1. Wavepath Migration versus Kirchhoff Migration: 3-D Prestack Examples H. Sun and G. T. Schuster University of Utah

2. Outline Problems in Kirchhoff Migration Problems in Kirchhoff Migration Wavepath Migration Wavepath Migration Implementation of WM Implementation of WM Numerical Results Numerical Results Conclusions Conclusions

3. Forward Modeling ( Xg, 0 ) ( Xs, 0 ) Specular Ray

4. 3D Kirchhoff Migration ( Xg, 0 ) ( Xs, 0 ) 3D Fat Ellipsoid

5. 3-D KM of a Single Trace RS A A B B C C

6. Problems in Kirchhoff Migration Traveltime Information Where Was Wave Reflected ? The Whole Fat Ellipsoid ! Problem 1 Strong Far-Field Migration Artifact Problem 2 Slow for 3-D Iterative Velocity Analysis

7. Outline Problems in Kirchhoff Migration Problems in Kirchhoff Migration Wavepath Migration Wavepath Migration Implementation of WM Implementation of WM Numerical Results Numerical Results Conclusions Conclusions

8. 3D Wavepath Migration ( Xg, 0 ) Fat Ray FatEllipsoid KM : Fat Ellipsoid, O(N ) WM: Hatching Area, O(N ) 31.5

9. 3-D WM of a Single Trace RS A B C A B C

10. Traveltime + Ray Direction True Reflection point Small Migration Aperture FewerArtifactsLessExpensive Wavepath Migration

11. To Achieve Higher CPU Efficiency To Achieve Higher CPU Efficiency Compared to 3-D KM Compared to 3-D KM To Generate Comparable or Better To Generate Comparable or Better Image Quality than 3-D KM Image Quality than 3-D KM Key Goals of 3-D WM

12. Related References Time-Map Migration Time-Map Migration Sherrif & Geldhart (1985) Sherrif & Geldhart (1985) Wave Equation Tomography Wave Equation Tomography Woodward & Rocca (1988) Woodward & Rocca (1988) Gaussian Beam Migration Gaussian Beam Migration Ross Hill (1990) Ross Hill (1990) Kirchhoff Beam Migration Kirchhoff Beam Migration Yonghe Sun et al., (1999) Yonghe Sun et al., (1999)

13. Outline Problems in Kirchhoff Migration Problems in Kirchhoff Migration Wavepath Migration Wavepath Migration Implementation of WM Implementation of WM Numerical Results Numerical Results Conclusions Conclusions

14. Key Steps in WM Raypath RSRaypath Fresnel Zone Migration Quasi-ellipsoidQuasi-ellipsoid

15. Outline Problems in Kirchhoff Migration Problems in Kirchhoff Migration Wavepath Migration Wavepath Migration Implementation of WM Implementation of WM Numerical Results Numerical Results 3-D Prestack Point Scatterer Data 3-D Prestack Point Scatterer Data 3-D Prestack SEG/EAGE Salt Data 3-D Prestack SEG/EAGE Salt Data 3-D Prestack West Texas Field Data 3-D Prestack West Texas Field Data Conclusions Conclusions

16. 3-D Prestack KM Point Scatterer Response Reflectivity Y Offset (km) X Offset (km) 1 -0.5 0 1 Reflectivity Y Offset (km) X Offset (km) 1 -0.01 0 0.02 Reflectivity Y Offset (km) X Offset (km) 1 -0.05 0 0.1 Reflectivity Y Offset (km) X Offset (km) 1 -0.2 0 0.4 1 11 1 Z0 Z0-1 Z0-9 Z0+8

17. Reflectivity Y Offset (km) X Offset (km) 1 -0.5 0 1 Reflectivity Y Offset (km) X Offset (km) 1 -0.01 0 0.02 Reflectivity Y Offset (km) X Offset (km) 1 -0.05 0 0.1 Reflectivity Y Offset (km) X Offset (km) 1 -0.2 0 0.4 1 11 1 3-D Prestack WM Point Scatterer Response Z0 Z0-1 Z0-9 Z0+8

18. Outline Problems in Kirchhoff Migration Problems in Kirchhoff Migration Wavepath Migration Wavepath Migration Implementation of WM Implementation of WM Numerical Results Numerical Results 3-D Prestack Point Scatterer Data 3-D Prestack Point Scatterer Data 3-D Prestack SEG/EAGE Salt Data 3-D Prestack SEG/EAGE Salt Data 3-D Prestack West Texas Field Data 3-D Prestack West Texas Field Data Conclusions Conclusions

19. A Common Shot Gather Trace Number 1390 Time (sec) 0 5.0

20. Inline Velocity Model Offset (km) 09.2 Depth (km) 0 3.8 SALT

21. Inline KM (CPU=1) Inline WM (CPU=1/33) Offset (km) 09.2 0 3.8 Depth (km) Offset (km) 09.2

22. Inline KM (CPU=1) Inline WM (CPU=1/170) Offset (km) 09.2 0 3.8 Depth (km) Offset (km) 09.2 (subsample)

23. Zoom Views of Inline Sections Offset: 3~6.5 km, Depth: 0.3~1.8 km WM Model KM SubWM

24. Offset: 1.8~4 km, Depth: 0.6~2.1 km WM Model KM SubWM Zoom Views of Crossline Sections

25. Inline: 1.8~7.2 km, Crossline: 0~4 km WM Model KM SubWM Horizontal Slices (Depth=1.4 km)

26. Outline Problems in Kirchhoff Migration Problems in Kirchhoff Migration Wavepath Migration Wavepath Migration Implementation of WM Implementation of WM Numerical Results Numerical Results 3-D Prestack Point Scatterer Data 3-D Prestack Point Scatterer Data 3-D Prestack SEG/EAGE Salt Data 3-D Prestack SEG/EAGE Salt Data 3-D Prestack West Texas Field Data 3-D Prestack West Texas Field Data Conclusions Conclusions

27. A Common Shot Gather Trace Number 54193 Time (sec) 0 3.4

28. Inline KM (CPU=1) Inline WM (CPU=1/14) Offset (km) 0.44.5 0.8 3.8 Depth (km) Offset (km) 0.44.5

29. Inline KM (CPU=1) Inline WM (CPU=1/50) Offset (km) 0.44.5 0.8 3.8 Depth (km) Offset (km) 0.44.5 (subsample)

30. Crossline KM (CPU=1) Crossline WM (CPU=1/14) Offset (km) 0.33.5 0.8 3.3 Depth (km) Offset (km) 0.33.5

31. Crossline KM (CPU=1) Crossline WM (CPU=1/50) (subsample) Offset (km) 0.33.5 0.8 3.3 Depth (km) Offset (km) 0.33.5

32. Inline: 0~4.6 km, Crossline: 0~3.8 KM (CPU=1) Horizontal Slices (Depth=2.5 km) WM (CPU=1/14) WM (Sub, CPU=1/50)

33. Outline Problems in Kirchhoff Migration Problems in Kirchhoff Migration Wavepath Migration Wavepath Migration Implementation of WM Implementation of WM Numerical Results Numerical Results Conclusions Conclusions

34. Conclusions SEG/EAGE Salt Data SEG/EAGE Salt Data Fewer Migration Artifacts Fewer Migration Artifacts Better for Complex Salt Boundary Better for Complex Salt Boundary Higher Computational Efficiency Higher Computational Efficiency CPU CPU KM: 1 WM: 1/33 KM: 1 WM: 1/33 Subsampled WM: 1/170 Subsampled WM: 1/170

35. Conclusions West Texas Field Data West Texas Field Data Fewer Migration Artifacts Fewer Migration Artifacts Similar Image Quality Similar Image Quality Higher Computational Efficiency Higher Computational Efficiency CPU CPU KM: 1 WM: 1/14 KM: 1 WM: 1/14 Subsampled WM: 1/50 Subsampled WM: 1/50

36. Acknowledgements Acknowledgements We thank UTAM sponsors for their financial support