1. Virtual Source Imaging vs Interferometric Imaging Gerard T. Schuster, Andrey Bakulin and Rodney Calvert

2. Outline Data Illustration Summary Theory

3. D(s’|s) s U(g’|s’) s’g’ U(g’|s) = G(g’|s’) D(s’|s)ds’ Greens Thm: Every pt along well acts as a secondary source Greens Function for s & g in well u = Dg u =[D*D] D*g G(g’|s’) ~ U(g’|s)D(s’|s)*ds Redatumed data for s & g in well W D(s’|s) g D*u (g, M,s)= d( g |s) d(M|s)* s,s

4. Outline Data Illustration Summary Theory

5. Time (s) 0.3 0 30 900 Depth (ft) Raw Data(CRG15) D(s’|s) U(g’|s) G(g’|s’) ~ U(g’|s)D(s’|s)*ds G(g’|s’)

6. Outline Data Illustration Summary Theory

7. Summary VSP Direct VSP Ghost u = Dg U(g’|s) = G(g’|s’) D(s’|s)ds’ 1. CDP Refl. g =[D*D] D*u 2. G(g’|s’) [D*D] ~ 1/W Interferometry Redatuming [D*D] ~ 1/D Virtual Source Readtuming

8. Time (s) 0.3 0 30 900 Depth (ft) Ghosts

9. Time (s) 0.3 0 30 900 Depth (ft) Exxon Raw Data(CRG15)

10. Time (s) 0.3 0 30 900 Depth (ft) Ghosts (Exxon) D(g’|s)

11. Time (s) 0.3 0 30 900 Depth (ft) Primary(Exxon)

12. 524 Trace No. Time (s) 1.2 0.2 xcorr data (muted) Time (s) 1.4 0.5 524 Trace No. Exxon CSG 25 Raw data (muted) Master trace

13. Depth (ft) 1300 200 0 400 X (ft) Xcorr. mig

14. Uninteresting Part of Medium of Medium Specular Reflection Time Fermat’s Principle: T+T – T >0 T – T > -T ghostdiffraction s min(T – T) = -T s Diffraction T TT

15. Uninteresting Part of Medium of Medium Specular Reflection Time Fermat’s Principle: T+T – T >0 T – T > -T ghostdiffraction s min(T – T) = -T s Diffraction T TT

16. Uninteresting Part of Medium of Medium Specular Reflection Time Diffraction Fermat’s Principle: T+T – T >0 T – T > -T ghostdiffraction min(T – T) = -T s s

17. Uninteresting Part of Medium of Medium Specular Reflection Time Diffraction Fermat’s Principle: T+T – T >0 T – T > -T ghostdiffraction min(T – T) = -T s s

18. Uninteresting Part of Medium of Medium Time Minimum Time Difference = Specular Reflection Time Fermat’s Principle: T+T – T >0 T – T > -T ghostdiffraction min(T – T) = -T s

19. Uninteresting Part of Medium of Medium Time Fermat’s Principle: T+T – T >0 T – T > -T ghostdiffraction min(T – T) = -T s

20. Summary1. Fermat’s Principle: min(T – T) = -T 2. No need to know velocity model or source location. 3. VSP Data  CDP Data + Tomography+Mig. 4. Redatums buried sources to surface

21. Outline Target Oriented Fermat’s Interferometric Principle Fermat’s Interferometric Principle Numerical Example Interferometry Background

22. Uninteresting Part of Medium of Medium VSP Tomostatics Problem: From VSP Data Find Full Coverage Velocity Tomogram

23. Uninteresting Part of Medium of Medium VSP Tomostatics Problem: From VSP Data Find Full Coverage Velocity Tomogram

24. Fermat’s Principle: T - T > 0 multmultsgsg = When is there equality? Fermat’s Interferometric Principle For VSP Multiple Tomography 0 600 m 0 m 3.5 km/s 1.4 km/s Weathering zone VSP Data: 120 shots on surface, 120 receivers in well Goal: Determine weathering zone velocity by interferometric tomography

25. Fermat’s Principle: T - T > 0 multmultsgsg = When is there equality? Fermat’s Interferometric Principle For Multiple Tomography 0 600 m 0 m 3.5 km/s 1.4 km/s Weathering zone min(T – T) = T TT

26. Fermat’s Principle: T - T > 0 multmultsgsg = When is there equality? Fermat’s Interferometric Principle For Multiple Tomography 0 600 m 0 s 0.135 s Time (s) Ghost Reflection min(T – T) = T Depth (m)

27. Fermat’s Principle: T - T > 0 multmultsgsg = When is there equality? Fermat’s Interferometric Principle For Multiple Tomography 0 600 m 0 s 0.135 s Time (s) Ghost Reflection Primary Reflection min(T – T) = T = Depth (m) X (m)

28. Fermat’s Principle: T - T > 0 multmultsgsg = When is there equality? Fermat’s Interferometric Principle For Multiple Tomography 0 600 m 0 s 0.135 s 3.5 km/s 1.4 km/s Time (s) Ghost Reflection Primary Reflection Interfer. Reflection min(T – T) = T Depth (m) X (m)

29. Fermat’s Principle: T - T > 0 multmultsgsg = When is there equality? Fermat’s Interferometric Principle For Multiple Tomography 0 600 m 1.35 km/s Velocity (km/s) 1.65 km/s Actual Interferometric min(T – T) = T

30. VSP Summary TT direct prim gggggggg sgsgsgsg - T > - mult sg min( ) g 1. 2. VSP  CDP traveltimes 3.Removes rec. statics & multiple tomo. Tcdp(s,g) =min[min( Tdirect(g,:) - Tmult(s,:) )] s g TTTg g

31. Outline Target Oriented Fermat’s Interferometric Principle Fermat’s Interferometric Principle Numerical Example Interferometry Background

32. Uninteresting Part of Medium of Medium Specular Reflection Fermat’s Principle: T+T – T >0 ghostdiffraction s Diffraction

33. Uninteresting Part of Medium of Medium Specular Reflection Fermat’s Principle: T+T – T >0 reflectiondiffraction s Diffraction Target Oriented Interferometric Tomography

34. Acknowledgments UTAM sponsors Exxon for 2-D field data J. Claerbout + J. Rickett II evolved from daylight imaging

35. Earthquake Data typically Use Direct Waves => Tomography Uninteresting Part of Medium of Medium Time Direct Direct Problem: Uninteresting Parts of Medium Distort Tomogram Goal: Transform Traveltimes into Primary Reflection Traveltimes Specular Reflection Basin

36. Uninteresting Part of Medium of Medium Direct Specular Reflection Time Goal: Transform Traveltimes into Primary Reflection Traveltimes

37. Fermat’s Principle: T - T > 0 multmultsgsg = When is there equality? Fermat’s Interferometric Principle For Multiple Tomography 0 600 m 0 s 0.135 s 3.5 km/s 1.4 km/s Time (s) Ghost Reflection Primary Reflection Interfer. Reflection min(T – T) = T

38. CDP Summary TT prim prim sgsgsgsg gggggggg - T > - mult sg min( ) s 1. 2. Extend CDP sources laterally 3.Removes 1/3 statics & multiple tomo. Tdatum(gp,g) =min[min( Tprim(:,gp) + Tmult(:,g) )] s g g TTT

39. Uninteresting Part of Medium of Medium Specular Reflection Fermat’s Principle: T+T – T >0 reflectiondiffraction s Diffraction