Wavefield Extrapolation for Migration and Velocity Analysis

1. paul.sava@stanford.edu

2. Migration and velocity analysis by wavefield extrapolation Paul Sava paul.sava@stanford.edu

3. Complex geology distance depth paul.sava@stanford.edu

4. Complex illumination distance depth paul.sava@stanford.edu

5. Complex wavefields distance depth paul.sava@stanford.edu

6. Imaging methods overview paul.sava@stanford.edu

7. Focus of my thesis paul.sava@stanford.edu

8. Imaging by wavefield extrapolation distance distance depth paul.sava@stanford.edu

9. Outline Wave-equation migration velocity analysis Operator Image perturbation Example Riemannian wavefield extrapolation paul.sava@stanford.edu

10. The problem distance depth paul.sava@stanford.edu

11. Objective function distance WEMVA operator Image perturbation Slowness perturbation depth paul.sava@stanford.edu

12. Traveltime MVA t: traveltime s: slowness T: operator Wave-equation MVA I: image s: slowness L: operator Comparison of MVA methods paul.sava@stanford.edu

13. Outline Wave-equation migration velocity analysis Operator Image perturbation Example Riemannian wavefield extrapolation paul.sava@stanford.edu

14. Requirements WEMVA operator • Image-slowness relation • Wavefield extrapolation • Use the entire image • Linear operator • Cost-effective optimization paul.sava@stanford.edu

15. Downward continuation WEMVA operator z z+Dz Phase-shift operator paul.sava@stanford.edu

16. Downward continuation linearization WEMVA operator z z+Dz linear nonlinear paul.sava@stanford.edu

17. Scattering operator WEMVA operator Wavefield perturbation Slowness perturbation linear nonlinear paul.sava@stanford.edu

18. WE MVA operator WEMVA operator Image perturbation Slowness perturbation paul.sava@stanford.edu

19. WE MVA operator example WEMVA operator Slowness perturbation Slowness perturbation Background slowness Background wavefield Forward operator Adjoint operator Wavefield perturbation Wavefield perturbation paul.sava@stanford.edu

20. WE MVA operator example WEMVA operator Forward operator Adjoint operator paul.sava@stanford.edu

21. Traveltime MVA Ray paths Infinite frequency band Unstable for sharp contrasts Large shadow zones Wave-equation MVA Wave paths Finite frequency band Stable for sharp contrasts Small shadow zones Sensitivity kernels Sensitivity kernels paul.sava@stanford.edu

22. Wavepaths gallery Sensitivity kernels distance depth paul.sava@stanford.edu

23. Multiple wavepaths Sensitivity kernels distance depth paul.sava@stanford.edu

24. Frequency dependence Sensitivity kernels distance depth paul.sava@stanford.edu

25. Outline Wave-equation migration velocity analysis Operator Image perturbation Example Riemannian wavefield extrapolation paul.sava@stanford.edu

26. Requirements Image perturbation • Use image information • Fast and robust • Interpretive control • Consistent with the operator paul.sava@stanford.edu

27. Focusing information Image perturbation distance depth paul.sava@stanford.edu

28. Moveout information Image perturbation distance angle depth paul.sava@stanford.edu

29. Residual migration Image perturbation distance angle depth Residual migration operator paul.sava@stanford.edu

30. Residual migration linearization Image perturbation distance angle depth nonlinear linear paul.sava@stanford.edu

31. Linear residual migration operator Image perturbation Image perturbation Ratio perturbation nonlinear linear paul.sava@stanford.edu

32. WEMVA algorithm Construct an image perturbation Invert for a slowness perturbation paul.sava@stanford.edu

33. WEMVA flowchart Slowness Slowness perturbation Data Image Image perturbation paul.sava@stanford.edu

34. Outline Wave-equation migration velocity analysis Operator Image perturbation Example Riemannian wavefield extrapolation paul.sava@stanford.edu

35. Background slowness WEMVA example Slowness Slowness perturbation Data Image perturbation Image paul.sava@stanford.edu

36. Background image WEMVA example Slowness Slowness perturbation Data Image perturbation Image paul.sava@stanford.edu

37. Background image WEMVA example Slowness Slowness perturbation Data Image perturbation Image paul.sava@stanford.edu

38. Residual migration WEMVA example Slowness Slowness perturbation Data Image perturbation Image paul.sava@stanford.edu

39. Residual migration WEMVA example Slowness Slowness perturbation Data Image perturbation Image paul.sava@stanford.edu

40. Image perturbation WEMVA example Slowness Slowness perturbation Data Image perturbation Image paul.sava@stanford.edu

41. Slowness perturbation WEMVA example Slowness Slowness perturbation Data Image perturbation Image paul.sava@stanford.edu

42. Slowness update WEMVA example Slowness Slowness perturbation Data Image perturbation Image paul.sava@stanford.edu

43. Image update WEMVA example Slowness Slowness perturbation Data Image perturbation Image paul.sava@stanford.edu

44. Image quality WEMVA example Slowness Slowness perturbation Data Image perturbation Image paul.sava@stanford.edu

45. Outline Wave-equation migration velocity analysis Operator Image perturbation Example Riemannian wavefield extrapolation paul.sava@stanford.edu

46. Downward continuation Wavefield extrapolation distance depth paul.sava@stanford.edu

47. Downward continuation limitation Wavefield extrapolation distance depth paul.sava@stanford.edu

48. Downward continuation limitation Wavefield extrapolation distance depth paul.sava@stanford.edu

49. Riemannian wavefield extrapolation Wavefield extrapolation • One-way wavefield extrapolation • Generalized coordinate system • Based on wave propagation • Based on acquisition geometry • … • Imaging applications: • Overturning waves • Steep dips • … paul.sava@stanford.edu

50. Space-domain: velocity Wavefield extrapolation distance depth paul.sava@stanford.edu