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

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

3 Scatterpoint T 0, z Scatterpoint CSP

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

7 DSR

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9 Pseudo depth

10 DSR

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14 Prestack volume

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

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

17 Flat reflector - Cheops pyramid h t x

18 Dipping reflector-Cheops pyramid h t x

19 Shuang Sun Prestack migration aperture Fresnel zone AVO

20 Prestack incidence angle

21 Fresnel zone – zero-offset

22 Fresnel zone – offset

23 h t x

24 Migration amplitude vs aperture Twice Fresnel zone

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

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

27 CMP Super gather

28 CSP gather

 Actual  CMP  CSP

30 CMP Super gather

31 CSP gather

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33 Marco Perez Gridded anisotropic traveltimes Tomographic velocity estimation

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

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

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

37 Anisotropic traveltimes Anisotropic Isotropic

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

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

40 “Cheops pyramid”??? Converted wave

41 Prestack incidence angle

42 “Zoeppritz” P-S amplitudes

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

44 Matched filter Conventional EOM stacks

45 Inversion and transpose Inversion Transpose Matched filtering

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47 1D convolution

48 Matrix convolution

49 Multiple cross-correlations

50 Cross-correlations

51 Auto-correlations: Identity matrix

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

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

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

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