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Multisource Least-squares Migration of Marine Data

Multisource Least-squares Migration of Marine Data. Xin Wang & Gerard Schuster Nov 7, 2012. Outline. Motivation Gain high quality image by least-squares migration Improve the efficiency by multisource technique Theory Multisource Kirchhoff migration Multisource least-squares migration

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Multisource Least-squares Migration of Marine Data

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  1. Multisource Least-squares Migration of Marine Data Xin Wang & Gerard Schuster Nov 7, 2012

  2. Outline • Motivation • Gain high quality image by least-squares migration • Improve the efficiency by multisource technique • Theory • Multisource Kirchhoff migration • Multisource least-squares migration • Numerical Tests • Synthetic data test • Marine data test • Conclusion

  3. Motivation of LSM KM Image Least-squares Migration Image 3.4 Z (km) 0 3.4 Z (km) 0 0 X (km) 14 0 X (km) 14 Advantages of LSM compared to KM: Decrease artifacts, balance amplitudes, increase resolution, natural anti-alias and anti-gap filter (Nemeth,1999). Drawbacks of LSM High computational, IO and memory cost.

  4. Motivation of MLSM Multisource -> Crosstalk Multisource LSM Image Multisource KM Image • MLSM To: • Increase efficiency • Remove artifacts • Suppress crosstalk Problems of LSM High computational, IO and memory cost. Solution: Multisource phase-encoding technique.

  5. Outline • Motivation • Gain high quality image by least-squares migration • Improve the efficiency by multisource technique • Theory • Multisource Kirchhoff migration • Multisource least-squares migration • Numerical Tests • Synthetic data test • Marine data test • Conclusion

  6. Generate Supergather Data Supergather CSG 1 CSG 2 d2 d1 P2 d P1 shift 1 s Encoding Time (s) Time (s) shift －0.5 s 0 0 Depth (km) + =

  7. Decoding CSG 1 CSG 2 Supergather P1T P2T d d Decoding shift -1 s Time (s) Time (s) shift 0.5 s 0 0 Depth (km) -> +

  8. Multisource Migration CSG 1 CSG 2 L2TP2Td2 L2TP2Td1 L1TP1Td1 L1TP1Td2 Time (s) 0 Depth (km) migration artifacts crosstalk noise

  9. Multisource Least-squares Migration L = N1 L1+ N2 L2 & d = N1 d1 + N2 d2 Given:Lm = d Find: m s.t. min || Lm – d ||2 Solution: m = [ LT L ]-1LTd or if L is too big m(k+1) = m(k) – a LT ( Lm – d ) = m(k) – a ( L1T ( L1m – d1) + L2T ( L2m – d2) + L2TN2T N1(L1m – d1) + L1TN1T N2 ( L2m – d2) ) Crosstalk

  10. Workflow Modeling supergather d = L m(k) MLSM calculate data residual d - dobs dobs Save IO and memory cost calculate gradient LT (d – dobs) calculate analytical step length LSM calculate numerical step length dobs dobs More IO save Update reflectivity m(k+1) and refresh Applicable to GPU

  11. Outline • Motivation • Gain high quality image by least-squares migration • Improve the efficiency by multisource technique • Theory • Multisource Kirchhoff migration • Multisource least-squares migration • Numerical Tests • Synthetic data test • Marine data test • Conclusion

  12. Numerical Results Marmousi2 Velocity Model 3.4 Z (km) 0 km/s 4.8 # of shots: 192, ds = 60 m # of receiver: 120, dg = 20 m Streamer length: 2.4 km # of supergather: 16 0 X（km) 14 1.0 # of shots in supergather: 12 Synthetic data are generated with FD solution to acoustic wave-equation.

  13. KM vs LSM KM Image 3.4 Z (km) 0 0 X（km) 14 LSM Image, 15 Iterations 3.4 Z (km) 0 0 X（km) 14

  14. KM vs LSM (zoom view) Zoom view of red box Velocity Model Reflectivity Model 1.2 Z (km) 0.6 True LSM KM LSM Image, 15 Iterations KM Image 1.2 Z (km) 0.6 6 X (km) 7 6 X (km) 7

  15. KM vs LSM (zoom view) Zoom view of blue box Reflectivity Model Velocity Model 2.6 Z (km) 2.2 KM Image LSM Image, 15 Iterations 2.6 Z (km) 2.2 5.2 X (km) 7.2 5.2 X (km) 7.2

  16. MLSM (static and hybrid encoding) MLSM Image, Static Encoding, 15 Iterations 3.4 Z (km) 0 Static encoding: Same N for all iterations. 0 X(km) 14 MLSM Image, Hybrid Encoding, 15 Iterations 3.4 Z (km) 0 Hybrid encoding: Change N for every 5 iterations. 0 X (km) 14

  17. MLSM (dynamic encoding) vs LSM MLSM Image, Dynamic Encoding, 15 Iterations 3.4 Z (km) 0 Dynamic encoding: Change N for every iteration. 0 X (km) 14 LSM Image, 15 Iterations 3.4 Z (km) 0 0 X (km) 14

  18. MSLSM (dynamic encoding) vs LSM Zoom view of red box MLSM Image, Static, 15 Iters LSM Image, 15 Iters 1.2 Z (km) 0.6 MLSM Image, Hybrid, 15 Iters MLSM Image, Dynamic, 15 Iters 1.2 Z (km) 0.6 6 X (km) 7 6 X (km) 7

  19. MLSM (dynamic encoding) vs LSM Zoom view of blue box MLSM Image, Static, 15 Iters LSM Image, 15 Iters 2.6 Z (km) 2.2 MSLSM Image, Hybrid, 15 Iters MLSM Image, Dynamic, 15 Iters 2.6 Z (km) 2.2 5.2 X (km) 7.2 5.2 X (km) 7.2

  20. Comparison of CPU and IO Cost Assumption: conventional data cannot be stored in memory, but supergather data are small enough to be kept in the memory.

  21. Marine Data Velocity Model km/s 2.2 2.5 Z (km) 0 # of shots: 496, ds = 37.5 m # of receiver: 480, dg = 12.5 m Streamer length: 6 km # of supergather: 32 1.5 # of shots in supergather: 16 0 X（km) 18.8 Velocity model is from FWI. (Boonyasiriwat et al., 2010) A 10-15-70-75 Hz bandpass filter is applied. Source wavelet is generated from stacking near offset ocean bottom reflections.

  22. Marine Data Test KM Image 1.88 Z (km) 0.6 5 X（km) 13.8

  23. Marine Data Test RTM Image 1.88 Z (km) 0.6 5 X（km) 13.8

  24. Marine Data Test LSM image, 30 iterations 1.88 Z (km) 0.6 5 X（km) 13.8

  25. Marine Data Test MLSM image, dynamic encoding, 50 iterations 1.88 Z (km) 0.6 5 X（km) 13.8

  26. KM vs RTM vs LSM vs MSLSM Zoom view of red box RTM Image KM Image 1.5 Z (km) 0.9 MLSM Image, Dynamic, 20 Iters LSM Image, 20 Iters 1.5 Z (km) 0.9 10.5 X (km) 11.5 10.5 X (km) 11.5

  27. KM vs RTM vs LSM vs MLSM KM Image 1.5 Z (km) 0.9 10.5 X (km) 11.5

  28. KM vs RTM vs LSM vs MLSM RTM Image 1.5 Z (km) 0.9 10.5 X (km) 11.5

  29. KM vs RTM vs LSM vs MLSM MLSM Image, Dynamic, 20 Iterations 1.5 Z (km) 0.9 10.5 X (km) 11.5

  30. Outline • Motivation • Gain high quality image by least-squares migration • Improve the efficiency by multisource technique • Theory • Multisource Kirchhoff migration • Multisource least-squares migration • Numerical Tests • Synthetic data test • Marine data test • Conclusion

  31. Conclusion • MLSM can improve image quality over conventional Migration. KM Image MLSM Image • MLSM can improve the efficiency, and save IO cost. • Dynamic MLSM reduces IO cost to 1/30. • Wave equation based migration method can save the computational cost.

  32. Acknowledgement We thank for the 2011 CSIM sponsors for their financial support.

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