1 interferometric interpolation and extrapolation of sparse obs and ssp data shuqian dong and...
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1
Interferometric Interpolation and Extrapolation of Sparse
OBS and SSP Data
Shuqian Dong and G.T.Schuster
2
OutlineOutline
• MotivationMotivation
• TheoryTheory
• ConclusionsConclusions
• Numerical TestsNumerical Tests
OBS interpolationOBS interpolation OBS extrapolationOBS extrapolation SSP extrapolationSSP extrapolation
3
OutlineOutline
• MotivationMotivation
• TheoryTheory
• ConclusionsConclusions
• Numerical TestsNumerical Tests
OBS interpolationOBS interpolation OBS extrapolationOBS extrapolation SSP extrapolationSSP extrapolation
4
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
5
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
6
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
7
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
8
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
9
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
10
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
11
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
12
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
13
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
14
SIGSBEE 2B velocity model
X (km)X (km)
Z (
km)
Z (
km)
00
8.58.5
00 2525
Sparse OBS InterpolationSparse OBS Interpolation
15
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
16
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
17
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
18
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
19
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
20
Z (
km)
Z (
km)
00
4.54.5X (km)X (km)00 6.06.0
Velocity model Velocity model
21
OutlineOutline
• MotivationMotivation
• TheoryTheory
• ConclusionsConclusions
• Numerical TestsNumerical Tests
OBS interpolationOBS interpolation OBS extrapolationOBS extrapolation SSP extrapolationSSP extrapolation
22
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
23
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
24
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
25
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
26
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
27
Velocity model Velocity model Z
(km
)Z
(km
)
00
4.54.5X (km)X (km)00 6.06.0
OBS ExtrapolationOBS Extrapolation
28
OutlineOutline
• MotivationMotivation
• TheoryTheory
• ConclusionsConclusions
• Numerical TestsNumerical Tests
OBS interpolationOBS interpolation OBS extrapolationOBS extrapolation SSP extrapolationSSP extrapolation
29
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
30
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
31
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
32
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
33
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
34
Velocity modelVelocity model
Z (
km)
Z (
km)
00
4.54.5X (km)X (km)00 6.06.0
SSP ExtrapolationSSP Extrapolation
35
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
36
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
37
ThanksThanks