stabilization of migration deconvolution jianxing hu university of utah
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![Page 1: Stabilization of Migration Deconvolution Jianxing Hu University of Utah](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d605503460f94a419a3/html5/thumbnails/1.jpg)
Stabilization of Migration Deconvolution
Jianxing HuUniversity of Utah
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OutlineOutline• MotivationMotivation
• MethodologyMethodology
• Numerical TestsNumerical Tests
• ConclusionsConclusions
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KMKM MDMD2420
1.5
2.3
Tim
e (s
)
X(km)24201.5
2.3
Tim
e (s
)
X(km)
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Comparison of RTM and MD ImagesComparison of RTM and MD Images 66
X(km)X(km)
55 11
22
33
D
epth
(k
m)
Dep
t h (
km
)
11 66
X(km)X(km)
55
22
33
D
epth
(k
m)
Dep
t h (
km
)
RTMRTM MDMD
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MotivationMotivationInvestigate banding noise in the MD image and improve the stability of MD system.
Banding
X(km)0 150
4
Dep
th(k
m)
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OutlineOutline• MotivationMotivation
• MethodologyMethodology
• Numerical TestsNumerical Tests
• ConclusionsConclusions
![Page 7: Stabilization of Migration Deconvolution Jianxing Hu University of Utah](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d605503460f94a419a3/html5/thumbnails/7.jpg)
Migration Noise ProblemsMigration Noise Problems• AliasingAliasing
• Recording FootprintRecording Footprint
• Limited ResolutionLimited Resolution
• Amplitude DistortionAmplitude Distortion 0 km0 km 15 km15 km
Migration noise and artifacts
Footprint Amplitude distortion
0
2
Tim
e (s
)
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Solution: Deconvolve the point Solution: Deconvolve the point scatterer response from the migrated scatterer response from the migrated imageimage
TTrr = ( = (L LL L ) m ) m
-1-1
Reflectivity MigratedReflectivity Migrated SectionSection
ReasonReason:: m = m = L dL dTT
MigratedMigratedSectionSection
DataData
butbut dd = L = L rrL rL r
Migration SectionMigration Section == Blured Blured Image ofImage of rr
= L LL LDefine T
as migration Green’sfunction
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Depth Slices of Point ScatterersDepth Slices of Point Scatterers
Kirch.Kirch. MigrationMigration ImageImage MD ImageMD Image
00 X(km)X(km) 11
Y
(km
)Y
(km
)
00
11
00 X(km)X(km) 11
Y
(km
)Y
(km
)
00
11
m = m = L LL L rrTT rr = ( = (L LL L ) m ) mTT -1 -1
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Migration DeconvolutionMigration Deconvolution
),,,,( oppoo zyxzyyxx
oooooo dzdydxzyxR ),,(Model Space
ooo rdrRrrrm
)()()( Model SpaceModel Space
),( pp yx --- --- reference position of migration Green’s functionreference position of migration Green’s function
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)(~.
)(~
)(~
),~,(~
...,),,~,(~
),,~,(~...
),~,(~
...,),,~,(~
),,~,(~
),~,(~
...,),,~,(~
),,~,(~
)(
.
)(~)(~
2
1
21
22212
12111
2
1
nnpnpnpn
nppp
nppp
n zkR
zkR
zkR
zxzkzxzkzxzk
zxzkzxzkzxzk
zxzkzxzkzxzk
zkm
zkm
zkm
MD System of Equations
where ),,(~
ipj zxzk represents the spectrum of
),,( ipj zxzx on the depth of with a scatterer
),( ip zxjz
located at
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Migration Green’s Function Coefficient Matrix Structure
Diagonal element
Off-diagonal element
Coefficient matrix regularization
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Artifacts in MDArtifacts in MD
Poststack Poststack
MD ImageMD Image
00
44
X (km)X (km) 1515
D
e pth
(km
)D
epth
(km
)
00
Banding Noise
Coefficient Matrix Condition Number v.s. Wavenumber
-0.02 0.02-0.01 0.010
Wavenumber (radian/m)
350
150
250
50
0
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Stabilization of MD Stabilization of MD System EquationsSystem Equations
Monitor the condition number of MD Monitor the condition number of MD
system equation for each wavenumbersystem equation for each wavenumber
mRI ~~)
~(
If wavenumber <preset tolerance
mR ~~~ Otherwise
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OutlineOutline• MotivationMotivation
• MethodologyMethodology
• Numerical TestsNumerical Tests
• ConclusionsConclusions
![Page 16: Stabilization of Migration Deconvolution Jianxing Hu University of Utah](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d605503460f94a419a3/html5/thumbnails/16.jpg)
Numerical TestsNumerical Tests• 2-D SEG/EAGE overthrust model 2-D SEG/EAGE overthrust model
poststack MDpoststack MD
• 3-D SEG/EAGE salt model 3-D SEG/EAGE salt model poststack MDpoststack MD
• 2-D SEG/EAGE overthrust model 2-D SEG/EAGE overthrust model prestack MDprestack MD
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Regularization of MD System EquationsRegularization of MD System Equations
Poststack Poststack MD ImageMD Image without without regularizationregularization
00
44
X (km)X (km) 1515
D
e pth
(km
)D
epth
(km
)
00
00
44
X (km)X (km) 1515
D
e pth
(km
)D
epth
(km
)
00
Poststack Poststack MD ImageMD Image with with regularizationregularization
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Numerical TestsNumerical Tests• 2-D SEG/EAGE Overthrust Model 2-D SEG/EAGE Overthrust Model
Poststack MDPoststack MD
• 3-D SEG/EAGE Salt Model 3-D SEG/EAGE Salt Model Poststack MDPoststack MD
• 2-D SEG/EAGE Overthrust Model 2-D SEG/EAGE Overthrust Model Prestack MDPrestack MD
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Kirchhoff Migration ImagesKirchhoff Migration Images
04 6 8
X (km)
Dep
t h (
km
)
4
3
2
1
Inline Section
Y (km)
04 6 8
Dep
th (
km
)
4
3
2
1
Crossline Section
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MD Images no RegularizationMD Images no Regularization
04 6 8
X (km)
Dep
t h (
km
)
4
3
2
1
Inline Section
Y (km)
04 6 8
Dep
th (
km
)
4
3
2
1
Crossline Section
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MD Images with RegularizationMD Images with Regularization
04 6 8
X (km)
Dep
t h (
km
)
4
3
2
1
Inline Section
Y (km)
04 6 8
Dep
th (
km
)
4
3
2
1
Crossline Section
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Comparison of Migration and MD ImageComparison of Migration and MD Image
04 6 8
X (km)
Dep
t h (
km
)
4
3
2
1
Migration Inline Section
X (km)
04 6 8
Dep
th (
km
)
4
3
2
1
MD inline Section
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Comparison of Migration and MD ImageComparison of Migration and MD Image
04 6 8
Y (km)
Dep
t h (
km
)
4
3
2
1
Migration Crossline Section
Y (km)
04 6 8
Dep
th (
km
)
4
3
2
1
MD Crossline Section
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KM Inline (97,Y) SectionKM Inline (97,Y) Section MD Inline (97,Y) SectionMD Inline (97,Y) Section
55 88Y (km)Y (km) 55 88Y (km)Y (km)00
44
22
00
44
22
Dep
th (
km
)D
epth
(k
m)
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KM Crossline (X,97) SectionKM Crossline (X,97) Section MD Crossline (X,97) SectionMD Crossline (X,97) Section
00
44
22
Dep
th (
km
)D
epth
(k
m)118
X (km)118
X (km)
00
44
22
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Numerical TestsNumerical Tests• 2-D SEG/EAGE Overthrust Model 2-D SEG/EAGE Overthrust Model
Poststack MDPoststack MD
• 3-D SEG/EAGE Salt Model 3-D SEG/EAGE Salt Model Poststack MDPoststack MD
• 2-D SEG/EAGE Overthrust Model 2-D SEG/EAGE Overthrust Model Prestack MD in COGPrestack MD in COG
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Regularization of MD System EquationsRegularization of MD System Equations
Prestack Prestack COGCOG Migration Migration ImageImage 0-450 m0-450 m withoutwithout regularizationregularization
00
44
X (km)X (km) 2020
D
e pth
(km
)D
epth
(km
)
00
00
44
X (km)X (km) 2020
D
e pth
(km
)D
epth
(km
)
00
Prestack Prestack COGCOG Migration Migration ImageImage 0-450 m0-450 m withwith regularizationregularization
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ConclusionsConclusions
Worse condition number causes the Worse condition number causes the banding noise in MD resultsbanding noise in MD results
Condition number is related to the waveletfrequency, position of migration Green’sfunction and velocity medium
Regularization of the MD system equations enhances the stability of MD system
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AcknowledgementAcknowledgement• Thanks to 2000 UTAM sponsors for their financial supportThanks to 2000 UTAM sponsors for their financial support• Thanks to Advanced Data Solutions for providing the SEG Thanks to Advanced Data Solutions for providing the SEG
salt model migration resultsalt model migration result
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MotivationMotivationInvestigate Banding Noise in the MD image and improve the stability of MD system.