multiscale waveform tomography c. boonyasiriwat, p. valasek, p. routh, b. macy, w. cao, and g. t....

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


• ResultsResults




3

• Goal and MotivationGoal and Motivation

?

IntroductionIntroduction

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X (km)

Tim

e (s

)

0 2 4 6 8 10 12 14 16

0

1

2

3

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Introduction: Traveltime TomographyIntroduction: Traveltime Tomography

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IntroductionIntroduction

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X (km)

Tim

e (s

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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


• ResultsResults




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.

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• 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

2 tsttPt

ttPc

rrrrrr

The waveform misfit function isThe waveform misfit function is

s g

sg tPdtf );,(21 2 rr

12


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


The gradient is calculated byThe gradient is calculated by

s

ss tPtPdtc

g );,(');,( )(

2)( rrrrr

r

wherewhere

);,'(),';0,(');,(' ss tstGdtP rrrrrrr

);,()();,( sggg

s tPts rrrrrr

14

OutlineOutline


• ResultsResults




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 fu

nctio

n ( 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).

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• 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


• ResultsResults




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• 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 DataGradient

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MWT Tomogram using 2.5-Hz DataMWT Tomogram using 2.5-Hz DataGradient

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MWT Tomogram using 5-Hz DataMWT Tomogram using 5-Hz Data2.5-Hz

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MWT Tomogram using 10-Hz DataMWT Tomogram using 10-Hz Data5 Hz

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MWT Tomogram using 15-Hz DataMWT Tomogram using 15-Hz Data10 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 Hz5 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

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MWT Tomogram MWT Tomogram (30, 50, 70 HZ)(30, 50, 70 HZ)

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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

1

1.5

2

2.5

3

Offset (km)

Tim

e (s

)

b) Original CSG 1

1 1.5 2 2.5

0

0.5

1

1.5

2

2.5

3

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

1

1.5

2

2.5

3

3.5

4

Offset (km)

Tim

e (s

)

(b) 5-Hz CSG

0 2 4

0

0.5

1

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2.5

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Offset (km)Ti

me

(s)

(c) 10-Hz CSG

0 2 4

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0.5

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1.5

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Reconstructed VelocityReconstructed Velocity

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X (km)

Z (k

m)

(a) Initial Velocity Modelm/s

0 2 4 6

0

0.2

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1

1.2

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2

1600

1700

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X (m)

Z (m

)

(b) MWT Tomogram m/s

0 2 4 6

0

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1

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X (km)

Z (k

m)

(a) Initial Velocity Modelm/s

0 2 4 6

0

0.2

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1

1.2

1.4

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1700

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X (m)

Z (m

)

(b) MWT Tomogram m/s

0 2 4 6

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1

1.2

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Observed Data vs Predicted DataObserved Data vs Predicted Data

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Offset (km)

Tim

e (s

)

(a) Observed Windowed CSG

0 2 4

0

0.5

1

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2

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Offset (km)

Tim

e (s

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(b) Predicted CSG using Initial Model

0 2 4

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Offset (km)Ti

me

(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

RMS

Wav

efor

m R

esid

ual

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

0

0.5

1

1.5

2

OutlineOutline


• ResultsResults




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.

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• 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.

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multiscale waveform tomography c. boonyasiriwat, p. valasek, p. routh, b. macy, w. cao, and g. t....

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