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Waveform Inversion for Crosswell Data

Waveform Inversion for Crosswell Data

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Waveform Inversion for Crosswell Data

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  1. Waveform Inversion for Crosswell Data M. Zhou Geology and Geophysics Department University of Utah

  2. Outline • Motivation • Objective • Theory • Examples • Synthetic Model 1 • Synthetic Model 2 • Conclusions

  3. Motivation • High resolution 2 m by 2 m • Analyses of lithology

  4. Outline • Motivation • Objective • Theory • Examples • Synthetic Model 1 • Synthetic Model 2 • Conclusions

  5. Objective • High resolution tomogram

  6. fast, insensitive to initial model low resolution (high freq. approx.) high resolution slow, sensitive to initial model Traveltime vs. Waveform • Traveltime Inversion • Waveform Inversion

  7. Traveltime • Waveform • Initial model • High resolution Objective • + • provide initil model

  8. Outline • Motivation • Objective • Theory • Examples • Synthetic Model 1 • Synthetic Model 2 • Conclusions

  9. D s(x) b(x,t) | t=0 f(x,t) Gradient Forward field Residual backward field Theory Waveform inversion: Misfit = S (dobs-dcal(s))2 Residual waveform = *

  10. Outline • Motivation • Objective • Theory • Examples • Synthetic Model 1 • Synthetic Model 2 • Conclusions

  11. X (m) 0 50 km/s 0 6.0 5.0 40 Depth (m) 4.0 3.0 80 Model Model 1: Model 1m X 1m grid 41 shots/geophones 200 Hz Ricker wavelet Shortest wavelength 20 m

  12. X (m) X (m) X (m) 0 0 0 50 50 50 km/s 0 6.0 5.0 40 Depth (m) 4.0 3.0 80 WI50 Model Tomo50 (ray-based) Model 1: Tomograms

  13. X (m) X (m) X (m) 0 0 0 50 50 50 km/s 0 6.0 5.0 40 Depth (m) 4.0 3.0 80 WIF30 + WI20 Model WIF30 Model 1: Tomograms

  14. X (m) X (m) X (m) 0 0 0 40 40 40 80 80 80 0 Time (sec) 0.1 Tomo50 (ray-based) Model WIF30 + WI20 Model 1: Synthetic CSG

  15. Time (s) Time (s) .01 .01 .04 .04 .025 .025 1. Amplitude 0. -1. Ray-based Traveltime Inversion WIF30 1. Amplitude 0. -1. WI50 WIF30 + WI20 Model 1: One trace

  16. Outline • Motivation • Objective • Theory • Examples • Synthetic Model 1 • Synthetic Model 2 • Conclusions

  17. X (m) 0 90 km/s 0 3.6 3.2 100 Depth (m) 2.8 2.4 210 Model Model 2: Model 3m X 3m grid 18 shots / 32 geophones 60 Hz Ricker wavelet

  18. X (m) X (m) X (m) 0 0 0 90 90 90 km/s 0 3.6 3.2 100 Depth (m) 2.8 2.4 210 WIF20 Model WT10 (wave eq.) Model 2: Tomograms

  19. X (m) X (m) X (m) 0 0 0 90 90 90 km/s 0 3.6 3.2 100 Depth (m) 2.8 2.4 210 WIF20 + WI10 Model WIF20 Model 2: Tomograms

  20. X (m) X (m) 0 0 0 100 100 100 200 200 200 X (m) 0 0.1 Time (sec) WT10 Model WIF20 Model 2: Synthetic CSG

  21. Time (s) .04 .12 .08 1. Amplitude 0. -1. Wave Eq. Traveltime (WT) 10 iterations 1. Amplitude 0. -1. WIF20 Model 2: One Trace

  22. Outline • Motivation • Objective • Theory • Examples • Synthetic Model 1 • Synthetic Model 2 • Conclusions

  23. WI vs. Traveltime Inversion: WIF + WI vs. WI: Conclusions • Higher resolution tomograms; • More sensitive to initial model. • Less sensitive to initial model.

  24. Future Work • Test on 2-D field data

  25. Acknowledgements • I am grateful for the financial • support from the members of • the 2001 UTAM consortium.