1. LSMF for Suppressing Multiples
Jianhua Yu
University of Utah

2. Contents
Motivation
LSMF Inversion
Numerical Examples
Conclusions

3. Contents
Motivation
LSMF Inversion
Numerical Examples:
Conclusions

4. Demultiple Methods Radon transform Inverse scattering theory
Prediction+subtraction

5. Benefits: Demultiple for coarse acquisition geometry
Use both primary and multiple information

6. Contents
Motivation
LSMF Inversion
Numerical Examples:
Conclusions

7. Assuming that seismic data can be written mathematically as
D : seismic data
L : Primary forward operator p
L : Multiple forward operator m
R : Primary model
R : Multiple model

8. LSMF equation (Nemeth, 1996) :
Minimize the misfit function
D : seismic data
obs
R : Primary model p
R : Multiple model m

9. LSMF Inversion:
Algorithm: Conjugate Gradient (CG)

10. Primary Modeling OperatorW p
a weight R
A primary model d
primary reflections

11. Multiple Modeling OperatorW m
a weight R m
A multiple model d m
multiples reflections

12. Operators for primary and multiple migration are the transpose of modeling operators
Multiple initial model
Wang (Geophys, 2003)

13. Demultiple Using LSMF Input CMP gathers
Solving the following equation by CG algorithm

14. Demultiple using LSMF P=D-M Predicted multiple M
Subtract multiple M from raw data D and get primary P
P=D-M

15. Contents
Motivation
LSMF Inversion
Numerical Examples
Conclusions

16. Model
Time (s)
P+M P M
LSMF
P+M P M

17. CMP 300 (NS)
Time (s)
P+M M P

18. CMP 1700 (NS)
Time (s)
P+M M P

19. CMP 1300 (NS)
Time (s)
P+M M P

20. Before LSMF
After LSMF
Velocity
Time (s)
CMP 1300 (NS)
3.5
1.4 4

21. Before LSMF
After LSMF
Velocity
Time (s)
CMP 1300 (NS)
3.5
1.4 4

22. CMP 800 (Unocal)
Time (s)
P+M M P

23. CMP 900 (Unocal)
Time (s)
P+M M P

24. CMP 1100 (Unocal)
Time (s)
P+M M P

25. Velocity
Velocity
1.4
3.2
1.4
3.2
Time (s) 4
Before LSMF
After LSMF

26. Contents
Motivation
LSMF Inversion
Numerical Examples:
Conclusions

27. Conclusions Works for synthetic data and real data
No limit to coarse geometry
Straightforward to extend to 3D
Regularization strategy required for shallow reflections
1-D model

28. ACKNOWLEDGMENTS 2003 UTAM Sponsors Unocal and Mobil for 2-D field data
CHPC