1. Migration Velocity Analysis 01

2. Outline  Motivation Estimate a more accurate velocity model for migration Tomographic migration velocity analysis 02  Theory  Numerical Results  Conclusions

3. Motivation 03 d = L m m mig = L T d Forward modeling Kirchhoff Migration Function of velocity:L T (s) Inaccurate velocity model m mig = L T d

4. Motivation 04 True velocity model Kirchhoff Migration Image Inaccurate velocity model Kirchhoff Migration Image Goal of MVA: To get a more accurate velocity model Structure error Position error

5. Outline  Motivation Estimate a more accurate velocity model for migration Tomographic Migration Velocity Analysis 05  Theory  Numerical Results  Conclusions

6. Theory 06 The fundamental principle underlying MVA is that the migration image of the same reflector should be the same for different source, when using the correct velocity, so pre-stack common image gather (CIG) provides the information of whether the migration velocity is correct and how far away it is from the true velocity.

7. Theory 07 Common Image Gather ( CIG) different CSGs CSG #1 CSG #2 CSG #3 Point scatterer

8. Theory 08 Common Image Gather ( CIG) Prestack migration s KM of CSG #1 x z x0x0 x z KM of CSG #2 x0x0 x z KM of CSG #3 x0x0 CIG

9. Theory 09 Tomographic MVA xx0x0 z x x0x0 z s z CIG Flat x x0x0 z Correct Velocity x z 2000 m/s x0x0

10. Theory 10 Tomographic MVA Curved Incorrect Velocity 1500 m/s x z x0x0 xx0x0 z s z CIG x x0x0 z z x x0x0

11. Theory 11 Z (km) 1.5 0 Offset (km)1 CIG Z (km) 1.5 0 CIG Offset (km)1 Tomographic MVA Hyperbolic approximation Z h 2 = Z 0 2 + A h 2 picking depth, ZhZh ZhZh Z0Z0 zero-offset depth, Z0Z0 Depth residual reference depth Usually choose Z 0 as Z ref ΔZ = Z h - Z ref Z ref x0x0 h offset, h

12. Theory 12 Tomographic MVA Convert depth residual to time residual x0x0 xsxs xgxg Find the source-receiver pair by ray tracing to obey Snell’s law θ1θ1 θ2θ2 x0x0 xsxs xgxg R reflector with reference depth Z ref R’ reflector with picked depth Z h t’ = L SR’ s + L RG s t = L SR s + L RG s Δt = t’ - t

13. Theory 13 For a small slowness perturbation traveltime, raypath operator, background slowness. t = L s t L s Δs Δt = t’-t 0 = LΔs = L(s’-s 0 ) Parameterize the model as a grid of cells traveltime residual for the raypath, slowness purturbation in grid cell Δt i = Σ Δs j Δl ij n j=1 Δt i i Δs j j Update the slowness with a steepest descent method Back projectalong the raypaths to get Δt i Δs j s j (k+1) = s j (k+1) – α Δs j (k+1) Tomographic MVA Update the slowness

14. Theory 14 Misfit function Iteration will stop when all curved events in CIG are flatten. picked depth residual for offsetin CIGof the iteration Tomographic MVA F misfit = Σ Σ (Δz ij ) 2 i=1 j=1 m n (k) Δz ij j i k (k)

15. 15 Migration velocity model s 0 Theory Predict travel time by eikonal solver Pre-stack KM, form CIGs Pick the reference depth residual (usually zero-offset) Find ray paths connecting the reflector to both S and R positionsConvert depth residual to travel time residualUpdate velocity model by back projecting the traveltime residuals along the raypaths. Work Flow: Migration velocity model s k Pick the depth residual automatically Observed data All events are flattened? Y MVA finished ! N

16. Outline  Motivation Estimate a more accurate velocity model for migration Tomographic migration velocity analysis 16  Theory  Numerical Results  Conclusions

17. Numerical Results 17 2D Synthetic Model KM image CIG True velocity model H. Sun. 1999

18. Numerical Results 18 2D Synthetic Model H. Sun. 1999 Homogeneous velocity model KM image CIG

19. Numerical Results 19 2D Synthetic Model H. Sun. 1999 Final updated velocity model KM image CIG

20. Initial Migration Velocity 0 0 18 1.5 Horizontal Distance (km) Depth (km) 2.1 1.5 (km /s) (km /s)

21. KM Image with Initial Velocity 0 0 18 km 1.5 Depth (km) 0 1.5 KMVA Velocity Changes in the 1st Iteration 50 0 (m /s) (m /s)

22. KM Image with Initial Velocity KM Image with Updated Velocity 9 km 1260 Depth (m) 2 km 1070 1260 Depth (m) 1070

23. KMVA CIGs with Initial Velocity 0 1.5 Depth (km) KMVA CIGs with Updated Velocity

24. 0 0 18 km 1.5 Depth (km) 0 1.5 KMVA Velocity Changes in the 1st Iteration (CPU=6) 50 0 (m /s) (m /s) WMVA Velocity Changes in the 1st Iteration (CPU=1) 50 0 (m /s) (m /s)

25. WM Image with Initial Velocity WM Image with Updated Velocity 9 km 1260 Depth (m) 2 km 1070 1260 Depth (m) 1070

26. WMVA CIGs with Initial Velocity 0 1.5 Depth (km) WMVA CIGs with Updated Velocity

27. KM Image with Initial Velocity 9 km 1260 Depth (m) 2 km 1070 KM Image with KMVA Updated Velocity 1260 Depth (m) 1070 KM Image with WMVA Updated Velocity 1260 Depth (m) 1070

28. Outline  Motivation Estimate a more accurate velocity model for migration Tomographic migration velocity analysis 26  Theory  Numerical Results  Conclusions

29. 27 Pre-stack migration with inaccurate velocity can bring curved events in CIGs, which provides the opportunity for migration velocity analysis. Iterative tomographic MVA can estimate better migration velocity and improve the migration image. Conclusions Question: what are the advantages and disadvantages of migration velocity analysis compared to velocity estimation in data domain ?

30. Numerical Results 20 2D Field Data H. Sun. 1999 0 0 18 1.5 Initial migration velocity from NMO Depth (km) 2.1 1.5 (km /s) (km /s) Horizontal distance (km)

31. Numerical Results 21 2D Field Data H. Sun. 1999 0 0 18 1.5 KM image with the initial velocity Depth (km) Horizontal distance (km)

32. Numerical Results 22 2D Field Data H. Sun. 1999 0 1.5 KM CIGs with the initial velocity Depth (km) 1.2

33. Numerical Results 23 KM Image with Initial Velocity 0 0 18 km 1.5 Depth (km) 0 1.5 KM Image with Updated Velocity 18

34. Numerical Results 24 KM Image with Initial Velocity KM Image with Updated Velocity 9 km 1260 Depth (m) 2 km 1070 1260 Depth (m) 1070

35. Numerical Results 25 KMVA CIGs with Initial Velocity 0 1.5 Depth (km) KMVA CIGs with Updated Velocity