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Waveform Inversion for Crosswell Data. M. Zhou. Geology and Geophysics Department University of Utah. Outline. Motivation Objective Theory Examples Synthetic Model 1 Synthetic Model 2 Conclusions. Motivation. High resolution 2 m by 2 m.
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Waveform Inversion for Crosswell Data M. Zhou Geology and Geophysics Department University of Utah
Outline • Motivation • Objective • Theory • Examples • Synthetic Model 1 • Synthetic Model 2 • Conclusions
Motivation • High resolution 2 m by 2 m • Analyses of lithology
Outline • Motivation • Objective • Theory • Examples • Synthetic Model 1 • Synthetic Model 2 • Conclusions
Objective • High resolution tomogram
fast, insensitive to initial model low resolution (high freq. approx.) high resolution slow, sensitive to initial model Traveltime vs. Waveform • Traveltime Inversion • Waveform Inversion
Traveltime • Waveform • Initial model • High resolution Objective • + • provide initil model
Outline • Motivation • Objective • Theory • Examples • Synthetic Model 1 • Synthetic Model 2 • Conclusions
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 = *
Outline • Motivation • Objective • Theory • Examples • Synthetic Model 1 • Synthetic Model 2 • Conclusions
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
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
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
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
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
Outline • Motivation • Objective • Theory • Examples • Synthetic Model 1 • Synthetic Model 2 • Conclusions
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
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
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
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
Time (s) .04 .12 .08 1. Amplitude 0. -1. Wave Eq. Traveltime (WT) 10 iterations 1. Amplitude 0. -1. WIF20 Model 2: One Trace
Outline • Motivation • Objective • Theory • Examples • Synthetic Model 1 • Synthetic Model 2 • Conclusions
WI vs. Traveltime Inversion: WIF + WI vs. WI: Conclusions • Higher resolution tomograms; • More sensitive to initial model. • Less sensitive to initial model.
Future Work • Test on 2-D field data
Acknowledgements • I am grateful for the financial • support from the members of • the 2001 UTAM consortium.