63
Seismic-to-well ties by smooth dynamic time warping M.Sc. thesis defense Tianci Cui and Gary Margrave 1
Seismic-to-well ties by smooth dynamic time warping
M.Sc. thesis defenseTianci Cui and Gary Margrave
1
Outline
• Introduction
• Smooth dynamic time warping
• Seismic-to-well ties on Hussar field data
• Conclusions
• Acknowledgements
2
Outline
• Introduction
• Smooth dynamic time warping
• Seismic-to-well ties on Hussar field data
• Conclusions
• Acknowledgements
3
Introduction
4
What are seismic-to-well ties for?
interpretation
impedance inversion
Introduction
5
How to tie wells to seismic?
1. Edit well logs and process seismic data 2. Calibrate sonic times to seismic times
• Q• Check-shot/VSP survey• Manually stretch and squeeze
3. Estimate wavelet and calculate reflectivity to create synthetic seismogram
4. Rotate the seismic trace by a single constant-phase
Smooth dynamic time warping
Time-variant constant-phase rotation
(Anelastic attenutation)
Outline
• Introduction
• Smooth dynamic time warping
• Seismic-to-well ties on Hussar field data
• Conclusions
• Acknowledgements
6
Dynamic time warping
7
Hale, D., 2013, Dynamic warping of seismic images: Geophysics
Dynamic time warping
8
Dynamic time warping
9
Dynamic time warping
10
( )( )
Dynamic time warping
11
( + )( )− ≤ ≤ ≤ ≤
( , ) = ( ) − ( + ) = , , … ,
Dynamic time warping
12
Dynamic time warping
13
infiniteConstraint: | − ( − )|≤1
Dynamic programmingAlignment error array e
2
1
0
-1
-2
1 2 3
m
125 possible paths
14
n
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
15
4
1
3
6
2
Distance array d
2
1
0
-1
-2
1 2 3n
m
?
Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
16
4
1
3
6
2
Distance array d
2
1
0
-1
-2
1 2 3n
m
?
Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
17
4
1
3
6
2
Distance array d
2
1
0
-1
-2
1 2 3n
m
?
Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
18
4 8
1
3
6
2
Distance array d
2
1
0
-1
-2
1 2 3n
m
?
Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
19
4 8
1
3
6
2
Distance array d
2
1
0
-1
-2
1 2 3n
m
?
Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
20
4 8
1 9
3
6
2
Distance array d
2
1
0
-1
-2
1 2 3n
m
Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
21
4 8
1 9
3
6
2
Distance array d
2
1
0
-1
-2
1 2 3n
m
Constraint: | − ( − )|≤1
?
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
22
4 8
1 9
3
6
2
Distance array d
2
1
0
-1
-2
1 2 3n
m
Constraint: | − ( − )|≤1
?
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
23
4 8
1 9
3 6
6
2
Distance array d
2
1
0
-1
-2
1 2 3n
m
Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
24
4 8
1 9
3 6
6 7
2 10
Distance array d
2
1
0
-1
-2
1 2 3n
m
Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
25
4 8 11
1 9 10
3 6 14
6 7 15
2 10 8
Distance array d
2
1
0
-1
-2
1 2 3n
m
Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
26
4 8 11
1 9 10
3 6 14
6 7 15
2 10 8
Distance array d
2
1
0
-1
-2
1 2 3n
m
Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
27
4 8 11
1 9 10
3 6 14
6 7 15
2 10 8
Distance array d
2
1
0
-1
-2
1 2 3n
m
Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
28
4 8 11
1 9 10
3 6 14
6 7 15
2 10 8
Distance array d
2
1
0
-1
-2
1 2 3n
m
Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
29
4 8 11
1 9 10
3 6 14
6 7 15
2 10 8
Distance array d
2
1
0
-1
-2
1 2 3n
m
Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
30
4 8 11
1 9 10
3 6 14
6 7 15
2 10 8
Distance array d
2
1
0
-1
-2
1 2 3n
m
Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
5 possible paths
Dynamic programming: backtrackingAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
31
4 8 11
1 9 10
3 6 14
6 7 15
2 10 8
Distance array d
2
1
0
-1
-2
1 2 3n
m
Constraint: | − ( − )|≤1
5 possible paths
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
Dynamic programming: backtrackingAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
32
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
4 8 11
1 9 10
3 6 14
6 7 15
2 10 8
Distance array d
2
1
0
-1
-2
1 2 3n
m
Constraint: | − ( − )|≤1
5 possible paths
Estimated lag sequence: ( ) = [− ,− ,− ]
Dynamic time warping
2
1
0
-1
-2
1 2 3n
m
33
4 8 11
1 9 10
3 6 14
6 7 15
2 10 8
Distance array d
2
1
0
-1
-2
1 2 3n
m
Distance array d
4 8
1 9
3 6
6 7
2 10
( ) = [− ,− ,− ]( ) = [ , ]Dynamic: optimal path varies at different stagesWarping path: lag sequence
34
Dynamic time warping
CREWES Matlab toolbox function: DTW
35
Smooth dynamic time warping
Dynamic time warping
Smooth dynamic time warpingCoarse sampling interval =
=
Compton, S., and Hale, D., 2014, Estimating V-P/V-S ratios using smooth dynamic image warping: Geophysics
Constraint: | − ( − 1)|≤1
36
Smooth dynamic time warping
CREWES Matlab toolbox function: DTWs=
Outline
• Introduction
• Smooth dynamic time warping
• Seismic-to-well ties on Hussar field data
• Conclusions
• Acknowledgements
37
Hussar experiment
38
Zero-offset seismic section
39
Estimate seismic wavelet
40
41
Well logs after editing
KB
42
Well reflectivity
Construct synthetic seismogram
43
Before seismic-to-well ties
44
Estimate time shift by SDTW
45
(Margrave et al., 2012)
Time calibration of reflectivity
46
Reconstruct synthetic seismogram
47
Estimate time-variant constant-phase
48
2-D time-variant constant-phase
49
degreeswell 14-35 well 14-27 well 12-27
Synthetic seismogram after time calibration once
50
Second iteration of time calibration
Second iteration of time calibration
51
Third iteration of time calibration
52
2-D time-variant constant-phase
53
Two iterations of time calibrationdegreeswell 14-35 well 14-27 well 12-27
Third iteration of time calibration
54
2-D time-variant amplitude scalar
55
Two iterations of time calibrationdegreeswell 14-35 well 14-27 well 12-27
After seismic-to-well ties
56
After seismic-to-well ties
57
Interpolated well impedance
58
well 14-35 well 14-27 well 12-27
Bandlimited impedance inversion
59
One iteration of time calibration Well: 0-3 HzSeismic: 3-75 Hz
well 14-35 well 14-27 well 12-27
Bandlimited impedance inversion
60
Two iterations of time calibration Well: 0-3 HzSeismic: 3-75 Hz
well 14-35 well 14-27 well 12-27
Errors between seismic and well impedance
61
impedance: 0-75 Hz
Conclusions
62
• Smooth dynamic time warping can accurately estimate the smooth time shift between two traces.
• Smooth dynamic time warping takes the place of the manual stretch-squeeze process in the Hussar well tying.
• The second iteration of time calibration reduces inversion errors around the well 12-27, verifying better seismic-to-well ties.
Acknowledgements
• CREWES sponsors
• NSERC: grant CRDPJ 379744-08
• CREWES staff and students
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