1. paul@sep.stanford.edu Analytical image perturbations for wave-equation migration velocity analysis Paul Sava & Biondo Biondi Stanford University

2. paul@sep.stanford.edu Wave-equation MVA (WEMVA) Wavefield-based MVA method Closely related to –Wave-equation migration –Wave-equation tomography Benefits –Finite-frequency –Multipathing –Hi resolution

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

4. paul@sep.stanford.edu Outline 1.WEMVA review 2.Image perturbation 3.Field data example

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

6. paul@sep.stanford.edu Born approximation

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

8. paul@sep.stanford.edu Slowness backprojection slowness perturbation image perturbation slowness perturbation image perturbation

9. paul@sep.stanford.edu MVA information Traveltime MVAWave-equation MVA Offset focusing (flat gathers) Spatial focusing Frequency redundancy  z  z xx

10. paul@sep.stanford.edu Outline 1.WEMVA review 2.Image perturbation 3.Field data example

11. 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

12. paul@sep.stanford.edu Prestack Stolt residual migration Background image R 1 Velocity ratio  Image perturbation  RR

13. paul@sep.stanford.edu Incorrect velocity Correct velocity Zero offset image Angle gathers Synthetic model

14. paul@sep.stanford.edu Residual migration: the problem

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

16. paul@sep.stanford.edu Background image Zero offset image Angle gathers Background image

17. paul@sep.stanford.edu Differential image Zero offset image Angle gathers

18. paul@sep.stanford.edu Image to slowness perturbation Slowness perturbation Image perturbation

19. paul@sep.stanford.edu Image comparison Updated slowness Correct slowness Zero offset image slowness

20. paul@sep.stanford.edu Outline 1.WEMVA review 2.Image perturbation 3.Field data example

21. paul@sep.stanford.edu Field data example North Sea –Salt environment –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

22. paul@sep.stanford.edu locationdepth Zero offset image Angle gathers Background slowness Background image

23. paul@sep.stanford.edu depth velocity ratio Semblance Angle-gathers

24. paul@sep.stanford.edu locationdepth Zero offset image Background image location “Ratio” map

25. paul@sep.stanford.edu locationdepthlocation Zero offset image Background image Image perturbation

26. paul@sep.stanford.edu locationdepthlocation Zero offset image Image perturbation Slowness perturbation

27. paul@sep.stanford.edu locationdepth Zero offset image Angle gathers Background slowness Background image

28. paul@sep.stanford.edu locationdepth Zero offset image Angle gathers Updated slowness Updated image

29. paul@sep.stanford.edu depth location Angle gathers “Correct” slowness Zero offset image “Correct” image

30. paul@sep.stanford.edu Summary Wave-equation MVA –Finite frequency –Multipathing –Hi resolution –Image space objective function Image perturbation –From prestack Stolt residual migration –Differential method –Compliant with the Born approximation