Imaging Multiple Imaging Multiple Reflections with Reverse-Reflections with Reverse-

Time MigrationTime Migration

Yue WangYue Wang

University of UtahUniversity of Utah

OutlineOutline

• BackgroundBackground

• Motivation & ObjectiveMotivation & Objective

• MethodologyMethodology

• Numerical ExamplesNumerical Examples

• ConclusionsConclusions

Forward ProcessForward Process

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00 4.54.5

*SourceSource Geophone LineGeophone Line

Forward ProcessForward Process

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00 4.54.5

*

obsobs

Reverse Time MigrationReverse Time Migration

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00 4.54.5

obsobs

Extrapolated WavefieldExtrapolated Wavefieldobsobs

Reversed tracesReversed traces

Reverse-Time MigrationReverse-Time Migration

Extrapolated WavefieldExtrapolated Wavefield

Imaging ConditionImaging Condition

Migration SectionMigration Section

OutlineOutline

• BackgroundBackground

• Motivation & ObjectiveMotivation & Objective

• MethodologyMethodology

• Numerical ExamplesNumerical Examples

• ConclusionsConclusions

Ocean-Bottom SurveyOcean-Bottom Survey

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00 4.54.5

*SourceSource Geophone LineGeophone Line

ProblemProblem

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00 4.54.5

*Receiver-side MultiplesReceiver-side Multiples

Synthetic Shot GatherSynthetic Shot GatherT

ime

(s)

Tim

e (s

)

Distance (km)Distance (km)

Receiver side multiplesReceiver side multiples

22

00

0.90.9 3.63.6

Field DataField DataT

ime

(s)

Tim

e (s

)

Distance (m)Distance (m)44

00

-80-80 19001900

Receiver side multiplesReceiver side multiples

Time MigrationTime MigrationT

ime

(s)

Tim

e (s

)

Distance (m)Distance (m)44

00

-80-80 19001900

Receiver side multiplesReceiver side multiples

ObjectiveObjective

• Using both primary and multiple Using both primary and multiple reflections for imaging by reverse-reflections for imaging by reverse-time migration.time migration.

OutlineOutline

• BackgroundBackground

• Motivation & ObjectiveMotivation & Objective

• MethodologyMethodology

• Numerical ExamplesNumerical Examples

• ConclusionsConclusions

Ocean-Bottom SurveyOcean-Bottom Survey

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00 4.54.5

*SourceSource Geophone LineGeophone Line

Ocean-Bottom SurveyOcean-Bottom Survey

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00

*PP

VV

Up-goingUp-going

Multi-Component DataMulti-Component Data

pressure + particle velocitypressure + particle velocity( P & V )( P & V )

ocean-bottom surveyocean-bottom survey

Reverse Time MigrationReverse Time Migration

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00

PPVV

Down-goingDown-going

PPVV

( P & V Scheme )( P & V Scheme )

Reverse Time MigrationReverse Time Migration

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00

VVVV

( Particle Velocity Only )( Particle Velocity Only )

Key IdeaKey IdeaPrimary + Multiple Primary + Multiple

Correct Positions Correct Positions

P & V Scheme P & V Scheme

Key IdeaKey IdeaPrimary + Multiple Primary + Multiple

Incorrect Positions Incorrect Positions

V-Only Scheme V-Only Scheme

Ocean-Bottom SurveyOcean-Bottom Survey

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00

*PP

VV

Up-going WavesUp-going Waves

P & V SchemeP & V Scheme

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00

PPVV

PPVV

Correct PositionCorrect Position

Down-going wavesDown-going waves

Particle Velocity Only SchemeParticle Velocity Only Scheme

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00

VVVV

IncorrectIncorrect

Ocean-Bottom SurveyOcean-Bottom Survey

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00

*PP

VV

Down-going wavesDown-going waves( Multiples )( Multiples )

P & V SchemeP & V Scheme

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00

PPVV

PPVV

Correct PositionCorrect Position Up-going wavesUp-going waves

Particle Velocity Only SchemeParticle Velocity Only Scheme

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00

VVVV

IncorrectIncorrect

OutlineOutline

• BackgroundBackground

• Motivation & ObjectiveMotivation & Objective

• MethodologyMethodology

• Numerical ExamplesNumerical Examples

Salt Dome ModelSalt Dome Model

• ConclusionsConclusions

Salt ModelSalt Model

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

2.72.7

00

00 4.54.5

Shot GatherShot GatherNormal StressNormal StressVerticalVerticalHorizontalHorizontal

Tim

e (s

) T

ime

(s)

Distance (km)Distance (km)22

00

0.90.9 3.63.6 Distance (km)Distance (km)0.90.9 3.63.6 Distance (km)Distance (km)0.90.9 3.63.6

MultiplesMultiples

Kirchhoff MigrationKirchhoff Migration

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

2.52.5

00

0.450.45 4.054.05

Kirchhoff MigrationKirchhoff Migration

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

2.52.5

00

0.450.45 4.054.05

Particle Velocity Only SchemeParticle Velocity Only Scheme

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

2.72.7

00

0.450.45 4.054.05

Particle Velocity Only SchemeParticle Velocity Only Scheme

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

2.72.7

00

0.450.45 4.054.05

P & V SchemeP & V Scheme

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

2.52.5

00

0.450.45 4.054.05

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

2.52.5

00

0.450.45 4.054.05

P & V SchemeP & V Scheme

Primary + Multiple Primary + Multiple

Correct Positions Correct Positions

ConclusionConclusion

P + V RTM P + V RTM

Future Work: Field Data TestFuture Work: Field Data TestT

ime

(s)

Tim

e (s

)

Distance (m)Distance (m)44

00

-80-80 19001900

Receiver side multiplesReceiver side multiples

AcknowledgementAcknowledgement

We are grateful to the 1999 sponsors We are grateful to the 1999 sponsors of the UTAM consortium for the of the UTAM consortium for the financial supportfinancial support

OutlineOutline

• BackgroundBackground

• Motivation & ObjectiveMotivation & Objective

• MethodologyMethodology

• Numerical ExamplesNumerical Examples

Plane-wave examplePlane-wave example

• ConclusionsConclusions

Forward ProcessForward Process

DistanceDistance

Dep

thD

epth

Up-going wavesUp-going waves

P & V SchemeP & V Scheme

DistanceDistance

Dep

thD

epth

Down-going wavesDown-going waves

P & V SchemeP & V Scheme

Time (s)Time (s)

Dep

th (

km

)D

epth

(k

m)

00 0.80.8

00

1.21.2

Down-going wavesDown-going waves

Particle Velocity Only SchemeParticle Velocity Only Scheme

DistanceDistance

Dep

thD

epth

Down-going wavesDown-going waves

Up-going wavesUp-going waves

Particle Velocity Only SchemeParticle Velocity Only Scheme

Time (s)Time (s)

Dep

th (

km

)D

epth

(k

m)

00 0.80.8

00

1.21.2

Down-going wavesDown-going waves

Up-going wavesUp-going waves

P + V RTMP + V RTM

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00

PP++VV

Up-going wavesUp-going waves

Correct PositionCorrect Position

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

11

00

00

PP

Down-going wavesDown-going waves

Up-going wavesUp-going waves