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Wei Dai Jan. 7, 2010

Multi-source Least-squares Migration with a Deblurring Filter. Wei Dai Jan. 7, 2010. Outline. Motivation Theory Numerical Tests Conclusion. 2. 2-source KM. 320-source KM. Single Source KM. Motivation.

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Wei Dai Jan. 7, 2010

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  1. Multi-source Least-squares Migration with a Deblurring Filter Wei Dai Jan. 7, 2010

  2. Outline • Motivation • Theory • Numerical Tests • Conclusion 2

  3. 2-source KM 320-source KM Single Source KM Motivation Multi-source acquisition can reduce economic cost of seismic acquisition, e.g., VSP, OBC, OBS. Standard migration and stacking can effectively remove crosstalk noise in 2-source data (Beasley, 2008; Hampson et al., 2008; Fromyr et al., 2008; etc). What will happen when there are hundreds of multiple sources? We propose to use LSM to suppress the crosstalk noise. 3

  4. is the time delay operator Is modeling operator associated with individual shot multi-source modeling operator as multi-source migration operator as Theory With multi-source data shots, the supergathers: 4

  5. noise signal (KM image) Least-squares migration image: is the step length (numerical line search). is preconditioner (deblurring filter). • Goals: • Suppress crosstalk noise • Invert the Hessian Theory Standard migration image: 5

  6. Calculate its standard migration image: Theory Reference model : grid model with evenly distributed point scatterers. 6

  7. so, Theory Construct an image, which is an approximation of Rewrite in matrix notation 7

  8. 0 Offset (m) 5800 0.2 0 Depth (ft) 0 1300 -0.2 Numerical Tests Model: 2D SEG/EAGE salt model Size: 645 X 150 Grid interval: 9.14 m Source: 320 Receiver: 320 Figure 1. 2D SEG/EAGE salt model (reflectivity). 8

  9. 0 Offset (m) 5800 0.2 0 Depth (m) 0 1300 -0.2 5x10-3 0 -5x10-3 Single source results Figure 2. Kirchhoff migration image for conventional source data. 0 Offset (m) 5800 0 Depth (m) 1300 Figure 3. KM image after deblurring (deblurred image). 9

  10. 0 Offset (m) 5800 0.2 0 Depth (m) 0 1300 -0.2 0.2 0 -0.2 Single source results Figure 4. Least-squares migration image after 30 CG iterations. 0 Offset (m) 5800 0 Depth (m) 1300 Figure 5. Preconditioned least-squares migration image after 30 PCG iterations 10

  11. Convergence curves of Single source data 0.45 Data Residual 0 0 Iterations 30 Figure 6. Normalized data residual plotted against iteration number. 11

  12. 0 Offset (m) 5800 0.2 0 Depth (m) 0 1300 -0.2 5x10-3 0 -5x10-3 10-source results Figure 7. KM image for 10-source supergathers. 0 Offset (m) 5800 0 Depth (m) 1300 Figure 8. Preconditioned LSM image for 10-source supergathers after 30 iterations. 12

  13. 0 Offset (m) 5800 0.2 0 Depth (m) 0 1300 -0.2 5x10-3 0 -5x10-3 20-source results Figure 9. KM image for 20-source supergathers. 0 Offset (m) 5800 0 Depth (m) 1300 Figure 10. Preconditioned LSM image for 20-source supergathers after 30 iterations. 13

  14. 0 Offset (m) 5800 0 Depth (m) 1300 0.2 2x10-3 0 0 -0.2 -2x10-3 40-source results Figure 11. KM image for 40-source supergathers. 0 Offset (m) 5800 0 Depth (m) 1300 Figure 12. Preconditioned LSM image for 40-source supergathers after 30 iterations. 14

  15. Convergence Curves of 40-source supergathers 1.4 Data Residual 0 0 Iterations 30 Figure 13. Normalized data residual plotted against iteration number for 40-source supergathers. 15

  16. 0 Offset (m) 5800 0 Depth (m) 1300 0.2 2x10-3 0 0 -0.2 -2x10-3 80-source results Figure 14. KM image for 80-source supergathers. 0 Offset (m) 5800 0 Depth (m) 1300 Figure 15. Preconditioned LSM image for 80-source supergathers after 30 iterations. 16

  17. 0 Offset (m) 5800 0 Depth (m) 1300 0.2 1x10-4 0 0 -0.2 -1x10-4 160-source results Figure 16. KM image for 160-source supergathers. 0 Offset (m) 5800 0 Depth (m) 1300 Figure 17. Preconditioned LSM image for 160-source supergathers after 30 iterations. 17

  18. 0 Offset (m) 5800 0 Depth (m) 1300 0.2 1x10-4 0 0 -0.2 -1x10-4 320-source results Figure 18. KM image for 320-source supergathers. 0 Offset (m) 5800 0 Depth (m) 1300 Figure 19. Preconditioned LSM image for 320-source supergathers after 30 iterations. 18

  19. Model and data residual of LSM V.S. number of multiple sources 0.7 Residual 0 100 200 300 0 Number of Multiple Sources Figure 20. Model and data residual of LSM images plotted against the number of multiple sources. 19

  20. Data residual of KM and deblurred image V.S. number of multiple sources 1.0 Data Residual 0 40 80 160 0 Number of Multiple Sources Figure 21. Data residual associated with KM images and deblurred images plotted as a function of the number of multiple sources. 20

  21. Conclusion • LSM can suppress cross-talk noise in multi-source data when supergathers consist of hundreds of shots. • The deblurring filter accelarates and • stabilizes the convergence. • In our algorithm, the size of data is reduced • by 320 times. Thus the I/O burden is lifted. It’s • perfect for implementation for GPUs. 21

  22. Limitations • Multi-source modeling and migrating operators are not linear operators. • The deblurring filter introduces artifacts. • LSM introduces high frequency noise. 22

  23. Acknowledgement We would like to thank the UTAM 2009 sponsors for their support. Thank You 23

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