Geostatistics applied to cross-well reflection seismic for ...
Seismic-to-well ties by smooth dynamic time warping...Introduction 5 How to tie wells to seismic? 1....
Transcript of Seismic-to-well ties by smooth dynamic time warping...Introduction 5 How to tie wells to seismic? 1....
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Seismic-to-well ties by smooth dynamic time warping
M.Sc. thesis defenseTianci Cui and Gary Margrave
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Outline
• Introduction
• Smooth dynamic time warping
• Seismic-to-well ties on Hussar field data
• Conclusions
• Acknowledgements
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Outline
• Introduction
• Smooth dynamic time warping
• Seismic-to-well ties on Hussar field data
• Conclusions
• Acknowledgements
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Introduction
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What are seismic-to-well ties for?
interpretation
impedance inversion
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Introduction
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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)
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Outline
• Introduction
• Smooth dynamic time warping
• Seismic-to-well ties on Hussar field data
• Conclusions
• Acknowledgements
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Dynamic time warping
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Hale, D., 2013, Dynamic warping of seismic images: Geophysics
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Dynamic time warping
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Dynamic time warping
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Dynamic time warping
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( )( )
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Dynamic time warping
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( + )( )− ≤ ≤ ≤ ≤
( , ) = ( ) − ( + ) = , , … ,
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Dynamic time warping
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Dynamic time warping
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infiniteConstraint: | − ( − )|≤1
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Dynamic programmingAlignment error array e
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m
125 possible paths
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n
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Dynamic programming: accumulationAlignment error array e
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Distance array d
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Constraint: | − ( − )|≤1
4 7 3
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3 5 8
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Dynamic programming: accumulationAlignment error array e
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1
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-1
-2
1 2 3n
m
125 possible paths
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4
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Distance array d
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Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
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Dynamic programming: accumulationAlignment error array e
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-1
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1 2 3n
m
125 possible paths
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4
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Distance array d
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1 2 3n
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?
Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
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Dynamic programming: accumulationAlignment error array e
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-1
-2
1 2 3n
m
125 possible paths
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4 8
1
3
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Distance array d
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-1
-2
1 2 3n
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?
Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
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Dynamic programming: accumulationAlignment error array e
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1
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-1
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1 2 3n
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125 possible paths
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4 8
1
3
6
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Distance array d
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1
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-1
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1 2 3n
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Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
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Dynamic programming: accumulationAlignment error array e
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1
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-1
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1 2 3n
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125 possible paths
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4 8
1 9
3
6
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Distance array d
2
1
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-1
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1 2 3n
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Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
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Dynamic programming: accumulationAlignment error array e
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1
0
-1
-2
1 2 3n
m
125 possible paths
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4 8
1 9
3
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Distance array d
2
1
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-1
-2
1 2 3n
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Constraint: | − ( − )|≤1
?
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
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Dynamic programming: accumulationAlignment error array e
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1
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-1
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1 2 3n
m
125 possible paths
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4 8
1 9
3
6
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Distance array d
2
1
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-1
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1 2 3n
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Constraint: | − ( − )|≤1
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4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
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Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
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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
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Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
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4 8
1 9
3 6
6 7
2 10
Distance array d
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1
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-1
-2
1 2 3n
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Constraint: | − ( − )|≤1
4 7 3
1 8 4
3 5 8
6 5 9
2 8 1
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Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
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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
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Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
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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
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Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
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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
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Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
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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
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Dynamic programming: accumulationAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
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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
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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
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Dynamic programming: backtrackingAlignment error array e
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125 possible paths
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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
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Dynamic programming: backtrackingAlignment error array e
2
1
0
-1
-2
1 2 3n
m
125 possible paths
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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: ( ) = [− ,− ,− ]
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Dynamic time warping
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1
0
-1
-2
1 2 3n
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4 8 11
1 9 10
3 6 14
6 7 15
2 10 8
Distance array d
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-1
-2
1 2 3n
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Distance array d
4 8
1 9
3 6
6 7
2 10
( ) = [− ,− ,− ]( ) = [ , ]Dynamic: optimal path varies at different stagesWarping path: lag sequence
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Dynamic time warping
CREWES Matlab toolbox function: DTW
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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
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Smooth dynamic time warping
CREWES Matlab toolbox function: DTWs=
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Outline
• Introduction
• Smooth dynamic time warping
• Seismic-to-well ties on Hussar field data
• Conclusions
• Acknowledgements
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Hussar experiment
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Zero-offset seismic section
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Estimate seismic wavelet
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Well logs after editing
KB
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Well reflectivity
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Construct synthetic seismogram
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Before seismic-to-well ties
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Estimate time shift by SDTW
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(Margrave et al., 2012)
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Time calibration of reflectivity
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Reconstruct synthetic seismogram
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Estimate time-variant constant-phase
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2-D time-variant constant-phase
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degreeswell 14-35 well 14-27 well 12-27
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Synthetic seismogram after time calibration once
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Second iteration of time calibration
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Second iteration of time calibration
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Third iteration of time calibration
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2-D time-variant constant-phase
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Two iterations of time calibrationdegreeswell 14-35 well 14-27 well 12-27
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Third iteration of time calibration
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2-D time-variant amplitude scalar
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Two iterations of time calibrationdegreeswell 14-35 well 14-27 well 12-27
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After seismic-to-well ties
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After seismic-to-well ties
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Interpolated well impedance
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well 14-35 well 14-27 well 12-27
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Bandlimited impedance inversion
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One iteration of time calibration Well: 0-3 HzSeismic: 3-75 Hz
well 14-35 well 14-27 well 12-27
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Bandlimited impedance inversion
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Two iterations of time calibration Well: 0-3 HzSeismic: 3-75 Hz
well 14-35 well 14-27 well 12-27
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Errors between seismic and well impedance
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impedance: 0-75 Hz
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Conclusions
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• 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.
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Acknowledgements
• CREWES sponsors
• NSERC: grant CRDPJ 379744-08
• CREWES staff and students
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