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Reduced-Time Migration of Converted Waves

This study explores reduced-time migration of converted waves through migration theory, error analysis, synthetic and field data results, and future work implications. The research examines PS transmission migration and offers insights into velocity models and imaging techniques.

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Reduced-Time Migration of Converted Waves

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

  2. Outline • Motivation • Migration Theory • Error Analysis • Synthetic Data Results • Field Data Result • Conclusions & Future Work

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

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

  5. Converted Wave Migration 0 Vp,Vs = ? P Depth P PS Source Well Receiver Well PS Z Offset 0 X =?

  6. Outline • Motivation • Migration Theory • Error Analysis • Synthetic Data Results • Field Data Result • Conclusions & Future Work

  7. m(r) = S(zg, tsr +trg) g Conventional Migration s g tsr trg r

  8. PS Transmission Migration m(r) = S(zg, dsr/Vp +drg/Vs) g s g drg/Vs dsr/Vp r

  9. km/sec 7.0 6.0 5.0 0 Problem Receiver Source Well Well 20 Depth (m) 40 60 Offset (m) 0 50

  10. Reduced-Time Migration obs • Data time shift S’(g, t) = S(zg, t + tsg ) tsg = Observed direct-P time obs

  11. Original Data Shifted Muted Data 0 0 Depth (m) Depth (m) P S PS PS SP SP 114 114 Time (ms) Time (s) 20 35 2 8 Data Shift

  12. m(r) = S’(zg, tsr +trg –tsg ) calc g Reduced-Time Migration obs • Data time shift S’(zg, t) = S(zg, t + tsg ) tsg = Observed direct-P time obs • Modify the migration equation • m(r) = S(zg, tsr +trg - tsg +tsg ) calc obs g

  13. Outline • Motivation • Migration Theory • Error Analysis • Synthetic Data Results • Field Data Result • Conclusions & Future Work

  14. Single trace Homogeneous media True velocity = c Migration velocity c’ = c + dc Vp/Vs = psr m(r) = S(zg, tsr +trg psr) m(r) = S(zg, (dsr +drg psr)/c’) g g l l Error Analysis -- CWM Assumptions:

  15. (dsr +drg psr)(s – s dc) (dsr +drg psr)/c’ (dsr +drg psr)/(c + dc) = l l l ~ ~ 2 e = -(dsr +drg psr) s dc 2 l cm Error Analysis Conventional Migration

  16. tsr +trg - tsg +tsg calc obs m(r) = S(g, g Error Analysis Reduced-Time Migration )

  17. tsr +trg - tsg +tsg calc obs = e = -(dsr +drg psr -dsg) s dc 2 l rtm (dsr +drg psr -dsg)(s – s dc) + dsg s 2 l l Error Analysis Reduced-Time Migration

  18. l l e = -(dsr +drg psr -dsg) s dc e = -(dsr +drg psr) s dc 2 2 rtm cm Error FunctionsCWM vs. RTM

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

  20. Outline • Motivation • Migration Theory • Error Analysis • Synthetic Data Results • Field Data Result • Conclusions & Future Work

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

  22. Original Data Shifted Muted Data 0 0 Depth (m) Depth (m) P S PS PS SP SP 114 114 Time (ms) Time (s) 20 35 2 8 Synthetic Data

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

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

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

  26. Outline • Motivation • Migration Theory • Error Analysis • Synthetic Data Results • Field Data Result • Conclusions & Future Work

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

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

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

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

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

  32. 0 20 Depth (m) 40 60 Offset (m) 0 50 RTM-PS CRG #8

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

  34. Outline • Motivation • Migration Theory • Error Analysis • Synthetic Data Results • Field Data Result • Conclusions & Future Work

  35. Discussion & Conclusions • PS migration can image structure invisible to reflection migration. • Reduced-time migraton decreases the error of an incorrect velocity model. • 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 test PP RTM. • Search for other applications of RTM. • Graduate.

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