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Wave-equation common-angle gathers for converted waves

Wave-equation common-angle gathers for converted waves. Paul Sava & Sergey Fomel Bureau of Economic Geology University of Texas at Austin. Imaging sketch. Wavefield reconstruction. Source wavefield. Receiver wavefield. Imaging condition. Image. Angle decomposition.

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Wave-equation common-angle gathers for converted waves

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

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

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

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

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

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

  7. PP reflection geometry 2pm 2ph ps pr paul.sava@beg.utexas.edu

  8. PS reflection geometry 2pm 2ph ps pr paul.sava@beg.utexas.edu

  9. PS reflection geometry 2pm 2ph ps pr paul.sava@beg.utexas.edu

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

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

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

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

  14. Example 1 distance 0 depth 15 vP=2 km/s vS=1 km/s 45 30 paul.sava@beg.utexas.edu

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

  16. PP image distance 0 depth 15 45 30 paul.sava@beg.utexas.edu

  17. PS image distance 0 depth 15 45 30 paul.sava@beg.utexas.edu

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

  19. PP angle-gather PS angle-gather tan(q0) tan(q0) depth depth 0 15 30 45 0 15 30 45 PP transformation paul.sava@beg.utexas.edu

  20. PP angle-gather PS angle-gather tan(q0) tan(q) depth depth 0 15 30 45 0 15 30 45 PS transformation paul.sava@beg.utexas.edu

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

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

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

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

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

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

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

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

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

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

  31. 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? paul.sava@beg.utexas.edu

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