fast least squares migration with a deblurring filter
DESCRIPTION
Fast Least Squares Migration with a Deblurring Filter. Naoshi Aoki Feb. 5, 2009. Outline. Motivation Theory Deblurring filter theory Deblurred LSM theory Numerical results of the deblurred LSM Marmousi2 model test 2D marine data test Conclusions. Outline. Motivation Theories - PowerPoint PPT PresentationTRANSCRIPT
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Fast Least SquaresFast Least Squares MigrationMigrationwith a Deblurring Filterwith a Deblurring Filter
Naoshi Aoki
Feb. 5, 2009
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OutlineOutline
• Motivation
• Theory– Deblurring filter theory– Deblurred LSM theory
• Numerical results of the deblurred LSM– Marmousi2 model test– 2D marine data test
• Conclusions
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OutlineOutline
• Motivation
• Theories– Deblurring filter theory– Deblurred LSM theory
• Numerical results of the deblurred LSM– Marmousi2 model test– 2D marine data test
• Conclusions
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Deblurring Migration ImageDeblurring Migration Image• Migration
• Two methods to deblur the migration image– Least Squares Migration (e.g., Nemeth et al.,1999)
– Migration Deconvolution (Hu and Schuster, 2001)
Tmigm = L d
( 1) ( ) ( ) ( ) ,k k k k Tm = m L (Lm - d)
T= L Lm
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1[ ]Tmigm = L L m
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MotivationMotivation• Problems
– LSM can be more than an order of magnitude more costly than standard migration.
– MD filter is characterized by image artifacts known as MD edge artifacts.
• Solution– Use an MD image as an a priori model for a
regularized LSM.– Use an MD filter as a preconditioner for LSM.
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OutlineOutline
• Motivation
• Theories– Deblurring filter theory– Deblurred LSM theory
• Numerical results of the deblurred LSM– Marmousi2 model test– 2D marine data test
• Conclusions
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Deblurring Filter Theory (1)Deblurring Filter Theory (1)
1. Actual Migration Image
2. Reference migration image
[ ]T TL d = L L m
[ ] 'T TL d' = L L m
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Migration Model
?
Reference Migration Reference Model
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Deblurring Filter Theory (2)Deblurring Filter Theory (2)
3. Find non-stationary matching operator
4. Apply the deblurring filter
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F
F
'TFL d' = mReference Migration Reference Model
TFL d mMigration Model
?
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OutlineOutline
• Motivation
• Theories– Deblurring filter theory– Deblurred LSM theory
• Numerical results of the deblurred LSM– Marmousi2 model test– 2D marine data test
• Conclusions
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Deblurred LSM (DLSM) TheoryDeblurred LSM (DLSM) Theory
• DLSM is a fast LSM with a deblurring filter.• Two types of DLSM algorithms are proposed:
– Method 1: Regularized DLSM (or RDLSM)
where is , and is a regularization parameter.
– Method 2: Preconditioned DLSM (or PDLSM)
,n Tn aprig L (Lm - d) m -m
TFL d
1 .n n nm = m Fg
10
aprim
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OutlineOutline
• Motivation
• Theories– Deblurring filter theory– Deblurred LSM theory
• Numerical results of the deblurred LSM– Marmousi2 model test– 2D marine data test
• Conclusions
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Marmousi2 Velocity ModelMarmousi2 Velocity Model
0
3
0 15
Z (
km)
X (km)
4.51.5P wave velocity (km/s)
AnticlineStructures
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Test WorkflowTest Workflow
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Migration ImageMigration Image
Velocity ModelVelocity Model
Reflectivity ModelReflectivity Model Reference Migration Reference Migration ImageImage
Reference Reference Reflectivity ModelReflectivity Model
Compute LSMCompute LSMDeblurred Migration Deblurred Migration ImageImage
Find deblurring Find deblurring operatoroperator
Data Preparation Part Deblurring Filter Part
DLSM Part
TFL d
F
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Data Preparation PartData Preparation Part
Poststack KM Image
0
3
Z (
km)
6 12X (km)
Actual Reflectivity Model
0
3
Z (
km)
6 12X (km)
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Migration ImageMigration Image
Velocity ModelVelocity Model
Reflectivity ModelReflectivity Model
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Deblurring Filter PartDeblurring Filter Part
Reference Migration Image
0
3
Z (
km)
6 12X (km)
Geological Reference Model
0
3
Z (
km)
6 12X (km)15
F
Reference Migration ImageReference Migration Image
Reference Reflectivity ModelReference Reflectivity Model
Find deblurring operatorFind deblurring operator
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Deblurred Migration Image
0
3
Z (
km)
6 12X (km)
Actual Migration Image
0
3
Z (
km)
6 12X (km)16
F
Deblurred Migration ImageDeblurred Migration Image
Reference Migration ImageReference Migration Image
Reference Reflectivity ModelReference Reflectivity Model
Find deblurring operatorFind deblurring operatorDeblurring Filter PartDeblurring Filter Part
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Method 2: PDLSM after 12 Iterations
Method 1:RDLSM after 20 Iterations
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0
3
Z (
km)
6 12X (km)
0
3
Z (
km)
6 12X (km)
Compute LSMCompute LSM
DLSM PartDLSM Part
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Image ComparisonImage Comparison
0
3
Z (
km)
6 12X (km)
Method 2: PDLSM after 12 Iterations
0
3
Z (
km)
6 12X (km)
Method 1:RDLSM after 20 Iterations
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Migration Image after Deblurring Filter0
3
Z (
km)
6 12X (km)
Migration Image
0
3
Z (
km)
6 12X (km)
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DLSM Residual CurvesDLSM Residual Curves
Method 2:Method 2:Preconditioned DLSMPreconditioned DLSM
1
01 30
Iteration Number
Res
idua
l
Method 1:Method 1:Regularized DLSMRegularized DLSM
1
01 30
Iteration Number
Res
idua
l
20 12
Damping parameter: Γ= 200000x0.5n-1, n=1,2,…,30
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Noise level
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OutlineOutline
• Motivation
• Theories– Deblurring filter theory– Deblurred LSM theory
• Numerical results of the deblurred LSM– Marmousi2 model test– 2D marine data test
• Conclusions
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2D Poststack2D PoststackKirchhoff MigrationKirchhoff Migration
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1
1.5
Z (
km)
X (km)
1310.5
0.5
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Test WorkflowTest Workflow
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Migration ImageMigration Image
Field DataField Data
Reference Migration Reference Migration ImageImage
Reference Reference Reflectivity ModelReflectivity Model
Compute LSMCompute LSMDeblurred Migration Deblurred Migration ImageImage
Find deblurring Find deblurring operatoroperator
Standard Processing Part Deblurring Filter Part
DLSM Part
TFL d
F
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Comparison of Imaging ResultsComparison of Imaging Results
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8
1
1.5
Z (
km)
X (km)
1310.5
0.5
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Comparison of Images: Box AComparison of Images: Box A
0.5
0.7
Z (
km)
9.6 10.6X (km)
Migration
0.5
0.7
Z (
km)
9.6 10.6X (km)
LSM after 3 Iterations
0.5
0.7
Z (
km)
9.6 10.6X (km)
DLSM after 3 Iterations
0.5
0.7
Z (
km)
9.6 10.6X (km)
LSM after 10 Iterations
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Comparison of Images: Box BComparison of Images: Box BMigration
1
1.2
Z (
km)
11 12X (km)
LSM after 3 Iterations
1.2
Z (
km)
11 12X (km)
1
DLSM after 3 Iterations
1.2Z (
km)
11 12X (km)
1
LSM after 10 Iterations
1.2
Z (
km)
11 12X (km)
1
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OutlineOutline
• Motivation
• Theories– Deblurring filter theory– Deblurred LSM theory
• Numerical results of the deblurred LSM– Marmousi2 model test– 2D marine data test
• Conclusions
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ConclusionsConclusions
• A deblurring filter provides a fine a priori model for a regularized LSM, and can be used as an effective preconditioning filter.
• DLSM algorithms provide acceptable LSM images with 1/3 – 2/3 the cost of standard LSM.
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Continued WorksContinued Works
• 3D DLSM is tested by Wei Dai.
• An improved migration deconvolution technique is presented in my next talk.
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ThanksThanks
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