1. Wave-Equation Waveform Inversion for Crosswell Data M. Zhou and Yue Wang Geology and Geophysics Department University of Utah

2. Outline Theory: Wave Equation Inversion Theory: Wave Equation Inversion 2 Problems: Local Minima & Visco 2 Problems: Local Minima & Visco McElroy Xwell data McElroy Xwell data Conclusions Conclusions

3. Waveform Inversion  = || P(x,t) – P(x,t) || 2 pred obs v(x,z)  v(x,z) -   v(x,z) P(x,t) pred [P(x,t) – P(x,t) ] pred obs Migration { Waveform Residual { Acooustic, Elastic or Viscoelastic

4. Why Waveform Inversion? 0 km Depth 0.2 km 0 1.5 km Better Resolution & Focusing Blurring Faults LithologyDistortion Gas

5. Outline Theory: Wave Equation Inversion Theory: Wave Equation Inversion 2 Problems: Local Minima & Visco 2 Problems: Local Minima & Visco McElroy Xwell data McElroy Xwell data Conclusions Conclusions

6. Why Waveform Inversion is Not Used? Poor Convergence, Local Minima, Cost Localminima   traveltime) v v 1 2   traveltime + 1 st Arrival) v v 1 2 v v 1 2 1 st -Arrival Waveforminversion Waveforminversion Global Minima

7. 3.2 3.6 2.4 2.8 km/s 0 100 210 Depth (m) 0 90 X (m) Model (Zhou et al., 1995) Model 1.5m X 1.5m grid 18 shots / 36 geophones 60 Hz Ricker wavelet

8. 0 90 X (m) WIF20 3.2 3.6 2.4 2.8 km/s 0 100 210 Depth (m) 0 90 X (m) Model 0 90 WT10 Model : Tomograms 0 90 X (m) WIF20 + WI10

9. 0100200 X (m) Model 0100200 WIF20 Time (sec) 0100200 0 0.1 X (m) WT10 Model 2: Synthetic CSG

10. Outline Theory: Wave Equation Inversion Theory: Wave Equation Inversion 2 Problems: Local Minima & Visco 2 Problems: Local Minima & Visco McElroy Xwell data McElroy Xwell data Conclusions Conclusions

11. Problem: Invert Vp & Vs by elastic wave inver. Vp accurate by elastic waveform inversion Vp accurate by elastic waveform inversion Vs inaccurate by elastic waveform inversion Vs inaccurate by elastic waveform inversion Why? Insufficient physics in forward modeler Anisotropy? Attenuation? Biot? Coupling? Source effects? 3-D scattering? Source effects? 3-D scattering? Conjecture: Add attenuation

12. Waveform Inversion  = || P(x,t) – P(x,t) || 2 pred obs v(x,z)  v(x,z) -   v(x,z) P(x,t) pred [P(x,t) – P(x,t) ] pred obs Migration { Waveform Residual { Viscoelastic Viscoelastic

13. 0 90 Offset (m) Depth (m) 0 210 P 0 90 Offset (m) S 2300 3650m/s 1150 1825m/s Fault Model

14. 0 Time (s) Depth (m) 0 210 0.2 Elastic Seismogram

15. 0 Time (s) Depth (m) 0 210 0.2 =40 Qp=40Qs=25 Viscoelastic Seismogram

16. 0 90 Offset (m) Depth (m) 0 210 P 0 90 Offset (m) S 2300 3650m/s 1150 1825m/s A B C Ray Tracing Tomograms

17. 0 90 Offset (m) Depth (m) 0 210 P 0 90 Offset (m) S 2300 3650m/s 1150 1825m/s A B C A B C D Viscoelastic Tomograms

18. 0 90 Offset (m) Depth (m) 0 210 P 0 90 Offset (m) S 2300 3650m/s 1150 1825m/s Elastic Tomograms

19. Outline Theory: Wave Equation Inversion Theory: Wave Equation Inversion 2 Problems: Local Minima & Visco 2 Problems: Local Minima & Visco McElroy Xwell data McElroy Xwell data Conclusions Conclusions

20. 200 Sources * 200 Receivers 180 ft 2700 ft McElroy Geometry 500 ft

21. 0 500 Depth (ft) Time (s) 0 0.05 Shot Gather 101

22. Bandpass Filter Median Filter 3D ==> 2D Borehole Filter, wavelet and radiation pattern Processing

23. 0 184 Offset (ft) Depth (ft) 0 500 P 0 184 Offset (ft) S B A C D 14000 22500ft/s 7750 12700ft/s Elastic Tomograms

24. 2700 V Depth (ft) 3150 Receiver Well P-Velocity Profile: Tomo vs Sonic Log

25. 2850 Depth (ft) 3050 V Source Well S-Velocity Profile: Tomo vs Sonic Log

26. Bandpass Filter Median Filter 3D ==> 2D Borehole filter, Wavelet and Src Rad. Qp and Qs by Harris’ Redshift Method Processing

27. Freq. ~ Time Covariance of Source Spectrum Appr. Qp Extract All Direct P Waves Estimate Q from 1 st Arrivals

28. Freq. vs Time Freq. vs Time Time (s) 0.0140.028 400 2000 Freq. (hz)

29. B A C D 0 184 Offset (ft) Depth (ft) 0 500 P 0 184 Offset (ft) S 14000 22500ft/s 7750 12700ft/s Viscoelastic Tomograms

30. 2850 Depth (ft) 3050 V Source Well S-Velocity Profile: ViscoTomo vs Sonic Log

31. 2850 Depth (ft) 3050 V Source Well S-Velocity Profile: ElasticTomo vs Sonic Log

32. 0 Offset (ft) Depth (ft) 0 250 184 A B Viscoelastic S-Tomogram

33. 0 Offset (ft) Depth (ft) 0 250 184 A B Elastic S-Tomogram

34. 0 Offset (ft) Depth (ft) 0 250 Visco. 184 C D 0.35 0.05 Poisson Ratio

35. 0 Offset (ft) Depth (ft) 0 250 Elastic 184 C D 0.35 0.05 Poisson Ratio

36. Conclusions 4 Iteration, Pressure Data, Visco.WTW4 Iteration, Pressure Data, Visco.WTW Visco better than ElasticVisco better than Elastic Issues:Issues: Q(z), multicomponent, anisotropy Q(z), multicomponent, anisotropy CPU Time CPU Time Intrinsic atten. vs Scattering atten.? Intrinsic atten. vs Scattering atten.? Scale of Q vs Velocity? Scale of Q vs Velocity? Need more Physics such as Anisotropy? Need more Physics such as Anisotropy?

37. B A C D Visco. WTW Tomograms 0 184 Offset (ft) Depth (ft) 0 500 P 0 184 Offset (ft) S 14000 22500ft/s 7750 12700ft/s

38. S Tomogram Comparison 0 Offset (ft) Depth (ft) 250 500 Visco. 184 C D

39. S Tomogram Comparison 0 Offset (ft) Depth (ft) 250 500 Elastic 184 C D

40. Conclusions Visco.WTW High-resolution P- and S-velocity ! YES

41. Conclusions Visco.WTW Visco.WTW Porosity, Lithology, AVO YES

42. Acknowledgments Acknowledgments We are grateful for the support of :  the 1997 members of University of Utah Tomography and Modeling/Migration Consortium http://utam.gg.utah.edu

43. Viscoelastic CSP Gather 101 0 500 Depth (ft) Time (s) 0 0.05

44. Evaluate Q Values Appr. Qp + Synthetic Modeling Test Qp Qs

45. CSP Gather 101 0 500 Depth (ft) Time (s) 0 0.05

46. Viscoelastic CSP Gather 101 0 500 Depth (ft) Time (s) 0 0.05

47. Elastic CSP Gather 101 0 500 Depth (ft) Time (s) 0 0.05

48. Viscoelastic Waveform Inversion 0 500 Depth (ft) Time (s) 00.05 0 500 Depth (ft) Time (s) 0 0.05 0 500 Depth (ft) Time (s) 00.05 Elastic Viscolastic CSG101

49. P-Velocity Profiles : P-sonic Logs : Elastic P-velocity Profiles : Visco. P-velocity Profiles

50. S-Velocity Profiles 2700 V Depth (ft) 3150 V Receiver Well Source Well

51. S-Velocity Profiles : S-sonic Logs : Elastic S-velocity Profiles : Visco. S-velocity Profiles

52. Elastic CSP Gather 101 0 500 Depth (ft) Time (s) 0 0.05

53. Viscoelastic CSP Gather 101 0 500 Depth (ft) Time (s) 0 0.05 Qp=80Qs=50

54. Outline Motivation+Theory WI Motivation+Theory WI Examples Examples Xwell Synthetic Xwell Synthetic CDP Synthetic : Chirp CDP Synthetic : Chirp CDP Gulf of Mexico CDP Gulf of Mexico Conclusions Conclusions

55. Synthetic CDP Model (FD Acoustic) 020 40 60 Depth (m) 0200100 Distance (m) 25001958 1416 873 331 (m/s) 40 m Synthetic CDP Model (100 shot gathers, 100 receivers/gather)

56. Traveltime Tomogram 020 40 60 Depth (m) 0200100 Distance (m) 25001958 1416 873 331 (m/s)

57. Multigrid for half comp. time 020 40 60 Depth (m) 0200100 Distance (m) 25001958 1416 873 331 (m/s)

58. Chevron Gulf of Mexico Seismic Line Courtesy of Alan Leeds Shots: 990 Channel: 180 Shot spacing: 25 m Receiver: 25 m Sample: 4 ms Length: 8 sec. Offset 173 – 4648 m

59. 2100 1500 1900 1700 (m/s) CDP NUMBER 5500 6500 1000 0 Depth (m) Traveltime Tomogram Waveform

60. Waveform vs. Traveltime 2100 1500 1900 1700 (m/s) CDP NUMBER 55006500 0 Depth (m) 200 0 200WaveformTraveltime Gas?

61. Amplitude Vs. Offset 0 -2 -3 Log10 Amplitude 2.23.8 Log10 Offset (m) Waveform Data Traveltime

62. 600 (msec.) 1200 Stacked Section (Waveform vs. Traveltime)

63. Conclusions Robust to initial model for Xwell. Robust to initial model for Xwell. High resolution tomograms. High resolution tomograms. WI vs. Traveltime Inversion: WIF + WI vs. WI: Stable for Models Tested. Stable for Models Tested. Sensitive to initial model. Sensitive to initial model. Will this approach work for Reflections? Will this approach work for Reflections?

64. Acknowledgements I am grateful for the financial I am grateful for the financial support from the members of support from the members of the UTAM consortium. the UTAM consortium.

65. Waveform Tomogram 020 40 60 Depth (m) 0200100 Distance (m) 25001958 1416 873 331 (m/s)

66. 2D Synthetic Data (Blind test) Courtesy of Konstantin Osypov Shots: 401 Channel: 241 Shot spacing: 50 m Receiver: 25 m Sample: 4 ms Length: 2 sec. Offset: -3000 – 3000 m

67. Traveltime Tomogram 2409 2057 1705 1352 1000 m/s 5.0 8.75 Horizontal distance (km) 0.0 0.4 Depth (km) 0.1 0.2 0.3

68. Amplitude 0.1.WIF20 Amplitude 0. 1. Time (s).04.12.08 WT10 Model 2: One Trace Examples ObjectiveTheoryConclusionsMotivation

69. Waveform Tomogram 2700 2275 1850 1425 1000 m/s 5.0 8.75 Horizontal distance (km) 0.0 0.4 Depth (km) 0.1 0.2 0.3

70. 600 (msec.) 1200 Stacked Section (Waveform vs. Traveltime) WaveformTraveltime

71. 600 (msec.) 1200

72. Summary Traveltime Inversion Traveltime Inversion Waveform Inversion Waveform Inversion slow, sensitive to initial model high resolution fast, insensitive to initial model low resolution

73. Model 1: Model 5.0 6.0 3.0 4.0 km/s 050 X (m) 0 40 80 Depth (m) Model 1m X 1m grid 41 shots/geophones 200 Hz Ricker wavelet

74. Model 1: Tomograms 050 X (m) WI50 5.0 6.0 3.0 4.0 km/s 050 0 40 80 Depth (m) Model 050 X (m) Tomo50

75. 050 WIF30 + WI20 5.0 6.0 3.0 4.0 km/s 050 X (m) 0 40 80 Depth (m) Model 050 X (m) WIF30 Model 1: Tomograms

76. 0 4080 Time (sec) 0 0.1 X (m) Tomo50 Model 0 4080 WIF30 + WI20 0 4080 Model 1: Synthetic CSG

77. RMS Waveform Residuals Number of Iterations 0. 0.05 0.1 0.15 010203040 50 Model 1: Residuals

78. Outline Motivation+Theory WI Motivation+Theory WI Examples Examples Xwell Synthetic Xwell Synthetic CDP Synthetic : Chirp CDP Synthetic : Chirp CDP Gulf of Mexico CDP Gulf of Mexico Conclusions Conclusions

79. Visco. Wave Equation Initial Velocity Model Vp, Vs, Qp, Qs Synthetic Seismograms Residuals = ||Syn. - Obs|| 2

80. u Perturbation of Lame parameters: Gradient Optimization f : from forward wavefield b: from adjoint wavefield

81. Spectrum Covariance Frequency (hz) 0 4000 Amplitude 1 1/e

82.  Problem & Methodology  Synthetic Data Example  Field Data Example  Conclusion and Discussion Outline

83. Full 2-D viscoelastic wave equationFull 2-D viscoelastic wave equation with memory variables. Standard with memory variables. Standard model spring-dashpot Qp and Qs model spring-dashpot Qp and Qs 2-D to 3-D conversion2-D to 3-D conversion Apply borehole transfer functionApply borehole transfer function Invert src waveletInvert src wavelet Invert src radiation patternInvert src radiation patternMethodology