Migration Deconvolution vs. Least Squares

Migration

Jianhua YuUniversity of Utah

OutlineOutline• MotivationMotivation

• MD vs. LSMMD vs. LSM

• Numerical TestsNumerical Tests

• ConclusionsConclusions

Migration Noise ProblemsMigration Noise Problems

Migration noise and artifacts

Footprint Amplitude distortion

Migration ProblemsMigration Problems

AliasingAliasing

Limited ResolutionLimited Resolution

MotivationMotivation

Investigate MD and LSM:

Improving resolution

Suppressing migration noiseComputational cost

Robustness

OutlineOutline• MotivationMotivation

• MD vs. LSMMD vs. LSM

• Numerical TestsNumerical Tests

• ConclusionsConclusions

m = (m = (L L L L )) L L ddTTTT -1

Least Squares Migration

Reflectivity

Modeling operator

Seismic data

Migration operator

TTmm = ( = (L LL L ) m’ ) m’

-1-1

ReflectivityReflectivity

MD deblurring operator

Migration SectionMigration Section

Migration Deconvolution

Solutions of MD vs. LSMSolutions of MD vs. LSM

m = (m = (L L L L )) L L ddTTTT -1LSM:

TTmm = ( = (L LL L ) ) mm’’

-1-1 MD:

Migrated image

Data

OutlineOutline• MotivationMotivation

• MD vs. LSMMD vs. LSM

• Numerical TestsNumerical Tests

• ConclusionsConclusions

Numerical TestsNumerical Tests

• Point Scatterer ModelPoint Scatterer Model

• 2-D SEG/EAGE overthrust model 2-D SEG/EAGE overthrust model poststack MD and LSMpoststack MD and LSM

Scatterer Model Kirchhoff MigrationD

epth

(k

m)

1.8

01.00 1.00

MD LSM Iter=15D

epth

(k

m)

1.8

01.00 1.00

• Point Scatterer ModelPoint Scatterer Model

• 2-D SEG/EAGE Overthrust Model 2-D SEG/EAGE Overthrust Model Poststack MD and LSMPoststack MD and LSM

Numerical TestsNumerical Tests

KM

Dep

th (

km

)

4.5

00 7.0

0 7.0

X (km)

X (km)

4.5

0

LSM 10

KM

Dep

th (

km

)

4.5

00 7.0

0 7.0

X (km)

X (km)

4.5

0

LSM 15

KM

Dep

th (

km

)

4.5

00 7.0

0 7.0

X (km)

X (km)

4.5

0

MD

Dep

th (

km

)

4.5

00 7.0

0 7.0

X (km)

X (km)

4.5

0

MD

LSM 15

LSM 15

MD

KM2

3.5

Dep

th (

km

)

LSM 192

3.5

Dep

th (

km

)Zoom View

Dep

th (

km

)

4.5

00 7.0

Why does MD perform better than LSM ?

4.5 MD

LSM 19

0

X (km)

OutlineOutline• MotivationMotivation

• MD vs. LSMMD vs. LSM

• Numerical TestsNumerical Tests

• ConclusionsConclusions

ConclusionsConclusions

Efficiency MD >> LSM

FunctionFunction PerformancPerformanceeResolutionResolution MD = LSMMD = LSM

.

Suppressing noise MD > LSM

Robustness MD < LSM

AcknowledgmentsAcknowledgments

• Thanks to 2001 UTAM sponsors Thanks to 2001 UTAM sponsors for their financial supportfor their financial support