1. paul.sava@beg.utexas.edu Time-shift imaging condition 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

4. paul.sava@beg.utexas.edu Wavefield reconstruction Source wavefield Receiver wavefield S R Reverse-time extrapolation Kirchhoff integral Wavefield extrapolation …

5. paul.sava@beg.utexas.edu Imaging condition

6. paul.sava@beg.utexas.edu Conventional imaging condition source wavefield receiver wavefield image position time

7. paul.sava@beg.utexas.edu Conventional imaging condition Claerbout (1985) position time

8. paul.sava@beg.utexas.edu Conventional imaging condition position frequency

9. paul.sava@beg.utexas.edu distance depth Conventional imaging condition example

10. paul.sava@beg.utexas.edu Space-shift imaging condition source wavefield receiver wavefield image position time space-shift

11. paul.sava@beg.utexas.edu Space-shift imaging condition position time space-shift Rickett & Sava (2002) Biondi & Symes (2004) Sava & Fomel (2005)

12. paul.sava@beg.utexas.edu Space-shift imaging condition position frequency space-shift

13. paul.sava@beg.utexas.edu distance depth Space-shift imaging condition example

14. paul.sava@beg.utexas.edu Time-shift imaging condition source wavefield receiver wavefield image position time time-shift

15. paul.sava@beg.utexas.edu Time-shift imaging condition position time time-shift

16. paul.sava@beg.utexas.edu Time-shift imaging condition position frequency time-shift

17. paul.sava@beg.utexas.edu Time-shift imaging condition example distance depth

18. paul.sava@beg.utexas.edu distance  h Imaging condition: example 1 depth space-shifttime-shift

19. paul.sava@beg.utexas.edu  h distance Imaging condition: example 2 depth space-shifttime-shift

20. paul.sava@beg.utexas.edu Imaging condition summary time-shift space-shift

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

22. paul.sava@beg.utexas.edu pmpm phph psps prpr  Angle decomposition Space-shiftTime-shift

23. paul.sava@beg.utexas.edu pmpm phph psps prpr  Vector geometry Space-shiftTime-shift

24. paul.sava@beg.utexas.edu Image-space angle decomposition Space-shiftTime-shift

25. paul.sava@beg.utexas.edu Angle decomposition algorithm Space-shiftTime-shift

26. paul.sava@beg.utexas.edu distance depth Space-shift angle decomposition example

27. paul.sava@beg.utexas.edu Time-shift angle decomposition example distance depth

28. paul.sava@beg.utexas.edu distance  Angle decomposition: example 1 depth space-shifttime-shift

29. paul.sava@beg.utexas.edu distance  Angle decomposition: example 2 depth space-shifttime-shift

30. paul.sava@beg.utexas.edu distance  Correct velocity depth space-shifttime-shift

31. paul.sava@beg.utexas.edu distance  Incorrect velocity depth space-shifttime-shift

32. paul.sava@beg.utexas.edu  Angle decomposition summary depth distance  h depth

33. paul.sava@beg.utexas.edu  Angle decomposition summary depth distance  h depth

34. paul.sava@beg.utexas.edu Summary Imaging condition and angle-decomposition –time-shifts of source/receiver wavefields –cheaper than space-shift imaging –storage –computations –wide applicability –migration by wavefield extrapolation –Kirchhoff migration –reverse-time migration