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1. Multiples Waveform Inversion DongliangZhang and Gerard Schuster King Abdullah University of Science and Technology 12/06/2013

2. Outline Motivation Multiples contain more information Theory Algorithm of MWI and generation of multiples Numerical Example Test Marmousi model Conclusions

3. Outline Motivation Multiples contain more information Theory Algorithm of MWI and generation of multiples Numerical Example Test Marmousi model Conclusions

4. Motivation multiples primary Multiples : wider coverage, denser illumination FWI MWI

5. Motivation Recorded data (primary + multiples) Impulsive wavelet Recorded data multiples Multiples waveform inversion vs full waveform inversion Natural source

6. Outline Motivation Multiples contain more information Theory Algorithm of MWI and generation of multiples Numerical Example Test Marmousi model Conclusions

7. Theory Algorithm of MWI 1. Misfit function 2. Gradient of data residual Multiples RTM

8. Algorithm of MWI Forward propagation Backpropagation 3. Update velocity/slowness

9. MWI Workflow Calculate multiples to get the multiples residual Multiples RTM to get gradient of misfit function Update the velocity Number of iterations >N No Yes Stop

10. GenerateMultiples homogeneous Step 1 direct propagation Pd+Md Line source (P +M) heterogeneous Mr reflected propagation Step 2 direct propagation Line source (P +M) Pd+Md heterogeneous homogeneous Step 3 Mr= (Pd+Md ) +Mr - (Pd+Md)

11. VirtualSource (P+M) (Pd+Md)+Mr (Pd+Md) Mr (multiples) 5.5 T (s) 0 0 X (km) 4 0 X (km) 4 0 X (km) 4 Example 5.5 T (s) 0 2 Z (km) 0 water homogeneous

12. Recorded data Multiples residual Conventional migration Multiples migration Gradient of MWI Impulsive wavelet Data residual Yike Liu (2011)

13. Outline Motivation Multiples contain more information Theory Algorithm of MWI and generation of multiples Numerical Example Test Marmousi model Conclusions

14. Numerical Example Initial Velocity Model 1.5 km/s 5.5 2 Z (km) 0 0 X (km) 4 True Velocity Model 1.5 km/s 5.5 2 Z (km) 0

15. Numerical Example Tomogram of MWI 1.5 km/s 5.5 2 Z (km) 0 0 X (km) 4 Tomogram of FWI 1.5 km/s 5.5 2 Z (km) 0

16. Numerical Example True True FWI FWI MWI MWI

17. Numerical Example RTM Image Using FWI Tomogram 2 Z (km) 0 0 X (km) 4

18. Numerical Example RTM Image Using MWI Tomogram 2 Z (km) 0 0 X (km) 4

19. Numerical Example Common Image Gather Using FWI Tomogram

20. Numerical Example Common Image Gather Using MWI Tomogram

21. Numerical Example Model Residual 11 Res (%) 14 MWI is more accurate than FWI FWI MWI 1 Iterations 100 Data Residual 20 Res (%) 100 Convergence of MWIis faster than that of FWI FWI MWI

22. Numerical Example FWI Gradient for One Shot MWI Gradient for One Shot 0 X (km) 4

23. Outline Motivation Multiples contain more information Theory Algorithm of MWI and generation of multiples Numerical Example Test Marmousi model Conclusions

24. FWI MWI FWI MWI Conclusions • Source wavelet is not required • Illuminations are denser • MWI converge faster than FWI in test on Marmousimodel • Tomogram of MWI is better than that of FWI in test on Marmousi model

25. Limitations: Dip angle vs Future work: P+M FWI P+M MVA

26. Thank you!