1. Reverse Time Migration Reverse Time Migration

2. Outline Outline Finding a Rock Splash at Liberty Park Finding a Rock Splash at Liberty Park ZO Reverse Time Migration (backwd in time) ZO Reverse Time Migration (backwd in time) ZO Reverse Time Migration (forwd in time) ZO Reverse Time Migration (forwd in time) ZO Reverse Time Migration Code ZO Reverse Time Migration Code Examples Examples

3. Liberty Park Lake Liberty Park Lake Rolls of Toilet Paper Time

4. Find Location of Rock Find Location of Rock Rolls of Toilet Paper Time

5. Find Location of Rock Find Location of Rock Rolls of Toilet Paper Time

6. Find Location of Rock Find Location of Rock Rolls of Toilet Paper Time

7. Find Location of Rock Find Location of Rock Rolls of Toilet Paper Time

8. Find Location of Rock Find Location of Rock Rolls of Toilet Paper Time

9. Find Location of Rock Find Location of Rock Rolls of Toilet Paper Time

10. Outline Outline Finding a Rock Splash at Liberty Park Finding a Rock Splash at Liberty Park ZO Reverse Time Migration (backwd in time) ZO Reverse Time Migration (backwd in time) ZO Reverse Time Migration (forwd in time) ZO Reverse Time Migration (forwd in time) ZO Reverse Time Migration Code ZO Reverse Time Migration Code Examples Examples

11. ZO Modeling 1-way time Reverse Order Traces in Time 0 5

12. 1-way time Reverse Time Migration (Go Backwards in Time) T=0 Focuses at Hand Grenades -5 0

13. Outline Outline Finding a Rock Splash at Liberty Park Finding a Rock Splash at Liberty Park ZO Reverse Time Migration (backwd in time) ZO Reverse Time Migration (backwd in time) ZO Reverse Time Migration (forwd in time) ZO Reverse Time Migration (forwd in time) ZO Reverse Time Migration Code ZO Reverse Time Migration Code Examples Examples

14. 1-way time Reverse Time Migration (Reverse Traces Go Forward in Time) T=0 Focuses at Hand Grenades -5 0

15. Poststack RTM 1. Reverse Time Order of Traces 5 1-way time 0 -50 2. Reversed Traces are Wavelets of loudspeakers

16. Outline Outline Finding a Rock Splash at Liberty Park Finding a Rock Splash at Liberty Park ZO Reverse Time Migration (backwd in time) ZO Reverse Time Migration (backwd in time) ZO Reverse Time Migration (forwd in time) ZO Reverse Time Migration (forwd in time) ZO Reverse Time Migration Code ZO Reverse Time Migration Code Examples Examples

17. Forward Modeling Forward Modeling for it=1:1:nt p2 = 2*p1 - p0 + cns.*del2(p1); p2(xs,zs) = p2(xs,zs) + RICKER(it); % Add bodypoint src term p0=p1;p1=p2; end for it=nt:-1:1 p2 = 2*p1 - p0 + cns.*del2(p1); p2(1:nx,2) = p2(1:nx,2) + data(1:nx,it); % Add bodypoint src term p0=p1;p1=p2; end Reverse Time Modeling Reverse Time Modeling

18. Recall Forward Modeling d=Lm d(x) = G(x|x’)m(x’)dx’  ~~~~~~ Fourier d(x,t) = G(x,t-t s |x’,0)m(x’,t s )dx’dt s   = G(x,t|x’,t s )m(x’,t s )dx’dt s  Stationarity x ztsrc Forward reconstruction of half circles

19. Migration = Adjoint of Data d=Lm d(x) = G(x|x’)m(x’)dx’  m=L d m(x’) = G(x|x’)*d(x)dx T Fourier m(x) = G(x,-t+t s |x’,0)d(x’,t s )dx’dt s   = G(x, t s |x’,t)d(x’,t s )dx’dt s  Stationarity x zt Note: t < t s t=0 t=0

20. Migration = Adjoint of Data d=Lm d(x) = G(x|x’)m(x’)dx’  m=L d m(x’) = G(x|x’)*d(x)dx T Fourier m(x) = G(x,-t+t s |x’,0)d(x’,t s )dx’dt s   = G(x, t s |x’,t)d(x’,t s )dx’dt s  Stationarity x zt Note: t < t s t=0 t=0

21. Migration = Adjoint of Data d=Lm d(x) = G(x|x’)m(x’)dx’  m=L d m(x’) = G(x|x’)*d(x)dx T Fourier m(x) = G(x,-t+t s |x’,0)d(x’,t s )dx’dt s   = G(x, t s |x’,t)d(x’,t s )dx’dt s  Stationarity x zt Note: t < t s t=0 t=0

22. Migration = Adjoint of Data d=Lm d(x) = G(x|x’)m(x’)dx’  m=L d m(x’) = G(x|x’)*d(x)dx T Fourier m(x) = G(x,-t+t s |x’,0)d(x’,t s )dx’dt s   = G(x, t s |x’,t)d(x’,t s )dx’dt s  Stationarity x zt Note: t < t s t=0 t=0

23. Migration = Adjoint of Data d=Lm d(x) = G(x|x’)m(x’)dx’  m=L d m(x’) = G(x|x’)*d(x)dx T Fourier m(x) = G(x,-t+t s |x’,0)d(x’,t s )dx’dt s   = G(x, t s |x’,t)d(x’,t s )dx’dt s  Stationarity x zt Note: t < t s Backward reconstruction of half circles t=0 t=0

24. Migration = Adjoint of Data d=Lm d(x) = G(x|x’)m(x’)dx’  m=L d m(x’) = G(x|x’)*d(x)dx T Fourier m(x) = G(x,-t+t s |x’,0)d(x’,t s )dx’dt s   = G(x, t s |x’,t)d(x’,t s )dx’dt s  Stationarity Note: t < t s x zt Backward reconstruction of half circles Let t s = -t s -- Note: t > t s x zt Backward reconstruction of half circles zx z t Forward prop. Of reverse time data t=0 t=0

25. Advantages of m(x’+dx) = d(x) G(x|x’+dx)* time time Multiples Primary Primary Kirchhoff Mig. vs Full Trace Migration 1. Low-Fold Stack vs Superstack 2. Poor Resolution vs Superresolution Multiples x

26. Outline Outline Finding a Rock Splash at Liberty Park Finding a Rock Splash at Liberty Park ZO Reverse Time Migration (backwd in time) ZO Reverse Time Migration (backwd in time) ZO Reverse Time Migration (forwd in time) ZO Reverse Time Migration (forwd in time) ZO Reverse Time Migration Code ZO Reverse Time Migration Code Examples Examples

27. Numerical Examples

28. 3D Synthetic Data 3D SEG/EAGE Salt Model Z 2.0 Km X 3.5 Km Y 3.5 Km 4

29. Cross line 160 Depth (Km) 0 W E 3D Synthetic Data 3.5 Offset (km) 0 2.0 3.5 Offset (km) 0 Kirchhoff Migration Redatum + KM 5

30. Cross line 180 Depth (Km) 0 W E 3.5 Offset (km) 0 2.0 3.5 Offset (km) 0 Kirchhoff Migration Redatum + KM 3D Synthetic Data 6

31. Cross line 200 Depth (Km) 0 W E 3.5 Offset (km) 0 2.0 3.5 Offset (km) 0 Kirchhoff Migration Redatum + KM 7

32. Numerical Examples GOM DataGOM Data Prism Synthetic ExamplePrism Synthetic Example

33. ? GOM Kirchhoff

34. ? GOM RTM

35. ?

36. Numerical Examples GOM DataGOM Data Prism Synthetic ExamplePrism Synthetic Example

37. Prism Wave Migration One Way Migration of Prestack Data RTM of Prestack Data Courtesy TLE: Farmer et al. (2006)

38. Summary 1. RTM much more expensive than Kirchhoff Mig. 2. If V(x,y,z) accurate then all multiples Included so better S/N ration and better Resolution. 3. If V(x,y,z) not accurate then smooth velocity Model seems to work better. Free surface multiples included. 4. RTM worth it for salt models, not layered V(x,y,z). 5. RTM is State of art for GOM and Salt Structures.

39. Solution Claim: Image both Primaries and MultiplesClaim: Image both Primaries and Multiples? ?AD Methods: RTMMethods: RTM

40. Piecemeal Methods Assume Knowledge of Important MirrorAssume Knowledge of Important Mirror? ?AD Reverse Time MigrationReverse Time Migration 2-Way Mirror Wave Migration: