Multiscale Waveform Tomography

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

4

IntroductionIntroduction

X (km)

Tim

e (s

)

0 2 4 6 8 10 12 14 16

0

1

2

3

4

5

65

Introduction: Traveltime TomographyIntroduction: Traveltime Tomography

6

IntroductionIntroduction

X (km)

Tim

e (s

)

0 2 4 6 8 10 12 14 16

0

1

2

3

4

5

67

Introduction: Waveform TomographyIntroduction: Waveform Tomography

8

Introduction: Waveform TomographyIntroduction: Waveform Tomography

9

Introduction: Waveform TomographyIntroduction: Waveform Tomography

10

• 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.

12

• 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

13

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

14

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

15

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 )

17

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)

18

• 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

19

Why a Wiener Filter?Why a Wiener Filter?

20

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

22

Three-Layer Velocity ModelThree-Layer Velocity Model

23

Initial Velocity ModelInitial Velocity Model

24

TRT TomogramTRT TomogramGradient

25

EWT TomogramEWT TomogramGradient

26

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

27

True Velocity Model 1True Velocity Model 1

28

Layered Model with ScattersLayered Model with Scatters

29

Initial Velocity ModelInitial Velocity Model

30

TRT TomogramTRT TomogramGradient

32

EWT Tomogram using 15-Hz DataEWT Tomogram using 15-Hz Data

Gradient

32

MWT Tomogram using 2.5-Hz DataMWT Tomogram using 2.5-Hz Data

Gradient

33

MWT Tomogram using 5-Hz DataMWT Tomogram using 5-Hz Data

2.5-Hz

34

MWT Tomogram using 10-Hz DataMWT Tomogram using 10-Hz Data

5 Hz

35

MWT Tomogram using 15-Hz DataMWT Tomogram using 15-Hz Data

10 Hz

36

Layered Model with ScattersLayered Model with Scatters

37

Comparison of Misfit FunctionComparison of Misfit Function

15 Hz

10 Hz5 Hz

2.5 Hz

15 Hz

38

SEG Salt Velocity ModelSEG Salt Velocity Model

39

TRT TomogramTRT TomogramGradient

40

MWT Tomogram (2.5,5 Hz)MWT Tomogram (2.5,5 Hz)TRT

41

SEG Salt Velocity ModelSEG Salt Velocity Model

42

Zhu’s Velocity ModelZhu’s Velocity Model

43

TRT TomogramTRT TomogramGradient

44

MWT Tomogram (2.5,5 Hz)MWT Tomogram (2.5,5 Hz)TRT

45

Zhu’s Velocity ModelZhu’s Velocity Model

46

Mapleton ModelMapleton Model

47

TRT TomogramTRT Tomogram

48

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

49

Mapleton ModelMapleton Model

50

Marine Data ResultsMarine Data Results

51

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

52

Low-pass FilteringLow-pass Filtering

53

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

1.5

2

2.5

3

3.5

4

Offset (km)Ti

me

(s)

(c) 10-Hz CSG

0 2 4

0

0.5

1

1.5

2

2.5

3

3.5

4

Reconstructed VelocityReconstructed Velocity

54

X (km)

Z (k

m)

(a) Initial Velocity Modelm/s

0 2 4 6

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1600

1700

1800

1900

2000

2100

2200

2300

X (m)

Z (m

)

(b) MWT Tomogram m/s

0 2 4 6

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1600

1700

1800

1900

2000

2100

2200

2300

X (km)

Z (k

m)

(a) Initial Velocity Modelm/s

0 2 4 6

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1600

1700

1800

1900

2000

2100

2200

2300

X (m)

Z (m

)

(b) MWT Tomogram m/s

0 2 4 6

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1600

1700

1800

1900

2000

2100

2200

2300

Observed Data vs Predicted DataObserved Data vs Predicted Data

55

Offset (km)

Tim

e (s

)

(a) Observed Windowed CSG

0 1 2 3 4 5

0

0.5

1

1.5

2

2.5

3

3.5

4

Offset (km)

Tim

e (s

)

(b) Predicted Windowed CSG

0 1 2 3 4 5

0

0.5

1

1.5

2

2.5

3

3.5

4

Waveform Residual vs Iteration NumberWaveform Residual vs Iteration Number

56

0 10 20 30 40 50450

500

550

600

650

700

Iteration Number

RM

S W

avef

orm

Res

idua

lWaveform Residual versus Iteration

5-Hz

10-Hz

5 Hz

10 Hz

Common Image GatherCommon Image Gather

57

5 Hz

10 Hz

Shot Number

Z (k

m)

(a) CIG using Initial Tomogram

20 40 60 80

0

0.5

1

1.5

Shot Number

Z (k

m)

(b) CIG using MWT Tomogram

20 40 60 80

0

0.5

1

1.5

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.

59

• 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.

60

• 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.

61