Multiscale Waveform TomographyMultiscale Waveform Tomography

C. Boonyasiriwat, P. ValasekC. Boonyasiriwat, P. Valasek**, P. Routh, P. Routh**, B. Macy, 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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IntroductionIntroduction

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Introduction: Traveltime TomographyIntroduction: Traveltime Tomography

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IntroductionIntroduction

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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 (2006) Pratt and Brenders (2004) and Sheng (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 approximationNo 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

11

• 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 wavefieldsUse 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 descend method is used to minimize The steepest descend method is used to minimize the misfit function:the misfit function:

)()()(1 rrr kkkk gcc

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Theory of Waveform TomographyTheory of Waveform Tomography

The gradient is calculated byThe gradient is calculated by

s

ss tPtPdtc

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

2)(

3rrrr

rr

wherewhere

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

);,()();,( sggg

s tPts rrrrrr

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OutlineOutline

• IntroductionIntroduction

• ResultsResults

• Multiscale Waveform TomographyMultiscale Waveform Tomography

• ConclusionsConclusions

• Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography

16

• GoalGoal

Why using Multiscale?Why using Multiscale?

Low Frequency

High Frequency

Coarse Scale

Fine Scale

Image from Bunk 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.Use a Wiener filter for low-pass filtering.

• 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 (Bunk et al., 1995)approach (Bunk et al., 1995)

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• Use an early-arrival window function to mute all Use an early-arrival window function to mute all energy except early arrivals.energy except early arrivals.

• Use multiscale V-cycles.Use multiscale V-cycles.

High Frequency Fine GridHigh Frequency Fine Grid

Low Frequency Coarse GridLow Frequency Coarse Grid

Multiscale V-CycleMultiscale V-Cycle

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Why a Wiener Filter?Why a Wiener Filter?

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Original Wavelet Target Wavelet

Wavelet: Hamming Window Wavelet: Wiener Filter

OutlineOutline

• IntroductionIntroduction

• ResultsResults

• Multiscale Waveform TomographyMultiscale Waveform Tomography

• ConclusionsConclusions

• Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography

21

• GoalGoal

Synthetic SSP Data ResultsSynthetic SSP Data Results

• Three-Layer ModelThree-Layer Model

• SEG Salt ModelSEG Salt Model

• Layered Model with ScattersLayered Model with Scatters

• Zhu’s ModelZhu’s Model

• Mapleton ModelMapleton Model

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Three-Layer Velocity ModelThree-Layer Velocity Model

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Initial Velocity ModelInitial Velocity Model

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TRT TomogramTRT TomogramGradient

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EWT TomogramEWT TomogramGradient

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MWT Tomogram (5,10 Hz)MWT Tomogram (5,10 Hz)Gradient

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True Velocity Model 1True Velocity Model 1

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Layered Model with ScattersLayered Model with Scatters

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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 ScattersLayered Model with Scatters

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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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Zhu’s Velocity ModelZhu’s 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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Zhu’s Velocity ModelZhu’s 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

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Low-pass FilteringLow-pass Filtering

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Reconstructed VelocityReconstructed Velocity

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m)

(a) Initial Velocity Modelm/s

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Observed Data vs Predicted DataObserved Data vs Predicted Data

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(a) Observed Windowed CSG

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Waveform Residual vs Iteration NumberWaveform Residual vs Iteration Number

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avef

orm

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idua

lWaveform Residual versus Iteration

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Common Image GatherCommon Image Gather

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10 Hz

Shot Number

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(a) CIG using Initial Tomogram

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OutlineOutline

• IntroductionIntroduction

• ResultsResults

• Multiscale Waveform TomographyMultiscale Waveform Tomography

• ConclusionsConclusions

• Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography

58

• 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.

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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