2. 1 Prestack migrations to inversion John C. Bancroft CREWES 20 November 2001

3. 2 EOM Basics: Scatterpoint, RMS, Cheops Specular reflections Reflection angles Anisotropy: estimation modelling

4. 3 Scatterpoint T 0, z Scatterpoint CSP

5. 4

6. 5

7. 6 Scatterpoint reflection T 0, z Scatterpoint TrTr TsTs x h h CSP R CMP S

8. 7 DSR

9. 8

10. 9 Pseudo depth

11. 10 DSR

12. 11

13. 12

14. 13

15. 14 Prestack volume

16. 15 Scatterpoint reflection T 0, z Scatterpoint TrTr TsTs x h h CSP R CMP S DSR

17. 16 Cheops pyramid P-P h x t Scatter- point

18. 17 Flat reflector - Cheops pyramid h t x

19. 18 Dipping reflector-Cheops pyramid h t x

20. 19 Shuang Sun Prestack migration aperture Fresnel zone AVO

21. 20 Prestack incidence angle

22. 21 Fresnel zone – zero-offset

23. 22 Fresnel zone – offset

24. 23 h t x

25. 24 Migration amplitude vs aperture Twice Fresnel zone

26. 25 Pavan Elapavuluri Estimate anisotropic parameters Seismic vs well-log velocities CMP gathers vs CSP gathers

27. 26 Anisotropy estimation Thompsen parameters (1986) Haase (1998) Half offset less than depth

28. 27 CMP Super gather

29. 28 CSP gather

30. 29 0.20 0.26 0.19 0.25 0.11 0.22 0.30 0.24 0.28 0.10 0.15 0.09 0.15 0.17 0.20 0.24 0.20 0.25 0.29 0.24 0.30 0.28 0.31  Actual  CMP  CSP

31. 30 CMP Super gather

32. 31 CSP gather

33. 32

34. 33 Marco Perez Gridded anisotropic traveltimes Tomographic velocity estimation

35. 34   Isotropic   Anisotropic Phase velocity Group velocity Anisotropic velocities

36. 35 h t 2 t 0 t 1 (t 2 -t 0 )  h t 2 t 0 t 1 2 -t 0 )  Three point projection

37. 36  1  3 t 0 t 1 t 2 t 3 Interpolated points  1  3 t 0 t 1 t 2 t 3 Linear projection

38. 37 Anisotropic traveltimes Anisotropic Isotropic

39. 38 Jeff Beckett Matched filters Prestack converted wave migration Maximize SNR of image

40. 39 Matched filters Signal detection in noise Cross-correlate with wavelet Event defined by zero-phase wavelet Maximize signal Band-limited noise

41. 40 “Cheops pyramid”??? Converted wave

42. 41 Prestack incidence angle

43. 42 “Zoeppritz” P-S amplitudes

44. 43 Time (s) 1 0 Example Shot Record Noisy P-S source record

45. 44 Matched filter Conventional EOM stacks

46. 45 Inversion and transpose Inversion Transpose Matched filtering

47. 46

48. 47 1D convolution

49. 48 Matrix convolution

50. 49 Multiple cross-correlations

51. 50 Cross-correlations

52. 51 Auto-correlations: Identity matrix

53. 52

54. 53 w n,m T s n T rmrm = Matched filter

55. 54 Many inverse processes are transposes Transpose is equivalent to a matched filter Kirchhoff migration tends to a transpose process

56. 55 That’s all folks Thanks to all the sponsoring companies

57. 56