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Reduced-Time Migration of Converted Waves

Reduced-Time Migration of Converted Waves. David Sheley University of Utah. Outline. Motivation Migration Theory Error Analysis Synthetic Data Results Field Data Result Conclusions & Future Work. PP vs PS Transmission Migration. 0. Depth. Source Well. Receiver Well. Z. Offset. 0.

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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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