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Iterative Migration Deconvolution (IMD) with Migration Green’s Functions as Preconditioners. Naoshi Aoki Feb. 5, 2009. Outline. Introduction Theory Inexpensive IMD Numerical results 2D model IMD test 3D model IMD test When should we use IMD and LSM ? Conclusions. Outline. Introduction - PowerPoint PPT Presentation
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Iterative Migration Deconvolution (IMD) Iterative Migration Deconvolution (IMD) with Migration Green’s Functions as with Migration Green’s Functions as
PreconditionersPreconditioners
Naoshi Aoki
Feb. 5, 2009
1
OutlineOutline• Introduction
• Theory– Inexpensive IMD
• Numerical results– 2D model IMD test– 3D model IMD test
• When should we use IMD and LSM ?
• Conclusions
2
OutlineOutline• Introduction
• Theory– Inexpensive IMD
• Numerical results– 2D model IMD test– 3D model IMD test
• When should we use IMD and LSM ?
• Conclusions
3
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)
4
Tmigm = L d T= L Lm
( 1) ( ) ( ) ( ) ,k k k k Tm = m L (Lm - d)
1[ ]Tmigm = L L m
Grid Reflectivity Model
Migration Green’s Function or MGFMigration Green’s Function or MGF
• is known as the migration Green’s function.
• It is an impulse response of migration operator.
• MGF variation depends on:– acquisition geometry,– and velocity distribution.
5
Z (
km)
X (km)
TW
T (
s)
Synthetic Data
MGFs
[ ]TL L
OutlineOutline• Introduction
• Theory– Inexpensive IMD
• Numerical results– 2D model IMD test– 3D model IMD test
• When should we use IMD and LSM ?
• Conclusions
6
Inexpensive IMD TheoryInexpensive IMD Theory
( 1) ( ) ( ) ( )[ ] [ ] ,k k k T T kmig m m L L L L m -m
Expensive IMD
Inexpensive IMD with Preconditioned MGFs
( 1) ( ) ( ) ( )ˆ ˆ ˆ ,k k k T kmig m m G Gm -m
where and represent the k+1 and k th models, is a step length, and is expensive MGF.
where represents a preconditioned normal matrix that contains the preconditioned MGF in each subsection, denotes amplitude compensated migration image.
[ ]TL L( )k
( 1)km ( )km
1ˆ ( )T Tmig xx
m L L L d
1ˆ ( ) [ ]T TxxG L L L L
Expensive and Inexpensive MGFsExpensive and Inexpensive MGFs
8
[ ]TL L 1ˆ ( ) [ ]T TxxG L L L L
OutlineOutline• Introduction
• Theory– Inexpensive IMD
• Numerical results– 2D model IMD test– 3D model IMD test
• When should we use IMD and LSM ?
• Conclusions
9
Test WorkflowTest Workflow
10
Migration ImageMigration Image
Reflectivity ModelReflectivity Model
Compute MGFsCompute MGFs
Point Scatterer ModelPoint Scatterer Model
Compute IMDCompute IMD
Data Preparation Part MGF Computation Part
IMD Computation Part
Compare with LSMCompare with LSM
Data Preparation PartData Preparation Part
0 1.8
0
1.8
X (km)
Z (
km)
11
2D Stick Model
0 1.8
0
1.8
X (km)
Z (
km)
Prestack Migration
Migration ImageMigration Image
Reflectivity ModelReflectivity Model
0 1.8
0
1.8
X (km)
Z (
km)
Scatterers
0 1.8
0
1.8
X (km)
Z (
km)
MGFs
12
MGF Computation PartMGF Computation PartCompute MGFsCompute MGFs
Point Scatterer ModelPoint Scatterer Model
0 1.8
0
1.8
X (km)
Z (
km)
IMD Imageafter 43 Iterations
130 1.8
0
1.8
X (km)
Z (
km)
Prestack Migration
IMD Computation PartIMD Computation PartCompute IMDCompute IMD
0 1.8
0
1.8
X (km)
Z (
km)
0 1.8
0
1.8
X (km)
Z (
km)
IMD Imageafter 43 Iterations
LSM Imageafter 30 Iterations
14
Compute IMDCompute IMD
Compare with LSMCompare with LSM
IMD vs LSMIMD vs LSM
Model ResidualModel Residual
7
5
Res
idua
l
1 4330
Iteration number 15
IMD Noise level
Computational CostsComputational Costs
Process Computational Costs(CPU seconds)
1 Migration
54 MGFs
43 IMD Iterations
30 LSM Iterations
9
640
55
860
16
Expensive and Inexpensive MGFsExpensive and Inexpensive MGFs
17
Compute MGFs One by One Compute MGFs at Once
Clean MGFs without interference A possible problem is interference from other MGFs.
OutlineOutline• Introduction
• Theory– Inexpensive IMD
• Numerical results– 2D model IMD test– 3D model IMD test
• When should we use IMD and LSM ?
• Conclusions
18
3D Model Test3D Model Test
Model Model Description• Model size:
– 1.8 x 1.8 x 1.8 km
• U shape reflectivity anomaly
• Cross-spread geometry– Source : 16 shots, 100 m int.– Receiver : 16 receivers , 100 m int.
Depth (m) Reflectivity
250 1
500 -1
750 1
1000 -1
1250 1
19
0
20
2
0
2X (km) Y (km)
Z (
km)
● Source● Receiver
Test WorkflowTest Workflow
20
Migration ImageMigration Image
Reflectivity ModelReflectivity Model
Compute MGFsCompute MGFs
Point Scatterer ModelPoint Scatterer Model
Compute IMDCompute IMD
Data Preparation Part MGF Computation Part
IMD Computation Part
Compare with LSMCompare with LSM
Data PreparationData Preparation
0
1.80 1.8
Z (
km)
Y (
km)
X (km)
Prestack MigrationY = 1 km
0
1.80 1.8
X (km)
Prestack MigrationZ = 750 m
21
Migration ImageMigration Image
Reflectivity ModelReflectivity Model
MGF Computation PartMGF Computation Part
0
1.80 1.8
Z (
km)
Y (
km)
X (km)
MGF ImageY = 1 km
0
1.80 1.8
X (km)
MGF ImageZ = 750 m
22
Compute MGFsCompute MGFs
Point Scatterer ModelPoint Scatterer Model
IMD Computation PartIMD Computation Part
IMD Image after 30 Iterations
Y = 1000 m
Z = 750 m
Z (
km)
X (km)0 1.8
Y (
km)
0
1.80 1.8
0
1.823
PrestackMigration
Z (
km)
X (km)0 1.8
Y (
km)
0
1.80 1.8
0
1.8
Compute IMDCompute IMD
IMD vs Prestack MigrationIMD vs Prestack Migration
750 m
0
1.8 0 1.8
Y (
km)
0 1.8 0 1.8 0 1.8 0 1.8X (km)
Z = 250 m 1000 m 1250 m 1500 m
1.80 1.8
Y (
km)
0 1.8 0 1.8 0 1.8 0 1.8X (km)
0
IMD after 30 Iterations
Prestack Migration
24
IMD vs LSMIMD vs LSM
IMD image after 30 Iterations
0
1.80 1.8
Z (
km)
Y = 1000 m
X (km)0 1.8
Z = 750 m
Y (
km)
Z (
km)
X (km)0 1.8
Y (
km)
0
1.8
0
1.80 1.8
0
1.8
LSM Image after 30 Iterations
25
Compute IMDCompute IMD
Compare with LSMCompare with LSM
IMD vs LSMIMD vs LSM
750 m
0
1.8 0 1.8
Y (
km)
0 1.8 0 1.8 0 1.8 0 1.8X (km)
Z = 250 m 1000 m 1250 m 1500 m
1.8 0 1.8
Y (
km)
0 1.8 0 1.8 0 1.8 0 1.8X (km)
0
IMD Images after 30 Iterations
LSM Images after 30 Iterations
26
Model ResidualModel Residual
84
76
Res
idua
l
1 30
Iteration number 27
IMD Noise level
Computational CostsComputational Costs
Process Computational Costs(CPU seconds)
1 Migration
486 MGFs
30 IMD Iterations
30 LSM Iterations
28
190
25500
65400
15400
Why Is IMD So Slow?Why Is IMD So Slow?
• Computational cost of IMD is 6 times higher than that of LSM because:– the cross-spread geometry has a large MGF
variation,– convolution / cross-correlation is used in the
space domain.
29
OutlineOutline• Introduction
• Theory– Inexpensive IMD
• Numerical results– 2D model IMD test– 3D model IMD test
• When should we use IMD and LSM ?
• Conclusions
30
Difference Between LSM and IMDDifference Between LSM and IMD• Both methods minimize the misfit with the data.
LSM IMD
31
( 1) ( ) ( ) ( )ˆ ˆ ˆk k k T kmig m m G Gm m- ( 1) ( ) ( ) ( )k k k T k m m L Lm - d
d
( )km ( )km
ˆ migm
When Should We Use IMD and LSM ?When Should We Use IMD and LSM ?
IMDLarger amount of 5-D data
provides smaller MGF variation.
LSMSmaller amount of 5-D data
provides larger MGF variation.
32
d d
Suitable ApplicationSuitable Application
IMD LSM
Large amount of data
Coarse acquisition geometry
Complicated geology
Target oriented deblurring
33
OutlineOutline• Introduction
• Theory– Inexpensive IMD
• Numerical results– 2D model IMD test– 3D model IMD test
• When should we use IMD and LSM ?
• Conclusions
34
ConclusionsConclusions• Inexpensive IMD method with preconditioned
MGF is developed.
• 2D IMD achieves a quality almost equal to that from LSM with cheaper computational cost.
• 3D IMD test suggests that IMD quality and cost depend on required MGF density, and investigation of the required MGF density is important.
35
Continued WorkContinued Work
• An IMD test on PEMEX RTM image is presented by Qiong Wu.
36
ThanksThanks
37
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