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Reverse Time Migration

Reverse Time Migration . 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. Liberty Park Lake . Rolls of Toilet Paper. Time. Find Location of Rock .

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Reverse Time Migration

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

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

  15. 1-way time 1-way time 0 0 -5 Poststack RTM 1. Reverse Time Order of Traces 5 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. Reverse Time Modeling 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 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

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

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

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

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

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

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

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

  25. m(x’+dx) = d(x) G(x|x’+dx)* Multiples time time Primary Primary Multiples x Advantages of Kirchhoff Mig. vs Full Trace Migration 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 3.5 Km Z 2.0 Km Y 3.5 Km 4

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

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

  31. 3D Synthetic Data Kirchhoff Migration W E 0 Redatum + KM Depth (Km) 2.0 Offset (km) 0 Offset (km) 3.5 0 3.5 7 Cross line 200

  32. Numerical Examples • GOM Data • Prism Synthetic Example

  33. GOM Kirchhoff ?

  34. GOM RTM ?

  35. ?

  36. Numerical Examples • GOM Data • Prism 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 Multiples • Methods: RTM A D

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

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