1. Multiscale Waveform Tomography C. Boonyasiriwat, P. Valasek *, P. Routh *, B. Macy *, W. Cao, and G. T. Schuster * ConocoPhillips

2. Outline IntroductionIntroduction ResultsResults Multiscale Waveform TomographyMultiscale Waveform Tomography ConclusionsConclusions Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography 1 GoalGoal

3. Goal 2

4. Outline IntroductionIntroduction ResultsResults Multiscale Waveform TomographyMultiscale Waveform Tomography ConclusionsConclusions Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography 3 Goal and MotivationGoal and Motivation

5. ? Introduction 4

6. Introduction 5

7. Introduction: Traveltime Tomography 6

8. Introduction 7

9. Introduction: Waveform Tomography 8

10. 9

11. 10 Pratt and Brenders (2004) and Sheng (2006) used early-arrival wavefields.Pratt and Brenders (2004) and Sheng (2006) 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. (2006), etc.Time domain: Zhou et al. (1995), Sheng et al. (2006), etc. Bunks et al. (1995) and Pratt et al. (1998) used multiscale approaches.Bunks et al. (1995) and Pratt et al. (1998) used multiscale approaches.

12. Outline IntroductionIntroduction ResultsResults Multiscale Waveform TomographyMultiscale Waveform Tomography ConclusionsConclusions Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography 11 GoalGoal

13. 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

14. Theory of Waveform Tomography An acoustic wave equation: The waveform misfit function is 13

15. Theory of Waveform Tomography The waveform residual is defined by The steepest descend method is used to minimize the misfit function: 14

16. Theory of Waveform Tomography The gradient is calculated by where 15

17. Outline IntroductionIntroduction ResultsResults Multiscale Waveform TomographyMultiscale Waveform Tomography ConclusionsConclusions Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography 16 GoalGoal

18. Why using Multiscale? Low Frequency High Frequency Coarse Scale Fine Scale Image from Bunk et al. (1995) Model parameter (m) Misfit function ( f ) 17

19. Our Multiscale Approach Use a Wiener filter for low-pass filtering.Use a Wiener filter for low-pass filtering. Combine Early-arrival Waveform Tomography (Sheng et al., 2006) and a time-domain multiscale approach (Bunk et al., 1995)Combine Early-arrival Waveform Tomography (Sheng et al., 2006) and a time-domain multiscale approach (Bunk et al., 1995) 18 Use an early-arrival window function to mute all energy except early arrivals.Use an early-arrival window function to mute all energy except early arrivals. Use multiscale V-cycles.Use multiscale V-cycles.

20. High Frequency Fine Grid Low Frequency Coarse Grid Multiscale V-Cycle 19

21. Why a Wiener Filter? 20 Original Wavelet Target Wavelet Wavelet: Hamming WindowWavelet: Wiener Filter

22. Outline IntroductionIntroduction ResultsResults Multiscale Waveform TomographyMultiscale Waveform Tomography ConclusionsConclusions Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography 21 GoalGoal

23. Synthetic 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

24. Three-Layer Velocity Model 23

25. Initial Velocity Model 24

26. TRT Tomogram Gradient 25

27. EWT Tomogram Gradient 26

28. MWT Tomogram (5,10 Hz) Gradient 27

29. True Velocity Model 1 28

30. Layered Model with Scatters 29

31. Initial Velocity Model 30

32. TRT Tomogram Gradient 32

33. EWT Tomogram using 15-Hz Data Gradient 32

34. MWT Tomogram using 2.5-Hz Data Gradient 33

35. MWT Tomogram using 5-Hz Data 2.5-Hz 34

36. MWT Tomogram using 10-Hz Data 5 Hz 35

37. MWT Tomogram using 15-Hz Data 10 Hz 36

38. Layered Model with Scatters 37

39. Comparison of Misfit Function 15 Hz 10 Hz5 Hz 2.5 Hz 15 Hz 38

40. SEG Salt Velocity Model 39

41. TRT Tomogram Gradient 40

42. MWT Tomogram (2.5,5 Hz) TRT 41

43. SEG Salt Velocity Model 42

44. Zhu’s Velocity Model 43

45. TRT Tomogram Gradient 44

46. MWT Tomogram (2.5,5 Hz) TRT 45

47. Zhu’s Velocity Model 46

48. Mapleton Model 47

49. TRT Tomogram 48

50. MWT Tomogram (30, 50, 70 HZ) 49

51. Mapleton Model 50

52. Marine Data Results 51

53. Marine Data 515 Shots 480 Hydrophones 12.5 m dt = 2 ms T max = 10 s 52

54. Low-pass Filtering 53

55. Reconstructed Velocity 54

56. Observed Data vs Predicted Data 55

57. Waveform Residual vs Iteration Number 56 5 Hz 10 Hz

58. Common Image Gather 57 5 Hz 10 Hz

59. Outline IntroductionIntroduction ResultsResults Multiscale Waveform TomographyMultiscale Waveform Tomography ConclusionsConclusions Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography 58 GoalGoal

60. Conclusions MWT partly overcomes the local minima problem.MWT partly overcomes the local minima problem. MWT provides more accurate and highly resolved than TRT and EWT.MWT provides more accurate and highly resolved than 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 data and shows encouraging results for the marine data.MWT provides very accurate tomograms for synthetic data and shows encouraging results for the marine data.

61. Future Work Apply MWT to land data.Apply MWT to land data. 60 Use wider-window data and finally use all the data to obtain more accurate velocity distributions.Use wider-window data and finally use all the data to obtain more accurate velocity distributions.

62. Acknowledgment We are grateful for the support from the sponsors of UTAM consortium.We are grateful for the support from the sponsors of UTAM consortium. Chaiwoot personally thanks ConocoPhillips for an internship and also appreciates the help from Seismic Technology Group at ConocoPhillips.Chaiwoot personally thanks ConocoPhillips for an internship and also appreciates the help from Seismic Technology Group at ConocoPhillips. 61