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![Page 1: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/1.jpg)
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Interferometric Interpolation and Extrapolation of Sparse
OBS and SSP Data
Shuqian Dong and G.T.Schuster
![Page 2: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/2.jpg)
2
OutlineOutline
• MotivationMotivation
• TheoryTheory
• ConclusionsConclusions
• Numerical TestsNumerical Tests
OBS interpolationOBS interpolation OBS extrapolationOBS extrapolation SSP extrapolationSSP extrapolation
![Page 3: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/3.jpg)
3
OutlineOutline
• MotivationMotivation
• TheoryTheory
• ConclusionsConclusions
• Numerical TestsNumerical Tests
OBS interpolationOBS interpolation OBS extrapolationOBS extrapolation SSP extrapolationSSP extrapolation
![Page 4: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/4.jpg)
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MotivationMotivation
Answer:Answer:
Interfer. predict. + matching filter Interfer. predict. + matching filter
Questions: Questions:
We have: We have:
Sparse OBS Sparse OBS
Sparse OBS Sparse OBS
?
Narrow aperture OBSNarrow aperture OBS ?Wide aperture OBSWide aperture OBS
Narrow aperture SSPNarrow aperture SSP ?Wide aperture SSPWide aperture SSP
SSP: Interferometric transform SSP: Interferometric transform
VSPVSP
Narrow apertureNarrow aperture wide aperturewide aperture
![Page 5: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/5.jpg)
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SeabedSeabed
ReflectorsReflectors
SeabedSeabed
ReflectorsReflectors
SeabedSeabed
ReflectorsReflectors
OBS SWP OBS
B
A
x B
A
x B
A
x
TheoryTheory• Sparse OBS interferometric interpolation Sparse OBS interferometric interpolation
NaturalGreen’s Function
Model basedGreen’s Function
Interpolated data
![Page 6: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/6.jpg)
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Z (
km)
Z (
km)
00
3.03.0X (km)X (km)00 4.54.5
Density model3.03.0
1.01.0Z
(km
)Z
(km
)
00
3.03.0X (km)X (km)00 4.54.5
Velocity model km/s3.63.6
1.51.5
kg/m33
Sparse OBS InterpolationSparse OBS Interpolation
![Page 7: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/7.jpg)
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Z (
km)
Z (
km)
00
3.03.0X (km)X (km)00 4.54.5
Density model3.03.0
1.01.0Z
(km
)Z
(km
)
00
3.03.0X (km)X (km)00 4.54.5
Velocity model km/s3.63.6
1.51.5
kg/m33
Sparse OBS InterpolationSparse OBS Interpolation
300 shots300 shotsdx = 16 m dx = 16 m
600 receivers600 receiversdx = 8 m dx = 8 m
![Page 8: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/8.jpg)
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X (km)X (km)00 4.54.5
Tim
e (s
)T
ime
(s)
00
3.03.0
Original CSG
Sparse OBS InterpolationSparse OBS Interpolation
Tim
e (s
)T
ime
(s)
00
3.03.0X (km)X (km)00 4.54.5
Virtual CSG
dx = 80 mdx = 80 mTotal traces: 60Total traces: 60
dx = 8 mdx = 8 m
![Page 9: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/9.jpg)
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X (km)X (km)00 4.54.5
Tim
e (s
)T
ime
(s)
00
3.03.0
Original CSG
Sparse OBS InterpolationSparse OBS Interpolation
Tim
e (s
)T
ime
(s)
00
3.03.0X (km)X (km)00 4.54.5
Virtual CSG
dx = 80 mdx = 80 mTotal traces: 60Total traces: 60
dx = 8 mdx = 8 m
** ff (t,x )(t,x )dd (t,x )(t,x )realreal
dd (t,x )(t,x )virtualvirtual00 00 00
xx00xx00
** ff (t,x )(t,x )dd (t,x’ )(t,x’ )realreal
dd (t,x’)(t,x’)virtualvirtual 00
![Page 10: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/10.jpg)
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Sparse OBS InterpolationSparse OBS Interpolation T
ime
(s)
Tim
e (s
)
00
3.03.0X (km)X (km)00 4.54.5
Virtual CSG
Tim
e (s
)T
ime
(s)
00
3.03.0X (km)X (km)00 4.54.5
Real CSG
Tim
e (s
)T
ime
(s)
00
3.03.0X (km)X (km)00 4.54.5
Filtered virtual CSG
![Page 11: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/11.jpg)
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X (km)X (km)00 4.54.5
Tim
e (s
)T
ime
(s)
00
3.03.0
Original CSG
X (km)X (km)00 4.54.5
Tim
e (s
)T
ime
(s)
00
3.03.0
Virtual CSG
X (km)X (km)00 4.54.5
Tim
e (s
)T
ime
(s)
00
3.03.0
Real CSG
X (km)X (km)00 4.54.5
Tim
e (s
)T
ime
(s)
00
3.03.0
Filtered virtual CSG
dx = 160 mdx = 160 mTotal traces: 30Total traces: 30
dx = 8 mdx = 8 mTotal traces: 600Total traces: 600
dx = 8 mdx = 8 mTotal traces: 600Total traces: 600
dx = 8 mdx = 8 mTotal traces: 600Total traces: 600
Sparse OBS InterpolationSparse OBS Interpolation
![Page 12: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/12.jpg)
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X (km)X (km)00 4.54.5
Tim
e (s
)T
ime
(s)
00
3.03.0
Original CSG
X (km)X (km)00 4.54.5
Tim
e (s
)T
ime
(s)
00
3.03.0
Virtual CSG
X (km)X (km)00 4.54.5
Tim
e (s
)T
ime
(s)
00
3.03.0
Real CSG
X (km)X (km)00 4.54.5
Tim
e (s
)T
ime
(s)
00
3.03.0
Filtered virtual CSG
dx = 320 mdx = 320 mTotal traces: 30Total traces: 30
dx = 8 mdx = 8 mTotal traces: 600Total traces: 600
dx = 8 mdx = 8 mTotal traces: 600Total traces: 600
dx = 8 mdx = 8 mTotal traces: 600Total traces: 600
Sparse OBS InterpolationSparse OBS Interpolation
![Page 13: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/13.jpg)
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Migration of interpolated OBS data Migration of interpolated OBS data
Z (
km)
Z (
km)
00
3.03.0
Migration of sparse OBS data
X (km)X (km)00 4.54.5
Z (
km)
Z (
km)
00
3.03.0X (km)X (km)00 4.54.5
300 shots300 shotsdx = 16 m dx = 16 m 6 receivers6 receivers
dx = 800 m dx = 800 m
Sparse OBS InterpolationSparse OBS Interpolation
![Page 14: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/14.jpg)
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SIGSBEE 2B velocity model
X (km)X (km)
Z (
km)
Z (
km)
00
8.58.5
00 2525
Sparse OBS InterpolationSparse OBS Interpolation
![Page 15: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/15.jpg)
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Velocity modelZ
(km
)Z
(km
)
00
4.54.5X (km)X (km)00 6.06.0
200 shots200 shotsdx = 30 m dx = 30 m
800 receivers800 receiversdx = 7.62 m dx = 7.62 m
Sparse OBS InterpolationSparse OBS Interpolation
![Page 16: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/16.jpg)
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X (km)X (km)00 6.06.0
Tim
e (s
)T
ime
(s)
00
3.03.0
Original CSG
X (km)X (km)00 6.06.0
Tim
e (s
)T
ime
(s)
00
3.03.0
Virtual CSG
X (km)X (km)00 6.06.0
Tim
e (s
)T
ime
(s)
00
3.03.0
Real CSG
X (km)X (km)00 6.06.0
Tim
e (s
)T
ime
(s)
00
3.03.0
Filtered virtual CSG
dx = 76.2 mdx = 76.2 mtraces: 80traces: 80
dx = 7.62 mdx = 7.62 mtraces: 800traces: 800
dx = 7.62 mdx = 7.62 mtraces: 800traces: 800
dx = 7.62 mdx = 7.62 mtraces: 800traces: 800
Sparse OBS InterpolationSparse OBS Interpolation
![Page 17: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/17.jpg)
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X (km)X (km)00 6.06.0
Tim
e (s
)T
ime
(s)
00
3.03.0
Original CSG
X (km)X (km)00 6.06.0
Tim
e (s
)T
ime
(s)
00
3.03.0
Virtual CSG
X (km)X (km)00 6.06.0
Tim
e (s
)T
ime
(s)
00
3.03.0
Real CSG
X (km)X (km)00 6.06.0
Tim
e (s
)T
ime
(s)
00
3.03.0
Filtered virtual CSG
dx = 300 mdx = 300 mtraces: 20traces: 20
dx = 7.62 mdx = 7.62 mtraces: 800traces: 800
dx = 7.62 mdx = 7.62 mtraces: 800traces: 800
dx = 7.62 mdx = 7.62 mtraces: 800traces: 800
Sparse OBS InterpolationSparse OBS Interpolation
![Page 18: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/18.jpg)
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Z (
km)
Z (
km)
00
4.54.5X (km)X (km)00 6.06.0
Migration of sparse OBS data
20 receivers20 receiversdx =300 m dx =300 m
200 shots200 shotsdx = 30 m dx = 30 m
Sparse OBS InterpolationSparse OBS Interpolation
![Page 19: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/19.jpg)
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Migration of interpolated OBS data Migration of interpolated OBS data
Z (
km)
Z (
km)
00
4.54.5X (km)X (km)00 6.06.0
![Page 20: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/20.jpg)
20
Z (
km)
Z (
km)
00
4.54.5X (km)X (km)00 6.06.0
Velocity model Velocity model
![Page 21: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/21.jpg)
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OutlineOutline
• MotivationMotivation
• TheoryTheory
• ConclusionsConclusions
• Numerical TestsNumerical Tests
OBS interpolationOBS interpolation OBS extrapolationOBS extrapolation SSP extrapolationSSP extrapolation
![Page 22: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/22.jpg)
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SeabedSeabed
ReflectorsReflectors
SeabedSeabed
ReflectorsReflectors
SeabedSeabed
ReflectorsReflectors
OBS SWP OBS
B
A
x B
A
x B
A
x
NaturalGreen’s Function
Model basedGreen’s Function
Etrapolated data
OBS ExtrapolationOBS Extrapolation
![Page 23: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/23.jpg)
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SIGSBEE 2B velocity model
X (km)X (km)
Z (
km)
Z (
km)
00
4.54.5
00 6.06.0
OBS ExtrapolationOBS Extrapolation
200 shots200 shotsdx = 30 m dx = 30 m
400 receivers400 receiversapertue: 3 kmapertue: 3 kmdx = 7.62 m dx = 7.62 m
![Page 24: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/24.jpg)
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OBS ExtrapolationOBS Extrapolation T
ime
(s)
Tim
e (s
)
0.80.8
4.04.0X (km)X (km)00 6.06.0
Original CSG
Tim
e (s
)T
ime
(s)
0.80.8
4.04.0X (km)X (km)00 6.06.0
Extrapolated CSG
Tim
e (s
)T
ime
(s)
0.80.8
4.04.0X (km)X (km)00 6.06.0
Real CSG
![Page 25: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/25.jpg)
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Migration of narrow aperture OBS data Migration of narrow aperture OBS data Z
(km
)Z
(km
)
00
4.54.5X (km)X (km)00 6.06.0
OBS ExtrapolationOBS Extrapolation
200 shots200 shotsdx = 30 m dx = 30 m
400 receivers400 receiversapertue: 3 kmapertue: 3 kmdx = 7.62 m dx = 7.62 m
![Page 26: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/26.jpg)
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Migration of extrapolated OBS data Migration of extrapolated OBS data Z
(km
)Z
(km
)
00
4.54.5X (km)X (km)00 6.06.0
OBS ExtrapolationOBS Extrapolation
![Page 27: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/27.jpg)
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Velocity model Velocity model Z
(km
)Z
(km
)
00
4.54.5X (km)X (km)00 6.06.0
OBS ExtrapolationOBS Extrapolation
![Page 28: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/28.jpg)
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OutlineOutline
• MotivationMotivation
• TheoryTheory
• ConclusionsConclusions
• Numerical TestsNumerical Tests
OBS interpolationOBS interpolation OBS extrapolationOBS extrapolation SSP extrapolationSSP extrapolation
![Page 29: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/29.jpg)
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SeabedSeabed
ReflectorsReflectors
SSP
BA
xSeabedSeabed
ReflectorsReflectors
SSP
BA
xSeabedSeabed
ReflectorsReflectors
SSP
BA
x
NaturalGreen’s Function
Model based
Green’s Function
Etrapolated data
Natural or
SSP ExtrapolationSSP Extrapolation
![Page 30: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/30.jpg)
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SIGSBEE 2B velocity modelZ
(km
)Z
(km
)00
4.54.5X (km)X (km)00 6.06.0
SSP ExtrapolationSSP Extrapolation
200 shots200 shotsdx = 30 m dx = 30 m
300 receivers300 receiversapertue: 2.4 kmapertue: 2.4 kmdx = 7.62 m dx = 7.62 m
![Page 31: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/31.jpg)
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Tim
e (s
)T
ime
(s)
0.80.8
4.04.0X (km)X (km)00 6.06.0
Original CSG
Tim
e (s
)T
ime
(s)
0.80.8
4.04.0X (km)X (km)00 6.06.0
Extrapolated CSG
Tim
e (s
)T
ime
(s)
0.80.8
4.04.0X (km)X (km)00 6.06.0
Real CSG
SSP ExtrapolationSSP Extrapolation
![Page 32: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/32.jpg)
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Migration of extrapolated SSP data Migration of extrapolated SSP data
Z (
km)
Z (
km)
00
4.54.5X (km)X (km)00 6.06.0
SSP ExtrapolationSSP Extrapolation
200 shots200 shotsdx = 30 m dx = 30 m
300 receivers300 receiversapertue: 2.4 kmapertue: 2.4 kmdx = 7.62 m dx = 7.62 m
![Page 33: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/33.jpg)
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Migration of extrapolated SSP data Migration of extrapolated SSP data
Z (
km)
Z (
km)
00
4.54.5X (km)X (km)00 6.06.0
SSP ExtrapolationSSP Extrapolation
![Page 34: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/34.jpg)
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Velocity modelVelocity model
Z (
km)
Z (
km)
00
4.54.5X (km)X (km)00 6.06.0
SSP ExtrapolationSSP Extrapolation
![Page 35: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/35.jpg)
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Future Work
Field data test.
3D test
Conclusion
Helpful for OBS and SSP survey design
Sparse OBS Sparse OBS
Sparse OBS Sparse OBS
Narrow aperture Narrow aperture Wide apertureWide aperture
![Page 36: 1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d585503460f94a37455/html5/thumbnails/36.jpg)
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We thank Utah Tomography and We thank Utah Tomography and Modeling/Migration ConsortiumModeling/Migration Consortium
sponsors for their financial supportsponsors for their financial support
AcknowledgementsAcknowledgements
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ThanksThanks