

)T

ime

(sec

)

00 6000060000X (ft)X (ft)

After AttenuationAfter Attenuation

5.005.00

1.251.25T

ime

(sec

)T

ime

(sec

)

00 6000060000X (ft)X (ft)


5.005.00

1.251.25T

ime

(sec

)T

ime

(sec

)

00 6000060000X (ft)X (ft)

22ndnd-order -order multiplemultiple

11stst-order -order multiplemultiple

Multiple Migration Image: Before AttenuationMultiple Migration Image: Before Attenuation

1010

2626

De

pth

(kft)

De

pth

(kft)

1616 3232X (kft)X (kft)

interference from high-interference from high-order multipleorder multiple

1010

2626

De

pth

(kft)

De

pth

(kft)

1616 3232X (kft)X (kft)

Multiple Migration Image: After Attenuation

Multiple Migration Images: ComparisonMultiple Migration Images: Comparison

1010

2626

De

pth

(kft)

De

pth

(kft)

1616 3232X (kft)X (kft)

• Attenuate high-order multiples to better imageAttenuate high-order multiples to better image low-order multiples, making multiple imaging alow-order multiples, making multiple imaging a more practical and useful toolmore practical and useful tool

SummarySummary

• Obtained cleaner and more accurate subsurface Obtained cleaner and more accurate subsurface images to help avoid misinterpretation and thusimages to help avoid misinterpretation and thus reduce risk in subsequent processesreduce risk in subsequent processes

• As shown in the numerical examples, As shown in the numerical examples, surface multiple imaging and interbedsurface multiple imaging and interbed multiple imaging can be important imagingmultiple imaging can be important imaging methods methods

ConclusionsConclusions

• The multiple attenuation process is effective in mitigating the interference in multiple imaging

• Apply data-based multiple prediction method in multiple filtering

Future WorkFuture Work

• Attenuate surface multiples prior to imaging interbed multiples

• Apply interbed multiple imaging to more field data sets

• My supervisory committee: Ronanld L. Bruhn,My supervisory committee: Ronanld L. Bruhn, Brian E. Hornby, Richard D. Jarrard, and Brian E. Hornby, Richard D. Jarrard, and Robert B. Smith

AcknowledgementsAcknowledgements

• My wife Weining and my daughter Julia

• My advisor: Gerard T. Schuster

• My UTAM colleagues and my other friends

migration and attenuation of surface-related and interbed multiple reflections

Documents

multiple imagingmx

attenuation of surface

surface multiples

imaging interbed multiples

d real data

d dipping layer model

sxxg0gg0 xg gg

sx xg gg dsdgdg