1. Reverse Time Migration

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

3. Liberty Park Lake
Rolls of Toilet Paper
Time

4. Find Location of Rock
Rolls of Toilet Paper
Time

5. Find Location of Rock
Rolls of Toilet Paper
Time

6. Find Location of Rock
Rolls of Toilet Paper
Time

7. Find Location of Rock
Rolls of Toilet Paper
Time

8. Find Location of Rock
Rolls of Toilet Paper
Time

9. Find Location of Rock
Rolls of Toilet Paper
Time

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

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

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

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

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

15. Poststack RTM 1. Reverse Time Order of Traces5
1-way time -5
1-way time
2. Reversed Traces are Wavelets of loudspeakers

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

17. Forward Modeling Reverse Time 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

18. Recall Forward Modeling d=Lm d(x) = G(x|x’)m(x’)dx’~ ~ ~ ~ ~ ~ ò
d=Lm d(x) = G(x|x’)m(x’)dx’
Fourier
d(x,t) = G(x,t-ts|x’,0)m(x’,ts)dx’dts ò
= G(x,t|x’,ts)m(x’,ts)dx’dts ò
Stationarity x z t
src
Forward reconstruction
of half circles

19. Migration = Adjoint of Data
d=Lm d(x) = G(x|x’)m(x’)dx’ ò
m=L d m(x’) = G(x|x’)*d(x)dx ò T
Fourier
t=0
m(x) = G(x,-t+ts|x’,0)d(x’,ts)dx’dts ò
Note: t < ts
= G(x, ts|x’,t)d(x’,ts)dx’dts ò
Stationarity x z t

20. Migration = Adjoint of Data
d=Lm d(x) = G(x|x’)m(x’)dx’ ò
m=L d m(x’) = G(x|x’)*d(x)dx ò T
Fourier
t=0
m(x) = G(x,-t+ts|x’,0)d(x’,ts)dx’dts ò
Note: t < ts
= G(x, ts|x’,t)d(x’,ts)dx’dts ò
Stationarity x z t

21. Migration = Adjoint of Data
d=Lm d(x) = G(x|x’)m(x’)dx’ ò
m=L d m(x’) = G(x|x’)*d(x)dx ò T
Fourier
t=0
m(x) = G(x,-t+ts|x’,0)d(x’,ts)dx’dts ò
Note: t < ts
= G(x, ts|x’,t)d(x’,ts)dx’dts ò
Stationarity x z t

22. Migration = Adjoint of Data
d=Lm d(x) = G(x|x’)m(x’)dx’ ò
m=L d m(x’) = G(x|x’)*d(x)dx ò T
Fourier
t=0
m(x) = G(x,-t+ts|x’,0)d(x’,ts)dx’dts ò
Note: t < ts
= G(x, ts|x’,t)d(x’,ts)dx’dts ò
Stationarity x z t

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

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

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

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

27. Numerical Examples

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

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

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

31. 3D Synthetic Data 7 Kirchhoff Migration W E Redatum + KM Depth (Km)
Redatum + KM
Depth (Km)
2.0
Offset (km)
Offset (km)
3.5
3.5 7
Cross line 200

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

33. GOM Kirchhoff ?

34. GOM RTM ?

35. ?

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

37. Prism Wave Migration Courtesy TLE: Farmer et al. (2006)
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 Multiples Methods: RTM A

40. ? ? Piecemeal Methods 2-Way Mirror Wave Migration:
Assume Knowledge of Important Mirror
Reverse Time Migration A D ? ?