1. paul.sava@stanford.edu Wave-equation migration velocity analysis Paul Sava* Stanford University Biondo Biondi Stanford University Sergey Fomel UT Austin

2. paul.sava@stanford.edu The problem Depth imaging –image: migration –velocity: migration velocity analysis Migration and MVA are inseparable “Everyhing depends on v(x,y,z)” »JF Claerbout, 1999

3. paul.sava@stanford.edu An approximation

4. paul.sava@stanford.edu A better approximation

5. paul.sava@stanford.edu In the “big picture” Kirchhoff migration traveltime tomography wavefronts wave-equation migration wave-equation MVA (WEMVA) wavefields

6. paul.sava@stanford.edu Agenda Theoretical background WEMVA methodology Scattering Imaging Non-linear operator Linear operator Image perturbation WEMVA applications

7. paul.sava@stanford.edu Wavefield scattering

8. paul.sava@stanford.edu Wavefield scattering

9. paul.sava@stanford.edu Scattered wavefield Medium perturbation Wavefield perturbation

10. paul.sava@stanford.edu Agenda Theoretical background WEMVA methodology Scattering Imaging Non-linear operator Linear operator Image perturbation WEMVA applications

11. paul.sava@stanford.edu Imaging: Correct velocity Background velocity Migrated image Reflectivity model What the data tell us...What migration does... location depth location depth

12. paul.sava@stanford.edu Imaging: Incorrect velocity Perturbed velocity Migrated image Reflectivity model What the data tell us...What migration does... location depth location depth

13. paul.sava@stanford.edu WEMVA objective Velocity perturbation Image perturbation slowness perturbation (unknown) WEMVA operator image perturbation (known) location depth location depth

14. paul.sava@stanford.edu Agenda Theoretical background WEMVA methodology Scattering Imaging Non-linear operator Linear operator Image perturbation WEMVA applications

15. paul.sava@stanford.edu Double Square-Root Equation Fourier Finite Difference Generalized Screen Propagator Wavefield extrapolation

16. paul.sava@stanford.edu Slowness perturbation

17. paul.sava@stanford.edu slowness perturbation background wavefield perturbation Wavefield perturbation

18. paul.sava@stanford.edu Agenda Theoretical background WEMVA methodology Scattering Imaging Non-linear operator Linear operator Image perturbation WEMVA applications

19. paul.sava@stanford.edu Linearizations Unit circle Born approximation

20. paul.sava@stanford.edu Linearizations Unit circle

21. paul.sava@stanford.edu Linearizations Unit circle

22. paul.sava@stanford.edu Linear WEMVA slowness perturbation (unknown) WEMVA operator image perturbation (known)

23. paul.sava@stanford.edu Agenda Theoretical background WEMVA methodology Scattering Imaging Non-linear operator Linear operator Image perturbation WEMVA applications

24. paul.sava@stanford.edu Correct velocity

25. paul.sava@stanford.edu Incorrect velocity

26. paul.sava@stanford.edu Image perturbation

27. paul.sava@stanford.edu Failure!

28. paul.sava@stanford.edu Small phase limitation

29. paul.sava@stanford.edu What can we do? Define another objective function –e.g. DSO Construct an image perturbation which obeys the Born approximation...

30. paul.sava@stanford.edu Residual migration

31. paul.sava@stanford.edu Analytical image perturbation Computed analytically Picked from data

32. paul.sava@stanford.edu Analytical image perturbation

33. paul.sava@stanford.edu Image perturbations comparison

34. paul.sava@stanford.edu Slowness perturbations

35. paul.sava@stanford.edu Migrated images

36. paul.sava@stanford.edu Migrated images: angle gathers

37. paul.sava@stanford.edu Agenda Theoretical background WEMVA methodology Scattering Imaging Non-linear operator Linear operator Image perturbation WEMVA applications

38. paul.sava@stanford.edu Other applications 4-D seismic monitoring –image perturbations over time –no need to construct Focusing MVA –zero offset data

39. paul.sava@stanford.edu 4D seismic monitoring

40. paul.sava@stanford.edu 4D seismic monitoring

41. paul.sava@stanford.edu 4D seismic monitoring

42. paul.sava@stanford.edu Focusing MVA Incorrect image Correct image

43. paul.sava@stanford.edu Focusing MVA

44. paul.sava@stanford.edu Focusing MVA

45. paul.sava@stanford.edu Focusing MVA

46. paul.sava@stanford.edu Focusing MVA

47. paul.sava@stanford.edu Focusing MVA

48. paul.sava@stanford.edu Focusing MVA

49. paul.sava@stanford.edu Summary Wave-equation MVA wavefield extrapolation image space objective focusing and moveouts interpretation guided Linearization linear operator construct image perturbations