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Multiscale Waveform Tomography

Multiscale Waveform Tomography. *. *. *. C. Boonyasiriwat, P. Valasek, P. Routh, B. Macy, W. Cao, and G. T. Schuster * ConocoPhillips. Outline. Goal. Introduction. Theory of Acoustic Waveform Tomography. Multiscale Waveform Tomography. Results. Conclusions. 1. Goal. 2. Outline.

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Multiscale Waveform Tomography

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  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: Traveltime Tomography 5

  7. Introduction 6

  8. Introduction: Waveform Tomography 7

  9. Introduction: Waveform Tomography 8

  10. 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 et al. (2006) used early-arrival wavefields. • Bunks et al. (1995) and Pratt et al. (1998) used multiscale approaches. 9

  11. Outline • Goal • Introduction • Theory of Acoustic Waveform Tomography • Multiscale Waveform Tomography • Results • Conclusions 10

  12. Why Acoustic? • Elastic wave equation is expensive. • Waveform inversion is also expensive. • Previous research shows acoustics is adequate. • Use acoustics and mute unpredicted wavefields. 11

  13. Theory of Waveform Tomography The waveform misfit function is An acoustic wave equation: 12

  14. Theory of Waveform Tomography The steepest descent method can be used to minimize the misfit function: The waveform residual is defined by 13

  15. Theory of Waveform Tomography where The gradient is calculated by 14

  16. Outline • Goal • Introduction • Theory of Acoustic Waveform Tomography • Multiscale Waveform Tomography • Results • Conclusions 15

  17. Why Use Multiscale? Misfit function ( f ) Model parameter (m) Low Frequency Coarse Scale High Frequency Fine Scale Image from Bunks et al. (1995) 16

  18. Our Multiscale Approach • Combine Early-arrival Waveform Tomography (Sheng et al., 2006) and a time-domain multiscale approach (Bunks et al., 1995). • Use a Wiener filter for low-pass filtering the data. • Use a window function to mute all energy except early arrivals. • Use multiscale V-cycles. 17

  19. Why a Wiener Filter? Target Wavelet Original Wavelet Wavelet: Hamming Window Wavelet: Wiener Filter 18

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

  21. Outline • Goal • Introduction • Theory of Acoustic Waveform Tomography • Multiscale Waveform Tomography • Results • Conclusions 20

  22. Synthetic SSP Data Results • Layered Model with Scatterers • SEG Salt Model • Mapleton Model 21

  23. Layered Model with Scatterers 22

  24. Initial Velocity Model 23

  25. TRT Tomogram Gradient 24

  26. EWT Tomogram using 15-Hz Data Gradient 25

  27. MWT Tomogram using 2.5-Hz Data Gradient 26

  28. MWT Tomogram using 5-Hz Data 2.5-Hz 27

  29. MWT Tomogram using 10-Hz Data 5 Hz 28

  30. MWT Tomogram using 15-Hz Data 10 Hz 29

  31. Layered Model with Scatterers 30

  32. Comparison of Misfit Function 15 Hz 15 Hz 5 Hz 10 Hz 2.5 Hz 31

  33. SEG Salt Velocity Model 32

  34. TRT Tomogram Gradient 33

  35. MWT Tomogram (2.5,5 Hz) TRT 34

  36. SEG Salt Velocity Model 35

  37. Mapleton Model 36

  38. TRT Tomogram 37

  39. MWT Tomogram (30, 50, 70 HZ) 38

  40. Mapleton Model 39

  41. Marine Data Results 40

  42. Marine Data 480 Hydrophones 515 Shots 12.5 m dt = 2 ms Tmax = 10 s 41

  43. Low-pass Filtering 42

  44. Reconstructed Velocity 43

  45. Observed Data vs Predicted Data 44

  46. Waveform Residual vs Iteration Number 1 s 2 s 5 Hz 5 Hz 5 Hz 10 Hz 10 Hz 5 Hz 10 Hz 45

  47. Common Image Gather 5 Hz 10 Hz 46

  48. Outline • Goal • Introduction • Theory of Acoustic Waveform Tomography • Multiscale Waveform Tomography • Results • Conclusions 47

  49. Conclusions • MWT partly overcomes the local minima problem. • MWT provides more accurate and highly resolved than TRT and EWT. • MWT is much more expensive than TRT. • Accuracy is more important than the cost. • MWT provides very accurate tomograms for synthetic data and shows encouraging results for the marine data. 48

  50. Future Work • Use wider-window data and finally use all the data to obtain more accurate velocity distributions. • Take into account the source radiation pattern. • Apply MWT to land data. 49

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