Interferometric Interpolation of 3D OBS Data
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Interferometric Interferometric Interpolation of 3D OBS Interpolation of 3D OBS
DataData
Weiping Cao, University of UtahWeiping Cao, University of Utah
Oct. 29 2009Oct. 29 2009
Outline
• Problems: Missing and sparse traces
• Methodology: Interferometric interpolation
• Numerical results: – 3D layered model– Anti-aliasing condition for
interferometric redatuming• Conclusions
• Problems: Missing and sparse traces
• Methodology : Interferometric interpolation
• Numerical results: – 3D layered model– Anti-aliasing condition for
interferometric redatuming• Conclusions
Outline
Motivations
Problem: Receiver interval of OBS data is (sometimes) too large
Solution: Interferometric interpolation
Water
Water
Benefits of Interferometric Benefits of Interferometric Interpolation: Interpolation:
• Accuracy (wave-equation based Accuracy (wave-equation based scheme)scheme)
• No sedimentary velocity neededNo sedimentary velocity needed
Outline
• Problems: Missing and sparse traces
• Methodology: Interferometric interpolation
• Numerical results: – 3D layered velocity model– Anti-aliasing condition for
interferometric redatuming• Conclusions
Interferometric Interpolation of OBS Data
G(B|A)Interpolated OBS
Data
Seabed
Reflectors
Ocean Surface
xB
A
G(x|A)Natural OBS
Green’s Function
Seabed
Reflectors
Ocean Surface
x
A
Go(x|B)*
Model based Green’s Function
B
Seabed
Ocean Surface
x
A
Dong S. and G. T. Schuster, 2008, Interferometric interpolation and extrapolation of sparse OBS and SSP data: UTAM 2007 annual meeting, 39 – 48.
Interferometric Interpolation of OBS Data
xx
x|Bx|A
x
x|Ax|BA|BA|B 2
*0*
0*
0
0
)()(
)()()()( d
GG
GGGG
S
2-state reciprocity equation:
xx|Ax|BA|BA|B 2**
0
00)()(2)()( dGGikGG
S
goingupgoingdown
Up-down separation, far-field approximationWater-layer
reflectionOBS reflection
Artifacts? (up-down separation, far-field approx., limited aperture, wavelet, sampling… Matching filter!
WorkflowInput Field Data
Water Layer Model
Generate GF for Water Multiples
Interpolate Missing Data
Max. Itr (MF)
Get Virtual CSG
Max Itr Intr/Extr Final CSGN
Matching Filter
N
YY
Tim
e (s
)T
ime
(s)
00
3.03.0X (km)X (km)00 4.54.5 Seabed
Ocean Surface
x
Tim
e (s
)T
ime
(s)
00
3.03.0X (km)X (km)00 4.54.5
Tim
e (s
)T
ime
(s)
00
3.03.0X (km)X (km)00 4.54.5
Input Data
Unfiltered Virtual
Filtered Virtual
Outline
• Problems: Missing and sparse traces
• Methodology: Interferometric interpolation
• Numerical results: – 3D layered velocity model– Anti-aliasing condition for
interferometric redatuming• Conclusions
Numerical Results
• 3D velocity model size: 3000 x 3000 x 1400 m3
• Source located at (10 m,10 m, 30
m)• 300 by 300 receivers dx = dy = 10 m• Sea bed is flat at a
depth of 750 m
3 km3
km
1.4 km
Source
Layered Velocity Model
Velocity (m/s)1500 2400
Sea bed
Reflector 1
Reflector 2
Synthetic DataLine y=1000m
0
5
Tim
e (s
)
0 3000X (m)
CSG in the x direction: y=1000 m, dx = 10 m
0
5
Tim
e (s
)
0 3000Y (m)
CSG in the y direction: x=1000 m, dx = 10 m
3D Interpolation
Goal: dense OBS data
• Recording interval:
10 m × 10 m
• Total number of receivers:
300 × 300 = 90, 000
Input: sparse OBS data
• Recording interval
50 m × 50 m ( =104 m )
• Total number of receivers:
60 × 60 = 3, 600
Sparse Data
0
5
Tim
e (s
)
0 3000X (m)
Line y=1000m
Decimated CSG in the X direction: Decimated CSG in the X direction: Y = 1000 m , dx = 50 m Y = 1000 m , dx = 50 m
0
5
Tim
e (s
)
0 3000Y (m)
Decimated CSG in the Y direction: Decimated CSG in the Y direction: X = 1000 m, dx = 50 m X = 1000 m, dx = 50 m
Interpolation Results: X direction
0
5
Tim
e (s
)
0 3000X (m)
Line y=1000m
Decimated CSG in the X direction: Decimated CSG in the X direction: Y =1000 m , dx = 50 mY =1000 m , dx = 50 m
0
5
Tim
e (s
)
0 3000Y (m)
Virtual dense data, dx = 10 mVirtual dense data, dx = 10 m
Tim
e (s
)T
ime
(s)
00
3.03.0X (km)X (km)00 4.54.5
Tim
e (s
)T
ime
(s)
00
3.03.0X (km)X (km)00 4.54.5
Local Matching Filter
000 ,*,, xtfxtdxtd virtualreal
0
5
Tim
e (s
)
0 3000X (m)
0
5
Tim
e (s
)
0 3000X (m)
Line y=1000m
Filtered virtual data, dx = 10 mDecimated CSG in the X direction: Y =1000 m , dx = 50 m
Interpolation Results: X direction
0
5
Tim
e (s
)
0 3000X (m)
0
5
Tim
e (s
)
0 3000X (m)
Line y=1000m
Real dense data, dx = 10 mReal dense data, dx = 10 mDecimated CSG in the X direction: Decimated CSG in the X direction: Y =1000 m , dx = 50 mY =1000 m , dx = 50 m
Interpolation Results: X direction
0
5
Tim
e (s
)
0 3000Y (m)
Line y=1000m
0
5
Tim
e (s
)
0 3000Y (m)
Virtual dense data, dx = 10 mVirtual dense data, dx = 10 mDecimated CSG in the Y direction: Decimated CSG in the Y direction: X =1000 m , dx = 50 mX =1000 m , dx = 50 m
Interpolation Results: Y direction
0
5
Tim
e (s
)
0 3000Y (m)
0
5
Tim
e (s
)
0 3000Y (m)
Line y=1000m
Virtual data after filtering, dx = 10 mVirtual data after filtering, dx = 10 mDecimated CSG in the Y direction: Decimated CSG in the Y direction: X =1000 m , dx = 50 mX =1000 m , dx = 50 m
Decimated CSG in the Y direction: Decimated CSG in the Y direction: X =1000 m , dx = 50 mX =1000 m , dx = 50 m
Interpolation Results: Y direction
0
5
Tim
e (s
)
0 3000Y (m)
0
5
Tim
e (s
)
0 3000Y (m)
Line y=1000m
Real dense data, dx = 10 mReal dense data, dx = 10 mDecimated CSG in the Y direction: Decimated CSG in the Y direction: X =1000 m , dx = 50 mX =1000 m , dx = 50 m
Interpolation Results: Y direction
1.0
3.5
Tim
e (s
)
10 2710X offset (m)
True vs. Virtual traces before Filtering
True
Virtual
Interpolation Results: Trace Comparison
1.0
3.5
Tim
e (s
)
True vs. the Virtual Traces after Filtering
True
Virtual
10 2710X offset (m)
Interpolation Results: Trace Comparison
1.0
3.5
Tim
e (s
)
True vs. the Virtual Traces after Filtering
10 2710X offset
Interpolation Results: Trace Comparison
Different Recording Spacings
0.5
1.2
Nor
mal
ized
err
or
0.20.05
Interpolation error vs. recording spacingInterpolation error vs. recording spacing
Recording spacing of input data (Recording spacing of input data (λλxxminmin))
The normalized error The normalized error ==
2
2
2
2
real
interp.real
d
dd
Outline
• Problems: Missing and sparse traces
• Methodology: Interferometric interpolation
• Numerical results: – 3D layered velocity model– Anti-aliasing condition for
interferometric redatuming• Conclusions
Interferometric redatuming equation:
Anti-aliasing Condition for Interferometric Redatuming
Phase difference between and
less than
G(A|x) G(B|x)
Axx
x
Bxx
x
Anti-aliasing condition
0
3
Tim
e (s
)
0.6 4X (km)
Remove Interf. Artifacts with the Anti-aliasing Condition
Anti-aliased Interf. ResultRegular Interf. Result
Recording interval 0.49 λ
0
3
Tim
e (s
)
0.6 4X (km)
0
3
Tim
e (s
)
0.6 4X (km)
Remove Interf. Artifacts with the Anti-aliasing ConditionAnti-aliased Interf. Result with Up-down Separation
Regular Interf. Result with Up-down Separation
Recording interval 0.97 λ
0
3
Tim
e (s
)
0.6 4X (km)
Outline
• Problems: Missing and sparse traces
• Methodology: Interferometric interpolation
• Numerical results: – 3D layered velocity model– Anti-aliasing condition for
interferometric redatuming• Conclusions
Conclusions
Encouraging results obtained for Encouraging results obtained for interpolating sparse OBS data interpolating sparse OBS data (recording spacing: )(recording spacing: )
Degraded interpolation results when the Degraded interpolation results when the recording spacing of the input sparse recording spacing of the input sparse data increasesdata increasesRemaining artifacts: Remaining artifacts:
up-down separation, anti-aliasing up-down separation, anti-aliasing conditioncondition
Acknowledgments
Thank UTAM 2008 sponsors for the support of the research.
Thank you all for your attention.