1. Reduced-Time Migration of Converted Waves David Sheley University of Utah

2. Outline MotivationMotivation Migration TheoryMigration Theory Error AnalysisError Analysis Synthetic Data ResultsSynthetic Data Results Field Data ResultField Data Result Conclusions & Future WorkConclusions & Future Work

3. PP vs PS Transmission Migration Depth Offset 0 Z Receiver Well Source Well X 0

4. PP Reflection Migration X Source Well Receiver WellP P = ? P =? 0 Depth Z 0 Offset

5. Receiver Well Converted Wave Migration Source Well X P PPS PS V p,V s = ? =? 0 Depth Z 0 Offset

6. Outline MotivationMotivation Migration TheoryMigration Theory Error AnalysisError Analysis Synthetic Data ResultsSynthetic Data Results Field Data ResultField Data Result Conclusions & Future WorkConclusions & Future Work

7. Conventional Migration m(r) = S(z g,  sr +  rg )   sr  rg s r g

8. PS Transmission Migration m(r) = S(z g, d sr /V p + d rg /V s )  d sr /V p d rg /V s s g r

9. km/sec6.0 5.0 7.0 Problem Well 0 20 40 60 50 0 Receiver Well Source Depth (m) Offset (m)

10. Reduced-Time Migration Data time shiftData time shift S’(g, t) = S(z g, t +  sg   sg  Observed direct-P time obs obs

11. Depth (m) 0 114 2035 Time (ms) Original Data Depth (m) 0 114 82 Time (s) Shifted Muted Data SP PSPPS S SP Data Shift

12. Reduced-Time Migration Data time shiftData time shift S’(z g, t) = S(z g, t +  sg   sg  Observed direct-P time obs obs Modify the migration equation Modify the migration equation m(r) = S(z g,  sr +  rg -  sg +  sg ) obs calc  calc m(r) = S’(z g,  sr +  rg –  sg ) 

13. Outline MotivationMotivation Migration TheoryMigration Theory Error AnalysisError Analysis Synthetic Data ResultsSynthetic Data Results Field Data ResultField Data Result Conclusions & Future WorkConclusions & Future Work

14. Error Analysis -- CWM Single traceSingle trace Homogeneous mediaHomogeneous media True velocity = cTrue velocity = c Migration velocityMigration velocity c’ = c +  c c’ = c +  c V p /V s = psrV p /V s = psr Assumptions: m(r) = S(z g,  sr +  rg psr )  l m(r) = S(z g, (d sr + d rg psr )/c’ )  l

15. Error Analysis Conventional Migration (d sr + d rg psr )/c’ l (d sr + d rg psr )/(c +  c) l = ~ (d sr + d rg psr )(s – s  c) l 2~  (d sr + d rg psr ) s  c 2 l cm

16. m(r) = S(g,  Error Analysis Reduced-Time Migration ) obscalc  sr +  rg -  sg +  sg

17. Error Analysis Reduced-Time Migration obscalc  sr +  rg -  sg +  sg =l (d sr + d rg psr - d sg )(s – s  c) + d sg s l 2  (d sr + d rg psr - d sg ) s  c rtm 2 l

18. Error Functions CWM vs. RTM rtm  (d sr + d rg psr - d sg ) s  c 2 l cm  (d sr + d rg psr ) s  c 2 l

19. rtm cm0 0 0 0 250 250 500 500 Depth (m) Offset (m) Depth (m) Offset (m) 0 12 8 4 16 Imaging-Time Error Imaging Error Error (ms) (ms)

20. Outline MotivationMotivation Migration TheoryMigration Theory Error AnalysisError Analysis Synthetic Data ResultsSynthetic Data Results Field Data ResultField Data Result Conclusions & Future WorkConclusions & Future Work

21. Crosswell Model Depth (m) Offset (m) 1140 114 0V2 V1 V = 5500 m/s 2 V = 5000 m/s 1 V p /V s = 1.5 Well Separation = 100 m = 100 m Source = 1500 Hz ds = 2 m dg = 2 m

22. Synthetic Data Depth (m) 0 114 2035 Time (ms) Original Data Depth (m) 0 114 82 Time (s) Shifted Muted Data SPPS PPS S SP

23. PS Transmission Migration True Velocity Depth (m) Offset (m) 0 114 0 114

24. Conventional PS Migration + 10 % Velocity Depth (m) Offset (m) 0 114 0 114

25. Reduced-Time PS Migration + 10% Velocity Depth (m) Offset (m) 0 114 0 114

26. Outline MotivationMotivation Migration TheoryMigration Theory Error AnalysisError Analysis Synthetic Data ResultsSynthetic Data Results Field Data ResultField Data Result Conclusions & Future WorkConclusions & Future Work

27. Time Delay = 3 ms ?Time Delay = 3 ms ? Well locationWell location Velocity ModelVelocity Model Data Problems

28. km/sec6.0 5.0 7.0 Kidd Creek Well 0 20 40 60 50 0 Receiver Well Source Depth (m) Offset (m)

29. 6 Time (ms) 0 20 40 60 Depth (m) 0 Time Shifted CRG

30. Conventional PS Migration 0 20 40 60 50 0 Depth (m) Offset (m)

31. Reduced-Time PS Migration 0 20 40 60 50 0 Depth (m) Offset (m)

32. RTM-PS CRG #8 020 40 60 50 0 Depth (m) Offset (m)

33. Kidd Creek 0 20 40 60 50 0 Offset (m) 50 0

34. Outline MotivationMotivation Migration TheoryMigration Theory Error AnalysisError Analysis Synthetic Data ResultsSynthetic Data Results Field Data ResultField Data Result Conclusions & Future WorkConclusions & Future Work

35. Discussion & Conclusions PS migration can image structure invisible to reflection migration.PS migration can image structure invisible to reflection migration. Reduced-time migraton decreases the error of an incorrect velocity model.Reduced-time migraton decreases the error of an incorrect velocity model. Converted wave reduced-time migration can successfully image a transmitting boundary.Converted wave reduced-time migration can successfully image a transmitting boundary.

36. Future Work Model and migrate salt proximity VSP data with converted wave RTM.Model and migrate salt proximity VSP data with converted wave RTM. Model and test PP RTM.Model and test PP RTM. Search for other applications of RTM.Search for other applications of RTM. Graduate.Graduate.