1. Reduced-Time Migration of Converted Waves David Sheley and Gerard T. Schuster University of Utah

2. Outline MotivationMotivation Reduced-Time Migration TheoryReduced-Time Migration Theory Error AnalysisError Analysis ResultsResults –Synthetic Data –Field Data ConclusionsConclusions

3. Outline MotivationMotivation Reduced-Time Migration TheoryReduced-Time Migration Theory Error AnalysisError Analysis ResultsResults –Synthetic Data –Field Data ConclusionsConclusions

4. Problem: Dark Flanks Depth Offset 0 Z Receiver Well Source Well X 0 ? ? P P ? ? ? ? m(r) = d(z g,  sr +  rg )

5. P Solution: PS Transmission Migration Depth Offset 0 Z Receiver Well Source Well X 0PSP PS m(r) = d(z g,  sr +  rg )

6. Motivation Solutions: Solutions: 1. PS Transmission Migration Problems: Problems: 1. Dark Flanks

7. Motivation Solutions: Solutions: 1. 1. PS Transmission Migration Problems: Problems: 1. 1. Dark Flanks 2. Velocity Errors (Vp, Vs)

8. Motivation Solutions: Solutions: 1. 1. PS Transmission Migration 2. Reduced-Time Migration Problems: Problems: 1. 1. Dark Flanks 2. Velocity Errors (Vp, Vs)

9. Outline MotivationMotivation Reduced-Time Migration TheoryReduced-Time Migration Theory Error AnalysisError Analysis ResultsResults –Synthetic Data –Field Data ConclusionsConclusions

10. Reduced-Time Migration 1. Data time shift Depth (m) Time (ms) P PS S d(z g, t  d(z g, t 

11. Reduced-Time Migration 1. Data time shift Time (ms) P PS S Depth (m) obs d’(g, t) = d(z g, t +  sg 

12. Reduced-Time Migration 1. Data time shift d’(z g, t) = d(z g, t    sg  Observed direct-P traveltime obs 2. Modify the migration equation m(r) = d’(z g,  sr +  rg ) obs  sg calc –  sg

13. Outline MotivationMotivation Reduced-Time Migration TheoryReduced-Time Migration Theory Error AnalysisError Analysis ResultsResults –Synthetic Data –Field Data ConclusionsConclusions

14. Focusing-Time Error Conventional vs. Reduced-Time Reduced-Time  (d sr + d rg psr - d sg)  c/c l Conventional  (d sr + d rg psr )  c/c l 2 2

15. 0 0 0 0 250 250 500 500 Depth (m) Offset (m) Depth (m) Offset (m) 0 12 8 4 16 Focusing-Time Error Imaging Error Error (ms) (ms) Conventional Trans. PS Migration Reduced-TimeMigration

16. Outline MotivationMotivation Reduced-Time Migration TheoryReduced-Time Migration Theory Error AnalysisError Analysis ResultsResults –Synthetic Data –Field Data ConclusionsConclusions

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

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

19. Conventional PS Transmission Migration Depth (m) Offset (m) 0 114 0 100 True Velocity

20. Conventional PS Transmission Migration Depth (m) Offset (m) 0 114 0 100 True Velocity + 10 % Velocity Offset (m) 0100

21. Depth (m) Offset (m) 0 114 0 100 True Velocity Reduced-Time PS Migration

22. Depth (m) Offset (m) 0 114 0 100 True Velocity Reduced-Time PS Migration + 10 % Velocity Offset (m) 0100

23. Depth (m) Offset (m) 0 114 0 100 Conventional PS Comparison +10% Velocity Recuced-Time Offset (m) 0100

24. Outline MotivationMotivation Reduced-Time Migration TheoryReduced-Time Migration Theory Error AnalysisError Analysis ResultsResults –Synthetic Data –Field Data ConclusionsConclusions

25. km/sec 6.0 5.0 7.0 Kidd Creek Crosswell Well 0 20 40 60 50 0 Receiver Well Source Depth (m) Offset (m)

26. Time Delay = 3 ms ?Time Delay = 3 ms ? Well LocationWell Location Velocity ModelVelocity Model Data Problems

27. 6 Time (ms) 0 20 40 60 Depth (m) 0 Time Shifted CRG

28. Conventional0 20 60 50 0 Offset (m) Depth (m)

29. Conventional0 20 60 50 0 Offset (m) 50 0Reduced-Time Depth (m)

30. Outline MotivationMotivation Reduced-Time Migration TheoryReduced-Time Migration Theory Error AnalysisError Analysis ResultsResults –Synthetic Data –Field Data ConclusionsConclusions

31. Conclusions Transmission PS migration can image structure invisible to reflection migration.Transmission PS migration can image structure invisible to reflection migration. Reduced-time migration decreases the migration error of an incorrect velocity model.Reduced-time migration decreases the migration error of an incorrect velocity model. PS reduced-time migration can successfully image a transmitting boundary.PS reduced-time migration can successfully image a transmitting boundary.

32. Acknowledgements I sincerely thank the 1999 sponsors of the UTAM consortium for their financial support. I sincerely thank the 1999 sponsors of the UTAM consortium for their financial support.