1. Local Reverse Time Migration with Extrapolated VSP Green’s Function Xiang Xiao UTAM, Univ. of Utah Feb. 7, 2008

2. 2 Outline Motivation Theory Numerical Tests Sigsbee VSP data set GOM VSP data set Conclusions Motivation TheoryNumerical Tests Conclusion

3. 3 VSP Forward Modeling s x g Motivation D(g|s) VSP data TheoryNumerical Tests Conclusion

4. 4 Reverse Time Migration s x g Motivation D(g|s) VSP data TheoryNumerical Tests Conclusion

5. 5 Reverse Time Migration s x G(x|g) g G(x|s) Backward D(g|s) Forward source m(x) ~ s ~ ds G(x|s) Forward source G(x|g)* D(g|s)dg Backward data g * Motivation TheoryNumerical Tests Conclusion

6. 6 Reverse Time Migration s x G(x|g) g G(x|s) Backward D(g,s) Forward source Motivation TheoryNumerical Tests Conclusion Forward source: 1)Need salt velocity model, hard to build. 2) Model-based, model not perfect. 3) Need to estimate the statics, anisotropy, etc.

7. 7 s g g’ x VSP  SWP Interferometry Migrate virtual source gather D(g|g’) Limitation: 1) s and x are at different side; 2) Image near vertical structures; Motivation TheoryNumerical Tests Conclusion

8. 8 Outline Motivation TheoryNumerical Tests Conclusions Motivation Theory Numerical Tests Sigsbee VSP data set GOM VSP data set Conclusion

9. 9 Local Reverse Time Migration, Key Idea (a) VSP data: P(g|s)=T(g|s)+R(g|s) Transmission T(g|s) s g Reflection R(g|s) x Theory Motivation TheoryNumerical Tests Conclusions

10. 10 Local Reverse Time Migration, Key Idea (a) VSP data: P(g|s)=T(g|s)+R(g|s) T(g|s) s g R(g|s) x s (b) Backward reflection R(g|s) g x R(x|s)= G(x|g)*R(g|s) g (c) Backward Transmission T(g|s) s g x T(x|s)= G(x|g)*T(g|s) g (d) Crosscorrelation: m(x)= R(x|s)*T(x|s) g Theory Motivation TheoryNumerical Tests Conclusions Local VSP Green’s function R(g|s) g x

11. 11 m(x) ~ s ~ ds g’ G(x|g’)* D(g’|s) dg’ Backward D(g’|s) G(x|g)* D(g|s)dg Backward D(g|s) g * x1x1 (1) (2) x2x2 x3x3 (3) s g g’ Illumination Zones (1) specular zone, (2)diffraction zone, (3) unreliable zone, Theory Motivation Numerical Tests Conclusions

12. 12 Benefits Target oriented! Introduction Numerical Tests –Only a local velocity model near the well is needed. –Salt and overburden is avoided. –Fast and easy to perform. Source statics are automatically accounted for. Immune to salt-related interbed cross- talk. Theory Conclusions

13. 13 Outline Motivation TheoryNumerical Tests Conclusions Motivation Theory Numerical Tests –Sigsbee VSP data set –GOM VSP data set Conclusion

14. 14 Sigsbee P-wave Velocity Model 0 Depth (km) 9.2 4500 1500 m/s -12.5 12.5Offset (km) 279 shots 150 receivers Motivation TheoryNumerical Tests Conclusions

15. 15 Local Reverse Time Migration Results 4.6 9.2 Depth (km) -33Offset (km) True modelMigration image f = fault f d d (1) (2) (3) (1)specular zone (2)diffraction zone (3)unreliable zone d = diffractor Motivation TheoryNumerical Tests Conclusions

16. 16 Outline Introduction TheoryNumerical Tests Conclusions Motivation Theory Numerical Tests Sigsbee VSP data set GOM VSP data set Conclusion

17. 17 Depth (m) Offset (m) 4878 0 1829 0 GOM VSP Well and Source Location Source @150 m offset Introduction TheoryNumerical Tests Conclusions 2800 m 3200 m Salt 82 receivers

18. 18 P-to-S ratio = 2.7 Velocity Profile S Wave P Wave Depth (m) 0 4500 050000 2800 m 3200 m Salt GOM Data Incorrect velocity model P-to-S ratio = 1.6 Introduction TheoryNumerical Tests Conclusions Velocity (m/s)

19. 19 Z-Component VSP Data Depth (m) Traveltime (s) 2652 3887 1.23.0 Salt Direct P Reflected P Reverberations Introduction TheoryNumerical Tests Conclusions

20. 20 X-Component VSP Data Depth (m) Traveltime (s) 2652 3887 1.23.0 Salt Direct P Reflected P ReverberationsDirect S Introduction TheoryNumerical Tests Conclusions

21. 21 Local Reverse Time Migration Result (1) (2) (3) (1) specular zone, (2) diffraction zone, (3) unreliable zone 0 Depth (km) 9 025Offset (km) Introduction TheoryNumerical Tests Conclusions

22. 22 Conclusions Target oriented! Introduction TheoryNumerical Tests Conclusions –Only local well model is needed. –Salt and overburden is avoided. –Fast and easy to perform. Source statics are automatically accounted for. Immune to salt-related interbed cross- talk.

23. 23 Thank you! Thank the sponsors of the 2007 UTAM consortium for their support.

24. 24 VSP WEM 0 Depth (km) 9 0 25Offset (km) SSP WEM 0 Depth (km) 9

25. 25 s s x G2G2 s (a) Approximate G 2 x G1 G1 g Forward wavelet (b) Compute G 1 x g’ G2G2 data D(g’|s) Backward x G1 G1 g G2G2 (c) Migrate data D(g|s) D(g|s) s Flow Chart

26. 26 ss (a) Approximate G 2 x G2G2 x g’ data D(g’|s) Backward g = s’ (b) Approximate G 1 x g’ x G1 G1 Forward Data D(g’|s’) G1 G1 x (c) Migrate data D(g|s) G1 G1 G2G2 D(g|s) sg SSP+VSP Imaging Theory

27. 27 (b) Backproject reflections R(x|s)= G(x|g)*R(g|s) g R(g|s) g x

28. 28 Outline Motivation TheoryNumerical Tests Conclusions Motivation Theory Numerical Tests Sigsbee VSP data set GOM VSP data set Conclusions