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Multiscale Waveform Tomography. *. *. *. C. Boonyasiriwat, P. Valasek, P. Routh, B. Macy, W. Cao, and G. T. Schuster * ConocoPhillips. Outline. Goal. Introduction. Theory of Acoustic Waveform Tomography. Multiscale Waveform Tomography. Results. Conclusions. 1. Goal. 2. Outline. - PowerPoint PPT Presentation
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Multiscale Waveform TomographyMultiscale Waveform Tomography
C. Boonyasiriwat, P. Valasek, P. Routh, B. Macy,C. Boonyasiriwat, P. Valasek, P. Routh, B. Macy,W. Cao, and G. T. SchusterW. Cao, and G. T. Schuster
** ConocoPhillips ConocoPhillips
* * *
OutlineOutline
• IntroductionIntroduction
• ResultsResults
• Multiscale Waveform TomographyMultiscale Waveform Tomography
• ConclusionsConclusions
• Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography
1
• GoalGoal
GoalGoal
2
OutlineOutline
• IntroductionIntroduction
• ResultsResults
• Multiscale Waveform TomographyMultiscale Waveform Tomography
• ConclusionsConclusions
• Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography
3
• Goal and MotivationGoal and Motivation
?
IntroductionIntroduction
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X (km)
Tim
e (s)
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Introduction: Traveltime TomographyIntroduction: Traveltime Tomography
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IntroductionIntroduction
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e (s)
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Introduction: Waveform TomographyIntroduction: Waveform Tomography
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Introduction: Waveform TomographyIntroduction: Waveform Tomography
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Introduction: Waveform TomographyIntroduction: Waveform Tomography
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• Pratt and Brenders (2004) and Sheng et al. (2006) Pratt and Brenders (2004) and Sheng et al. (2006) used early-arrival wavefields.used early-arrival wavefields.
• Frequency domain: Pratt et al. (1998), etc.Frequency domain: Pratt et al. (1998), etc.
• No high frequency approximation.No high frequency approximation.
• Time domain: Zhou et al. (1995), Sheng et al. Time domain: Zhou et al. (1995), Sheng et al. (2006), etc.(2006), etc.
• Bunks et al. (1995) and Pratt et al. (1998) used Bunks et al. (1995) and Pratt et al. (1998) used multiscale approaches.multiscale approaches.
OutlineOutline
• IntroductionIntroduction
• ResultsResults
• Multiscale Waveform TomographyMultiscale Waveform Tomography
• ConclusionsConclusions
• Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography
10
• GoalGoal
Why Acoustic?Why Acoustic?
• Waveform inversion is also expensive.Waveform inversion is also expensive.
• Previous research shows acoustics is adequate.Previous research shows acoustics is adequate.
11
• Elastic wave equation is expensive.Elastic wave equation is expensive.
• Use acoustics and mute unpredicted wavefields.Use acoustics and mute unpredicted wavefields.
Theory of Waveform TomographyTheory of Waveform Tomography
An acoustic wave equation:An acoustic wave equation:
),()',';,()',';,(
)(
1 22
2
2tsttP
t
ttP
crrr
rr
r
The waveform misfit function isThe waveform misfit function is
s g
sg tPdtf );,(2
1 2 rr
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Theory of Waveform TomographyTheory of Waveform Tomography
The waveform residual is defined byThe waveform residual is defined by
calcsgobssgsg tPtPtP );,();,();,( rrrrrr
The steepest descent method can be used to The steepest descent method can be used to minimize the misfit function:minimize the misfit function:
)()()(1 rrr kkkk gcc
13
Theory of Waveform TomographyTheory of Waveform Tomography
The gradient is calculated byThe gradient is calculated by
s
ss tPtPdtc
g );,(');,( )(
2)( rrrr
rr
wherewhere
);,'(),';0,(');,(' ss tstGdtP rrrrrrr
);,()();,( sggg
s tPts rrrrrr
14
OutlineOutline
• IntroductionIntroduction
• ResultsResults
• Multiscale Waveform TomographyMultiscale Waveform Tomography
• ConclusionsConclusions
• Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography
15
• GoalGoal
Why Use Multiscale?Why Use Multiscale?
Low Frequency
High Frequency
Coarse Scale
Fine Scale
Image from Bunks et al. (1995)
Model parameter (m)
Mis
fit f
unct
ion
( f )
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Our Multiscale ApproachOur Multiscale Approach
• Use a Wiener filter for low-pass filtering the data.Use a Wiener filter for low-pass filtering the data.
• Combine Early-arrival Waveform Tomography Combine Early-arrival Waveform Tomography (Sheng et al., 2006) and a time-domain multiscale (Sheng et al., 2006) and a time-domain multiscale approach (Bunks et al., 1995).approach (Bunks et al., 1995).
17
• Use a window function to mute all energy except Use a window function to mute all energy except early arrivals.early arrivals.
• Use multiscale V-cycles.Use multiscale V-cycles.
Why a Wiener Filter?Why a Wiener Filter?
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Original Wavelet Target Wavelet
Wavelet: Hamming Window Wavelet: Wiener Filter
High Frequency Fine GridHigh Frequency Fine Grid
Low Frequency Coarse GridLow Frequency Coarse Grid
Multiscale V-CycleMultiscale V-Cycle
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OutlineOutline
• IntroductionIntroduction
• ResultsResults
• Multiscale Waveform TomographyMultiscale Waveform Tomography
• ConclusionsConclusions
• Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography
20
• GoalGoal
Synthetic SSP Data ResultsSynthetic SSP Data Results
• SEG Salt ModelSEG Salt Model
• Layered Model with ScatterersLayered Model with Scatterers
• Mapleton ModelMapleton Model
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Layered Model with ScatterersLayered Model with Scatterers
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Initial Velocity ModelInitial Velocity Model
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TRT TomogramTRT TomogramGradient
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EWT Tomogram using 15-Hz DataEWT Tomogram using 15-Hz Data
Gradient
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MWT Tomogram using 2.5-Hz DataMWT Tomogram using 2.5-Hz Data
Gradient
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MWT Tomogram using 5-Hz DataMWT Tomogram using 5-Hz Data
2.5-Hz
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MWT Tomogram using 10-Hz DataMWT Tomogram using 10-Hz Data
5 Hz
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MWT Tomogram using 15-Hz DataMWT Tomogram using 15-Hz Data
10 Hz
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Layered Model with ScatterersLayered Model with Scatterers
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Comparison of Misfit FunctionComparison of Misfit Function
15 Hz
10 Hz
5 Hz
2.5 Hz
15 Hz
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SEG Salt Velocity ModelSEG Salt Velocity Model
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TRT TomogramTRT TomogramGradient
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MWT Tomogram (2.5,5 Hz)MWT Tomogram (2.5,5 Hz)TRT
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SEG Salt Velocity ModelSEG Salt Velocity Model
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Mapleton ModelMapleton Model
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TRT TomogramTRT Tomogram
37
MWT Tomogram MWT Tomogram (30, 50, 70 HZ)(30, 50, 70 HZ)
38
Mapleton ModelMapleton Model
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Marine Data ResultsMarine Data Results
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Marine Data
515 Shots480 Hydrophones
12.5 mdt = 2 msTmax = 10 s
1 1.5 2 2.5
0
0.5
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Offset (km)
Tim
e (s)
b) Original CSG 1
1 1.5 2 2.5
0
0.5
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2.5
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Offset (km)
Tim
e (s)
a) Virtual CSG 1
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Low-pass FilteringLow-pass Filtering
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Offset (km)
Tim
e (s
)
(a) Original CSG
0 2 4
0
0.5
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Offset (km)
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e (s
)
(b) 5-Hz CSG
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Reconstructed VelocityReconstructed Velocity
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X (km)
Z (k
m)
(a) Initial Velocity Modelm/s
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)
(b) MWT Tomogram m/s
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(a) Initial Velocity Modelm/s
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(b) MWT Tomogram m/s
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Observed Data vs Predicted DataObserved Data vs Predicted Data
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Offset (km)
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e (s
)
(a) Observed Windowed CSG
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(b) Predicted CSG using Initial Model
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Tim
e (s
)
(c) Predicted CSG using MWT Tomogram
0 2 4
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0 50 100 150 200 250 300450
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Iteration Number
RM
S W
avef
orm
Res
idua
l
Waveform Residual versus Iteration
Waveform Residual vs Iteration NumberWaveform Residual vs Iteration Number
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1 s2 s
5 Hz
10 Hz
5 Hz
5 Hz
10 Hz 10 Hz5 Hz
Common Image GatherCommon Image Gather
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5 Hz
10 Hz
Shot Number
Z (k
m)
(a) CIG using Initial Tomogram
20 40 60 80
0
0.5
1
1.5
2
Shot Number
Z (k
m)
(b) CIG using MWT Tomogram
20 40 60 80
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1
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OutlineOutline
• IntroductionIntroduction
• ResultsResults
• Multiscale Waveform TomographyMultiscale Waveform Tomography
• ConclusionsConclusions
• Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography
47
• GoalGoal
ConclusionsConclusions• MWT partly overcomes the local minima problem.MWT partly overcomes the local minima problem.
• MWT provides more accurate and highly resolved than MWT provides more accurate and highly resolved than TRT and EWT.TRT and EWT.
• MWT is much more expensive than TRT.MWT is much more expensive than TRT.
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• Accuracy is more important than the cost.Accuracy is more important than the cost.
• MWT provides very accurate tomograms for synthetic MWT provides very accurate tomograms for synthetic data and shows encouraging results for the marine data.data and shows encouraging results for the marine data.
Future WorkFuture Work
• Apply MWT to land data.Apply MWT to land data.
49
• Use wider-window data and finally use all the Use wider-window data and finally use all the data to obtain more accurate velocity data to obtain more accurate velocity distributions.distributions.
• Take into account the source radiation pattern.Take into account the source radiation pattern.
AcknowledgmentAcknowledgment
• We are grateful for the support from the We are grateful for the support from the sponsors of UTAM consortium.sponsors of UTAM consortium.
• Chaiwoot personally thanks ConocoPhillips Chaiwoot personally thanks ConocoPhillips for an internship and also appreciates the help for an internship and also appreciates the help from Seismic Technology Group at from Seismic Technology Group at ConocoPhillips.ConocoPhillips.
50