Transcript No Slide Title

Waveform Inversion for
Crosswell Data
M. Zhou
Geology and Geophysics Department
University of Utah
Outline
•
•
•
•
Motivation
Objective
Theory
Examples
Synthetic Model 1
Synthetic Model 2
• Conclusions
Motivation
High resolution 2 m by 2 m
Analyses of lithology
Outline
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•
•
•
Motivation
Objective
Theory
Examples
Synthetic Model 1
Synthetic Model 2
• Conclusions
Objective
High resolution tomogram
Traveltime vs. Waveform
Traveltime Inversion
fast, insensitive to initial model
low resolution (high freq. approx.)
Waveform Inversion
high resolution
slow, sensitive to initial model
Objective
Traveltime
+ Waveform
Initial model
High resolution
Outline
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•
•
•
Motivation
Objective
Theory
Examples
Synthetic Model 1
Synthetic Model 2
• Conclusions
Theory
Waveform inversion:
Misfit = S (dobs-dcal(s))2
Residual waveform
D
s(x) = f(x,t)
Gradient
Forward field
* b(x,t)
| t=0
Residual backward field
Outline
•
•
•
•
Motivation
Objective
Theory
Examples
Synthetic Model 1
Synthetic Model 2
• Conclusions
Model 1: Model
0
0
X (m)
50
km/s
1m X 1m grid
Depth (m)
6.0
41 shots/geophones
5.0
40
200 Hz Ricker wavelet
4.0
Shortest wavelength 20 m
3.0
80
Model
Model 1: Tomograms
0
0
X (m)
50
0
X (m)
50
0
X (m)
50
km/s
Depth (m)
6.0
5.0
40
4.0
3.0
80
Model
Tomo50 (ray-based)
WI50
Model 1: Tomograms
0
0
X (m)
50
0
X (m)
50
0
X (m)
50
km/s
Depth (m)
6.0
5.0
40
4.0
3.0
80
Model
WIF30
WIF30 + WI20
Model 1: Synthetic CSG
Time (sec)
0
0
X (m)
40
80
0
X (m)
40
80
0
X (m)
40
0.1
Tomo50 (ray-based)
Model
WIF30 + WI20
80
Model 1: One trace
Amplitude
.01
1.
Time (s)
.025
.04
.01
Time (s)
.025
0.
-1.
Ray-based Traveltime Inversion
WIF30
Amplitude
1.
0.
-1.
WI50
WIF30 + WI20
.04
Outline
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•
•
•
Motivation
Objective
Theory
Examples
Synthetic Model 1
Synthetic Model 2
• Conclusions
Model 2: Model
X (m)
Depth (m)
0
0
90
km/s
3m X 3m grid
3.6
18 shots / 32 geophones
3.2
60 Hz Ricker wavelet
2.8
100
2.4
210
Model
Model 2: Tomograms
X (m)
X (m)
0
0
90
0
X (m)
90
0
90
km/s
3.6
Depth (m)
3.2
100
2.8
2.4
210
Model
WT10 (wave eq.)
WIF20
Model 2: Tomograms
X (m)
X (m)
0
0
90
0
X (m)
90
0
90
km/s
3.6
Depth (m)
3.2
100
2.8
2.4
210
Model
WIF20
WIF20 + WI10
Model 2: Synthetic CSG
Time (sec)
0
0
X (m)
100
200
0
X (m)
100
200
0
X (m)
100
0.1
WT10
Model
WIF20
200
Model 2: One Trace
Time (s)
Amplitude
1.
.04
.08
0.
-1.
Wave Eq. Traveltime (WT) 10 iterations
Amplitude
1.
0.
-1.
WIF20
.12
Outline
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•
•
•
Motivation
Objective
Theory
Examples
Synthetic Model 1
Synthetic Model 2
• Conclusions
Conclusions
WI vs. Traveltime Inversion:
• Higher resolution tomograms;
• More sensitive to initial model.
WIF + WI vs. WI:
• Less sensitive to initial model.
Future Work
Test on 2-D field data
Acknowledgements
I am grateful for the financial
support from the members of
the 2001 UTAM consortium.