Multiscale Waveform Tomography

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

2. Outline • Goal • Introduction • Theory of Acoustic Waveform Tomography • Multiscale Waveform Tomography • Results • Conclusions 1

3. Goal 2

4. Outline • Goal and Motivation • Introduction • Theory of Acoustic Waveform Tomography • Multiscale Waveform Tomography • Results • Conclusions 3

5. Introduction ? 4

6. Introduction 5

7. Introduction: Traveltime Tomography 6

8. Introduction 7

9. Introduction: Waveform Tomography 8

10. Introduction: Waveform Tomography 9

11. Introduction: Waveform Tomography • No high frequency approximation • Frequency domain: Pratt et al. (1998), etc. • Time domain: Zhou et al. (1995), Sheng et al. (2006), etc. • Pratt and Brenders (2004) and Sheng (2006) used early-arrival wavefields. • Bunks et al. (1995) and Pratt et al. (1998) used multiscale approaches. 10

12. Outline • Goal • Introduction • Theory of Acoustic Waveform Tomography • Multiscale Waveform Tomography • Results • Conclusions 11

13. Why Acoustic? • Elastic wave equation is expensive. • Waveform inversion is also expensive. • Previous research shows acoustics is adequate. • Use acoustics and mute unpredicted wavefields 12

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

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

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

17. Outline • Goal • Introduction • Theory of Acoustic Waveform Tomography • Multiscale Waveform Tomography • Results • Conclusions 16

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

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

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

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

22. Outline • Goal • Introduction • Theory of Acoustic Waveform Tomography • Multiscale Waveform Tomography • Results • Conclusions 21

23. Synthetic SSP Data Results • Three-Layer Model • Layered Model with Scatters • SEG Salt Model • Zhu’s Model • Mapleton 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 15 Hz 5 Hz 10 Hz 2.5 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