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Multiscale Waveform Tomography

Multiscale Waveform Tomography

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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 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