1. paul@sep.stanford.edu Wave-equation MVA by inversion of differential image perturbations Paul Sava & Biondo Biondi Stanford University SEP

2. paul@sep.stanford.edu Motivation

3. paul@sep.stanford.edu Wave-equation MVA (WEMVA) Band-limited Multi-pathing Resolution Born approximation –small anomaly Rytov approximation –phase unwrapping

4. paul@sep.stanford.edu Wave-equation MVA (WEMVA) WE tomography –data space WE MVA –image space

5. paul@sep.stanford.edu Outline 1.WEMVA overview 2.Born image perturbation 3.Differential image perturbation 4.Example

6. paul@sep.stanford.edu A tomography problem Traveltime MVA Wave-equation tomography Wave-equation MVA qq  t traveltime  d data  R image L ray fieldwavefield

7. paul@sep.stanford.edu WEMVA: main idea

8. paul@sep.stanford.edu Born approximation

9. paul@sep.stanford.edu WEMVA: objective function slowness perturbation image perturbation slowness perturbation (unknown) Linear WEMVA operator image perturbation (known)

10. paul@sep.stanford.edu WEMVA: objective function Traveltime MVA Wave-equation tomography Wave-equation MVA tt dd RR

11. paul@sep.stanford.edu Fat ray: GOM example

12. paul@sep.stanford.edu Outline 1.WEMVA overview 2.Born image perturbation 3.Differential image perturbation 4.Example

13. paul@sep.stanford.edu “Data” estimate Traveltime MVA Wave-equation tomography Wave-equation MVA tt dd RR ray tracing data modeling residual migration

14. paul@sep.stanford.edu Prestack Stolt residual migration Background image R 0 Velocity ratio   RR0R0

15. paul@sep.stanford.edu Prestack Stolt residual migration Image perturbation  RR0R0

16. paul@sep.stanford.edu Born approximation

17. paul@sep.stanford.edu Residual migration: the problem Correct velocityIncorrect velocity Zero offset image Angle gathers Zero offset image Angle gathers

18. paul@sep.stanford.edu Born approximation

19. paul@sep.stanford.edu Outline 1.WEMVA overview 2.Born image perturbation 3.Differential image perturbation 4.Example

20. paul@sep.stanford.edu Differential image perturbation Image difference Image differential ComputedMeasured

21. paul@sep.stanford.edu Differential image perturbation RR RR  R 

22. paul@sep.stanford.edu Phase perturbation        

23. paul@sep.stanford.edu Differential image perturbation

24. paul@sep.stanford.edu Born approximation

25. paul@sep.stanford.edu Example: background image Zero offset image Angle gathers Background image

26. paul@sep.stanford.edu Example: differential image Zero offset image Angle gathers Differential image

27. paul@sep.stanford.edu Example: slowness inversion Slowness perturbation Image perturbation

28. paul@sep.stanford.edu Example: updated image Updated slowness Updated image

29. paul@sep.stanford.edu Example: correct image Correct slowness Correct image

30. paul@sep.stanford.edu Outline 1.WEMVA overview 2.Born image perturbation 3.Differential image perturbation 4.Example

31. paul@sep.stanford.edu Field data example North Sea –Salt environment –Subset –One non-linear iteration Migration (background image) Residual migration (image perturbation) Slowness inversion (slowness perturbation) Slowness update (updated slowness) Re-migration (updated image) location depth

32. paul@sep.stanford.edu locationdepth

33. paul@sep.stanford.edu depth velocity ratio

34. paul@sep.stanford.edu locationdepth

35. paul@sep.stanford.edu locationdepthlocation

36. paul@sep.stanford.edu locationdepthlocation

37. paul@sep.stanford.edu locationdepth

38. paul@sep.stanford.edu locationdepth

39. paul@sep.stanford.edu Summary MVA –Wavefield extrapolation methods –Born linearization –Differential image perturbations Key points –Band-limited (sharp velocity contrasts) –Multi-pathing (complicated wavefields) –Resolution (frequency redundancy)

40. paul@sep.stanford.edu

41. MVA information (a) Traveltime MVAWave-equation MVA Offset focusing (flat ADCIG)  z  z xx

42. paul@sep.stanford.edu MVA information (b) Traveltime MVAWave-equation MVA Offset focusing (flat ADCIG) Spatial focusing  z  z xx

43. paul@sep.stanford.edu MVA information (c) Traveltime MVAWave-equation MVA Offset focusing (flat ADCIG) Spatial focusing Frequency redundancy    

44. paul@sep.stanford.edu     WEMVA cost reduction Full image –Offset focusing –Spatial focusing –Frequency Normal incidence image –Spatial focusing –“fat” rays

45. paul@sep.stanford.edu Another example

46. paul@sep.stanford.edu Example: correct model Zero offset image Angle gathers

47. paul@sep.stanford.edu Example: background model Zero offset image Angle gathers

48. paul@sep.stanford.edu Example: correct perturbation Zero offset image Angle gathers

49. paul@sep.stanford.edu Example: differential perturbation Zero offset image Angle gathers

50. paul@sep.stanford.edu Example: perturbations comparison Differential Difference Correct

51. paul@sep.stanford.edu Example: differential perturbation Zero offset image Angle gathers

52. paul@sep.stanford.edu Example: difference perturbation Zero offset image Angle gathers

53. paul@sep.stanford.edu Example: updated model Zero offset image Angle gathers

54. paul@sep.stanford.edu Example: correct model Zero offset image Angle gathers