1. paul.sava@beg.utexas.edu Wave-equation common-angle gathers for converted waves Paul Sava & Sergey Fomel Bureau of Economic Geology University of Texas at Austin

2. paul.sava@beg.utexas.edu Imaging condition Image Source wavefield Receiver wavefield Wavefield reconstruction Imaging sketch S R Angle decomposition Angle-dependent reflectivity

3. paul.sava@beg.utexas.edu Wavefield reconstruction Source wavefield Receiver wavefield S R

4. paul.sava@beg.utexas.edu Imaging condition Rickett & Sava (2002) Biondi & Symes (2004) Sava & Fomel (2005) Claerbout (1985) Space shift: h={h x,h y,h z } Location: m={x,y,z}

5. paul.sava@beg.utexas.edu Angle decomposition Reflection angle Azimuth angle Space shift: h={h x,h y,h z } Location: m={x,y,z} Message: images obtained by space-shift imaging contain sufficient information for converted-wave angle decomposition!

6. paul.sava@beg.utexas.edu Angle decomposition

7. paul.sava@beg.utexas.edu PP reflection geometry psps prpr 2p m 2p h

8. paul.sava@beg.utexas.edu PS reflection geometry psps prpr 2p h 2p m

9. paul.sava@beg.utexas.edu PS reflection geometry psps prpr 2p h 2p m

10. paul.sava@beg.utexas.edu PS reflection geometry 3 relations, can eliminate 2 variables:

11. paul.sava@beg.utexas.edu PS transformation Example: eliminate  and. 3 relations, can eliminate 2 variables. Sava & Fomel (2005)

12. paul.sava@beg.utexas.edu PS transformation (2D) Example: eliminate  and. 3 relations, can eliminate 2 variables. Weglein & Stolt (1985) Sava & Fomel (2003)

13. paul.sava@beg.utexas.edu Angle decomposition algorithm

14. paul.sava@beg.utexas.edu Example 1 0 15 3045 distance depth v P =2 km/s v S =1 km/s

15. paul.sava@beg.utexas.edu PP dataPS data surface offset time surface offset time 0 15 30 45

16. paul.sava@beg.utexas.edu PP image distance depth 0 15 3045

17. paul.sava@beg.utexas.edu PS image distance depth 0 15 3045

18. paul.sava@beg.utexas.edu PP offset-gatherPS offset-gather space-shift depth space-shift depth

19. paul.sava@beg.utexas.edu PP angle-gatherPS angle-gather tan(  0 ) depth tan(  0 ) depth 01530450153045 PP transformation

20. paul.sava@beg.utexas.edu PP angle-gatherPS angle-gather depth 01530450153045 PS transformation tan(  0 )tan(  )

21. paul.sava@beg.utexas.edu Example 2 distance depth acquisition shots: 51 at 0.2km receivers: 401 at 0.025km Modified from Baina et al. (2005):

22. paul.sava@beg.utexas.edu PP dataPS data surface offset time surface offset time

23. paul.sava@beg.utexas.edu PP imagePS image distance depth distance depth Uneven amplitude

24. paul.sava@beg.utexas.edu PP offset-gathersPS offset-gathers depth space-shift

25. paul.sava@beg.utexas.edu PP angle-gathersPS angle-gathers depth angle

26. paul.sava@beg.utexas.edu PP angle-gatherPS angle-gather angle depth angle depth PP transformation

27. paul.sava@beg.utexas.edu PP angle-gatherPS angle-gather angle depth angle depth PS transformation

28. paul.sava@beg.utexas.edu PP angle-gathersPS angle-gathers depth angle Normal polarity

29. paul.sava@beg.utexas.edu PP angle-gathersPS angle-gathers depth angle Reversed polarity

30. paul.sava@beg.utexas.edu PP stackPS stack distance depth distance depth

31. paul.sava@beg.utexas.edu Conclusions Angle decomposition for converted-waves Space-shift imaging condition –Independent of extrapolation method –Contains all required information Real challenge: what are the velocity models?