Transcript Slide 1

LEAST SQUARES DATUMING
AND SURFACE
WAVES PREDICTION WITH
INTERFEROMETRY
Yanwei Xue
Department of Geology & Geophysics
University of Utah
1
OUTLINE
• VSP to SWP
• VSP surface related multiple to
SSP
• Surface waves prediction and
subtraction
• Summary
2
OUTLINE
• VSP to SWP
• Motivation
• Theory
• Numerical Results
• Conclusion
3
Why least squares datuming?
Ideal case for datumimg
Single ray-path
4
Why least squares datuming?
Real case for datumimg
Multi ray-path
5
OUTLINE
• VSP to SWP
• Motivation
• Theory
• Numerical Results
• Conclusion
6
Two state model
State 1
State 2
S0
B
x
S1
x
S1
S
7
8
S
8
A
State 1
State 2
S0
B
x
x
S1
8
8
A
S1
S
G( B | x) (2  k 2 )G0 ( A | x)   ( x  A)
(2  k 2 )G( B | x)   ( x  B) G0 ( A | x)
G( B | x)2G0 ( A | x)  G0 ( A | x)2G(B | x)   ( x  B)G0 ( A | x)   ( x  A)G(B | x)
G ( A | B)    G ( B | x )
S1
G0 ( A | x)
G( B | x)
 G0 ( A | x)
dx
nx
nx
8
State 1
State 2
S0
B
x
S1
S1
8
8
A
x
S
G0 ( A | x)  G0 ( A | x)
G( B | x)  G  ( B | x)  G  ( B | x)
G0 ( A | x)
 ikG0 ( A | x)
nx
G( B | x)
 ikG ( B | x)  ikG ( B | x)
nx
G( A | B)  2ik  G  ( B | x)G0 ( A | x)dx
S1
P  ( A | B)  2ik  G  ( B | x) P0 ( A | x)dx
S1
9
OUTLINE
• VSP to SWP
• Motivation
• Theory
• Numerical Results
• Conclusion
10
Velocity Model
Sources at surface: [-1500:15:1500]
Receiver at datum: [0]
v=1500 m/s, d=500 m
v=2000 m/s, d=800 m
v=2500 m/s,
d=1200 m
v=3000 m/s
11
Interferometric datuming with
direct waves
S.I
L.S.I
2.0
-2.0
Offset (Km)
2.0
2.0
-2.0
Time (s)
0
Time (s)
0
Time (s)
0
Ideal
Offset (Km)
2.0
2.0
-2.0
12
Offset (Km)
2.0
Interferometric datuming with
down-going waves
S.I
L.S.I
2.0
-2.0
Time (s)
0
Offset (Km)
2.0
2.0
-2.0
Time (s)
0
Time (s)
0
Ideal
Offset (Km)
2.0
2.0
-2.0
13
Offset (Km)
2.0
Limited acquisition
aperture problem
14
L.S. Interferometric datuming
with direct waves
Time (s)
0
5.2
15
-4.0
Offset (Km)
4.0
L.S. Interferometric datuming
with down-going waves
Time (s)
0
5.2
16
-4.0
Offset (Km)
4.0
Difference between full&partial
G’s function
Time (s)
0
5.2
17
-4.0
Offset (Km)
4.0
OUTLINE
• VSP to SWP
• Motivation
• Theory
• Numerical Results
• Conclusion
18
Conclusion
• Least squares interferometric datuming
with up-down going wavefields
separation can provides datumed
results without reflection from the
structures above the datum line.
• Factors affect results:
– Quality of up-down going separation;
– Quality of acquisition geometry.
19
OUTLINE
• VSP to SWP
• VSP surface related multiple to
SSP
• Surface waves prediction and
subtraction
• Summary
20
OUTLINE
• VSP to SSP
• Motivation
• Theory
• Numerical Results
• Synthetic data test
• Field data test
• Conclusion
21
3D VSP Survey
Z
22
OUTLINE
• VSP to SSP
• Motivation
• Theory
• Numerical Results
• Synthetic data test
• Field data test
• Conclusion
23
Two state model
State 1
State 2
S0
A
x
x
S1
S1
S
24
8
S
8
B
State 1
A
State 2
x
S0
x
S1
S1
G( B | x) (2  k 2 )G0 ( A | x)   ( x  A)
S
(2  k 2 )G( B | x)   ( x  B) G0 ( A | x)
G( B | x)2G0 ( A | x)  G0 ( A | x)2G(B | x)   ( x  B)G0 ( A | x)   ( x  A)G(B | x)
G ( A | B)   G ( B | x)
S1
8
S
8
B
G0 ( A | x)
G( B | x)
 G0 ( A | x)
dx
nx
nx
25
State 1
A
State 2
x
S0
x
S1
S1
S
G0 ( A | x)  G0 ( A | x)
G( B | x)  G  ( B | x)  G  ( B | x)
G0 ( A | x)
 ikG0 ( A | x)
nx
G( B | x)
 ikG ( B | x)  ikG ( B | x)
nx
G( A | B)  2ik  G  ( B | x)G0 ( A | x)dx
S1
P  ( A | B)  2ik  G  ( B | x) P0 ( A | x)dx
S1
26
8
S
8
B
Downgoing Multiples
d1
x1 
xs
d1  2h
d2
x2 
xs
d 2  2h
R2
d2
s
x1
x2
x1
R1
x2
R1
d1
h
R2
s
27
Upgoing Multiples
R2
R1
s
x1
x2
x1
x2
R1
R2
s
28
Comments
Increase order of multiples, illumination
area goes away from the well
The deeper the reflectors, the narrower
the illumination area. The illumination
area goes closer to the well.
29
OUTLINE
• VSP to SSP
• Motivation
• Theory
• Numerical Results
• Synthetic data test
•Virtual source close to well.
•Virtual source far from well.
• Field data test
• Conclusion
30
3-layer Velocity Model
0
4000
0
4000
31
SI SSP
Real SSP
0
0
Artifacts
Primaries
Time (s)
Time (s)
Primaries
10
10
0
Offset (Km)
350
0
32
Offset (Km)
350
LSI SSP of Downgoing
Real SSP
0
0
Primaries
Time (s)
Time (s)
Primaries
10
10
0
Offset (Km)
350
0
33
Offset (Km)
350
LSI SSP of Upgoing
Real SSP
0
0
Primaries
Time (s)
Time (s)
Primaries
10
10
0
Offset (Km)
350
0
34
Offset (Km)
350
Corrected LSI SSP
Real SSP
0
0
Primaries
Time (s)
Time (s)
Primaries
10
10
0
Offset (Km)
350
0
35
Offset (Km)
350
primaries
multiples
36
primaries
multiples
37
primaries
multiples
38
OUTLINE
• VSP to SSP
• Motivation
• Theory
• Numerical Results
• Synthetic data test
•Virtual source close to well.
•Virtual source far from well.
• Field data test
• Conclusion
39
SI SSP
Real SSP
0
0
Artifacts
Primaries
Time (s)
Time (s)
Primaries
10
10
0
Offset (Km)
750
0
40
Offset (Km)
750
LSI SSP of Downgoing
Real SSP
0
0
Primaries
Time (s)
Time (s)
Primaries
10
10
0
Offset (Km)
750
0
41
Offset (Km)
750
LSI SSP of Upgoing
Real SSP
0
0
Primaries
Time (s)
Time (s)
Primaries
10
10
0
Offset (Km)
750
0
42
Offset (Km)
750
Corrected LSI SSP
Real SSP
0
0
Primaries
Time (s)
Time (s)
Primaries
10
10
0
Offset (Km)
750
0
43
Offset (Km)
750
Left side
primaries
multiples
44
Left side
primaries
multiples
45
Left side
primaries
multiples
46
Middle
primaries
multiples
47
Middle
primaries
multiples
48
Middle
primaries
multiples
49
Right side
primaries
multiples
50
Right side
primaries
multiples
51
Right side
primaries
multiples
52
OUTLINE
• VSP to SSP
• Motivation
• Theory
• Numerical Results
• Synthetic data test
•Virtual source close to well.
•Virtual source far from well.
• Field data test
• Conclusion
53
Standard Interferometric SSP
S.I (Down)
S.I (up)
0.6
550
offset (ft)
0
0.6
550
Time (s)
0
Time (s)
0
Time (s)
0
Reference
Offset (ft)
0
0.6
600
54
Offset (ft)
0
L.S. Interferometric SSP
L.S.I (Down)
L.S.I (up)
0.6
550
Offset (ft)
0
0.6
550
Time (s)
0
Time (s)
0
Time (s)
0
Reference
Offset (ft)
0
0.6
600
55
Offset (ft)
0
0
0
Time (s)
Real SSP
Time (s)
Corrected LSI SSP
0.6
550
Offset (ft)
0
0.6
600
56
Offset (ft)
0
OUTLINE
• VSP to SSP
• Motivation
• Theory
• Numerical Results
• Conclusion
57
Conclusion
• Least squares interferometric VSP to
SSP transform can attenuate the
surface related multiples and crosstalk
artifacts.
• A matching filter correction can
attenuate more artifacts caused by
limited acquisition geometry.
• Problem:
– Non-surface related multiples may cause artifacts.
58
OUTLINE
• VSP to SWP
• VSP surface related multiple to
SSP
• Surface waves prediction and
subtraction
• Summary
59
OUTLINE
• Surface Wave Prediction
• 2D problem
• 3D problem
60
OUTLINE
• Surface Wave Prediction (2D)
• Motivation
• Methodology
• Field data
• Conclusion
61
Problem: Surface waves blur the
seismogram.
surf
d
d =
+ d ref
Time (s)
0
Receiver (m)
7200
Reflectio
waves
Surface
waves
2.0
A seismogram with surface waves and reflection
data
62
Solution:
Filter the surface waves by NLF
and Interferometric method
63
OUTLINE
• Surface Wave Prediction (2D)
• Motivation
• Methodology
• Field data test
• Conclusion
64
Prediction of Surface
Waves
Near-Offset
Surf. Wave
Mid-Offset
Surf. Wave
Near-Offset
Surf. Wave
65
The work flow
Input
data d
Filter the surface
waves by NLF
Predict the residual and
primaries by
interferometry
Predict the surface
waves by NLF or
wavelet transform
Least square
subtraction
No
Output
data
Lowpass
Surface waves are
removed completely?
Yes
66
OUTLINE
• Surface Wave Prediction (2D)
• Motivation
• Methodology
• Field data test
• Conclusion
67
The original data from
Saudi
Remove surface waves only
by NLF
d
Time (s)
0
Time (s)
0
2.0
2.0
0
Receiver (m)
3600
0
Receiver (m)
360068
Remove surface waves only
by NLF
Time (s)
0
Time (s)
0
Remove surface waves
Int.+NLF
2.0
2.0
0
Receiver (m)
3600
0
Receiver (m)
360069
Remove surface waves
Int.+NLF
The original data from
Saudi
d
0
Time (s)
Time (s)
0
2.0
2.0
0
Receiver (m)
3600
0
Receiver (m)
360070
Surface waves predicted
by NLF
Time (s)
0
Time (s)
0
Remaining SW predicted by
Int.+NLF
2.0
2.0
0
Receiver (m)
3600
0
Receiver (m)
360071
Remove surface waves
by F-K
Time (s)
0
Time (s)
0
Remove surface waves by
Int.+NLF
2.0
2.0
0
Receiver (m)
3600
0
Receiver (m)
360072
Surface waves predicted
by F-K
Time (s)
0
Time (s)
0
Surface waves predicted by
Int.+NLF
2.0
2.0
0
Receiver (m)
3600
0
Receiver (m)
360073
OUTLINE
• Surface Wave Prediction (2D)
• Motivation
• Methodology
• Field data test
• Conclusion
74
•The NLF+interferometry method can
remove the surface waves successfully.
•The NLF+interferometry method can
keep more details than the fk method.
•The NLF+interferometry method can
remove surface waves with very low
energy.
75
OUTLINE
• Surface Wave Prediction
• 2D problem
• 3D problem
76
OUTLINE
• Surface Wave Prediction (3D)
• Motivation
• Methodology
• Field data test
• Conclusion
77
Problem: No perfect geometry
for 3D interferometry
Solution: Convert the 3D
problem to 2D problem
78
A 3D seismic data with surface waves
0
Time (s)
Nonlinear moveout
4.0
Highly aliased
0
Receiver (m)
5000
79
OUTLINE
• Surface Wave Prediction (3D)
• Motivation
• Methodology
• Field data test
• Conclusion
80
time shift
nonlinear moveout
linear moveout
d
Sqrt(d^2+x^2)
x
Shift(x)={Sqrt(d^2+x^2)-x}/v
81
Shifted data
Time Shift
Time (s)
Time (s)
Original data
Linearized
moveout
surface wave
receiver (m)
receiver (m)
Predicted reflections
Match filter
predicted surface wave
receiver (m)
Time (s)
Time (s)
Predicted surface
waves
Predicted reflections
receiver (m)
82
The work flow
Input data
d
Time shift d to make
the surface waves
linear moveout
Filter the surface waves
by NLF
Predict the residual and
primaries by interferometry
Predict the surface
waves by NLF or
wavelet transform
Least square subtraction
No
Output
Lowpass filter
data
Surface waves are
removed completely?
Yes
83
OUTLINE
• Surface Wave Prediction (3D)
• Motivation
• Methodology
• Field data test
• Conclusion
84
Line8 before and after removing surface waves
Time (s)
0
Time (s)
0
4.0
0
Receiver (m)
4.0
5000 0
Receiver (m)
85
5000
Line9 before and after removing surface waves
0
Time (s)
Time (s)
0
4.0
0
Receiver (m)
4.0
5000 0
Receiver (m)
86
5000
Line10 before and after removing surface waves
0
Time (s)
Time (s)
0
4.0
0
Receiver (m)
4.0
5000 0
Receiver (m)
87
5000
Line11 before and after removing surface waves
0
Time (s)
Time (s)
0
4.0
0
Receiver (m)
4.0
5000 0
Receiver (m)
88
5000
Line12 before and after removing surface waves
4.0
0
Time (s)
0
Time (s)
0
Receiver (m)
4.0
5000 0
Receiver (m)
89
5000
OUTLINE
• Surface Wave Prediction (3D)
• Motivation
• Methodology
• Field data test
• Conclusion
90
• The nonlinear time shift can make a
nonlinear event a linear event.
• The linear shift can weaken the
aliasing problem
• After the nolinear and linear shift,
the 2D surface waves elimination
technique can be apply on the 3D
data.
• This technique solves 3D
interferometry geometry problem.
91
problems
• The angle between the signal events
and the noise event are too small. It
will be not easy for the nonlinear local
filter to choose the noise from signal
• Both the signal events and the noise
event are nearly linear. They share the
same stationary phase points and this
leads to a low contrast of signal/noise
in the interferometry and make it
difficult to separate the noise from the
92
data
OUTLINE
• VSP to SWP
• VSP surface related multiple to
SSP
• Surface waves prediction and
subtraction
• Summary
93
Summary
• Wavefield decomposition improves the
interferometric results.
• Least squares interferometric scheme
can attenuate surface related multiples
and crosstalk artifacts.
• Matching filter help to improve
interferometric prediction results
94
Future Work
• Apply LSD to target oriented RTM
• Up-down going wavefields separation
for complicated medium
• 3D data test on least squares
interferometric techniques
95
Acknowledgements
• My advisor: Gerard T. Schuster
• My supervisory committee: Ronanld L. Bruhn,
Hugues Djikpesse, Richard D. Jarrard, and
Michael S. Thorne
• My wife Jing and my Son Daniel
• My UTAM colleagues and my other friends
96
Thank you
97