1. paul@sep.stanford.edu Wave-equation migration velocity analysis Paul Sava* Stanford University Biondo Biondi Stanford University

2. paul@sep.stanford.edu Imaging=MVA+Migration Migration wavefield based Migration velocity analysis (MVA) traveltime based Compatible migration and MVA methods

3. paul@sep.stanford.edu Imaging: the “big picture” Kirchhoff migration traveltime tomography wavefronts wave-equation migration wave-equation MVA (WEMVA) wavefields

4. paul@sep.stanford.edu Agenda Theoretical background WEMVA methodology Scattering Imaging Image perturbations Wavefield extrapolation Born linearization WEMVA applications

5. paul@sep.stanford.edu Wavefield scattering

6. paul@sep.stanford.edu Wavefield scattering

7. paul@sep.stanford.edu Scattered wavefield Medium perturbation Wavefield perturbation

8. paul@sep.stanford.edu Agenda Theoretical background WEMVA methodology Scattering Imaging Image perturbations Wavefield extrapolation Born linearization WEMVA applications

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

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

11. paul@sep.stanford.edu Wave-equation MVA: Objective Velocity perturbation Image perturbation slowness perturbation (unknown) WEMVA operator image perturbation (known) location depth location depth

12. paul@sep.stanford.edu –migrated images –moveout and focusing –amplitudes –parabolic wave equation –multipathing –slow –picked traveltimes –moveout –eikonal equation –fast Comparison: WEMVA vs TT Wave-equation MVATraveltime tomography

13. paul@sep.stanford.edu –migrated images –interpretive control –parabolic wave equation –slow –recorded data –two-way wave equation –slow Comparison: WEMVA vs WET Wave-equation MVAWave-equation tomography

14. paul@sep.stanford.edu Agenda Theoretical background WEMVA methodology Scattering Imaging Image perturbations Wavefield extrapolation Born linearization WEMVA applications

15. paul@sep.stanford.edu Image perturbations FocusingFlatness Residual process: moveout migration focusing slowness perturbation (unknown) WEMVA operator image perturbation (known) location depth angle

16. paul@sep.stanford.edu Image perturbations

17. paul@sep.stanford.edu Agenda Theoretical background WEMVA methodology Scattering Imaging Image perturbations Wavefield extrapolation Born linearization WEMVA applications

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

19. paul@sep.stanford.edu “Wave-equation” migration

20. paul@sep.stanford.edu Slowness perturbation

21. paul@sep.stanford.edu slowness perturbation background wavefield perturbation Wavefield perturbation

22. paul@sep.stanford.edu Agenda Theoretical background WEMVA methodology Scattering Imaging Image perturbations Wavefield extrapolation Born linearization WEMVA applications

23. paul@sep.stanford.edu Born approximation Small perturbations! Born linearization Non-linear WEMVA slowness perturbation (unknown) WEMVA operator image perturbation (known) Unit circle

24. paul@sep.stanford.edu Agenda Theoretical background WEMVA methodology Scattering Imaging Image perturbations Wavefield extrapolation Born linearization WEMVA applications

25. paul@sep.stanford.edu Applications “Image perturbation” image difference image “differential” Examples –Structural imaging –Overpressure prediction –4-D seismic monitoring –Diffraction focusing MVA

26. paul@sep.stanford.edu Application 1: Structural imaging Velocity analysis in complex areas multipathing high velocity contrast Full images vs. picked events Spatial focusing + offset focusing Traveltimes & amplitudes

27. paul@sep.stanford.edu Structural imaging: methodology DataImageVelocity Image perturbation

28. paul@sep.stanford.edu Location [km] Depth [km] Location [km] Depth [km] Location [km] Depth [km] Location [km] Depth [km] Structural imaging: example

29. paul@sep.stanford.edu Application 2: Overpressure Overpressure zone Complicated salt Complicated propagation

30. paul@sep.stanford.edu Overpressure: motivation Pressure creates time/moveout changes cannot be picked with enough accuracy Complicated overburden ray-based methods fail

31. paul@sep.stanford.edu Overpressure: methodology DataImageVelocity Image perturbation

32. paul@sep.stanford.edu Overpressure: proof of concept

33. paul@sep.stanford.edu Application 3: 4D monitoring Small traveltime changes cannot be picked with enough accuracy Amplitude variations ignored by traveltime methods Cumulative phase and amplitude effects mask deeper effects

34. paul@sep.stanford.edu 4D monitoring: methodology DataImageVelocity 4D difference data

35. paul@sep.stanford.edu 4D monitoring: proof of concept

36. paul@sep.stanford.edu Application 4: Focusing MVA Moveout information missing or hard to use Focusing information ignored by moveout / traveltime based methods focusing moveout

37. paul@sep.stanford.edu Focusing MVA: methodology DataImageVelocity Image perturbation

38. paul@sep.stanford.edu Focusing MVA: proof of concept

39. paul@sep.stanford.edu Agenda Theoretical background WEMVA methodology Scattering Imaging Image perturbations Wavefield extrapolation Born linearization WEMVA applications

40. paul@sep.stanford.edu WEMVA summary Methodology –“wave-equation” –image optimization focusing and moveouts –interpretive control Applications –any image perturbation repeated images over time optimized and reference images