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CRS stacking: a simplified explanation Mann et al. CRS stacking: a simplified explanation Motivation CRS stack Jrgen Mann 1 , Jrg Schleicher 2 , Stacking parameters and Thomas Hertweck 3 What about 3D? Practical aspects Conclusion

  1. CRS stacking: a Basic idea simplified explanation Mann et al. Observations: Motivation ◮ conventional stack implicitly relies on reflector CRS stack continuity Stacking parameters (this also applies to NMO + DMO correction) What about 3D? ◮ based on normal rays for offset zero Practical aspects Conclusion ◮ we have band-limited data Acknowledgments ➥ Fresnel zone concept Consequences: If conventional stack works ◮ there are neighboring reflection points W I T

  2. CRS stacking: a Basic idea simplified explanation Mann et al. Observations: Motivation ◮ conventional stack implicitly relies on reflector CRS stack continuity Stacking parameters (this also applies to NMO + DMO correction) What about 3D? ◮ based on normal rays for offset zero Practical aspects Conclusion ◮ we have band-limited data Acknowledgments ➥ Fresnel zone concept Consequences: If conventional stack works ◮ there are neighboring reflection points ◮ they physically contribute to the wavefield at a considered CMP W I T

  3. CRS stacking: a Basic idea simplified explanation Mann et al. Observations: Motivation ◮ conventional stack implicitly relies on reflector CRS stack continuity Stacking parameters (this also applies to NMO + DMO correction) What about 3D? ◮ based on normal rays for offset zero Practical aspects Conclusion ◮ we have band-limited data Acknowledgments ➥ Fresnel zone concept Consequences: If conventional stack works ◮ there are neighboring reflection points ◮ they physically contribute to the wavefield at a considered CMP Why shouldn’t we incorporate these W I T neighboring reflection points?

  4. CRS stacking: a Coverage of one CMP ray family simplified explanation Mann et al. 3000 Motivation CRS stack 2500 Stacking parameters What about 3D? 2000 Practical aspects Offset [m] Conclusion 1500 Acknowledgments 1000 500 0 400 600 800 1000 1200 1400 1600 1800 Midpoint [m] W I T Traces with reflection points on reflector area illuminated by one CMP ray family

  5. CRS stacking: a Projected Fresnel zone simplified explanation Mann et al. 3000 Motivation CRS stack 2500 Stacking parameters What about 3D? 2000 Practical aspects Offset [m] Conclusion 1500 Acknowledgments 1000 500 0 400 600 800 1000 1200 1400 1600 1800 Midpoint [m] W I T Projected Fresnel zone of the reflector area illuminated by one CMP ray family

  6. CRS stacking: a CRS stack simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion Acknowledgments W I T

  7. CRS stacking: a CRS stack simplified explanation Mann et al. Features inherited from conventional stack: Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion Acknowledgments W I T

  8. CRS stacking: a CRS stack simplified explanation Mann et al. Features inherited from conventional stack: Motivation CRS stack ◮ normal ray concept Stacking parameters What about 3D? Practical aspects Conclusion Acknowledgments W I T

  9. CRS stacking: a CRS stack simplified explanation Mann et al. Features inherited from conventional stack: Motivation CRS stack ◮ normal ray concept Stacking parameters ◮ assumption of reflector continuity What about 3D? Practical aspects Conclusion Acknowledgments W I T

  10. CRS stacking: a CRS stack simplified explanation Mann et al. Features inherited from conventional stack: Motivation CRS stack ◮ normal ray concept Stacking parameters ◮ assumption of reflector continuity What about 3D? Practical aspects ◮ analytical traveltime approximation (2nd order) Conclusion Acknowledgments W I T

  11. CRS stacking: a CRS stack simplified explanation Mann et al. Features inherited from conventional stack: Motivation CRS stack ◮ normal ray concept Stacking parameters ◮ assumption of reflector continuity What about 3D? Practical aspects ◮ analytical traveltime approximation (2nd order) Conclusion ◮ coherence analysis yields stacking parameters Acknowledgments W I T

  12. CRS stacking: a CRS stack simplified explanation Mann et al. Features inherited from conventional stack: Motivation CRS stack ◮ normal ray concept Stacking parameters ◮ assumption of reflector continuity What about 3D? Practical aspects ◮ analytical traveltime approximation (2nd order) Conclusion ◮ coherence analysis yields stacking parameters Acknowledgments ◮ stack yields simulated zero-offset section W I T

  13. CRS stacking: a CRS stack simplified explanation Mann et al. Features inherited from conventional stack: Motivation CRS stack ◮ normal ray concept Stacking parameters ◮ assumption of reflector continuity What about 3D? Practical aspects ◮ analytical traveltime approximation (2nd order) Conclusion ◮ coherence analysis yields stacking parameters Acknowledgments ◮ stack yields simulated zero-offset section Additional features: W I T

  14. CRS stacking: a CRS stack simplified explanation Mann et al. Features inherited from conventional stack: Motivation CRS stack ◮ normal ray concept Stacking parameters ◮ assumption of reflector continuity What about 3D? Practical aspects ◮ analytical traveltime approximation (2nd order) Conclusion ◮ coherence analysis yields stacking parameters Acknowledgments ◮ stack yields simulated zero-offset section Additional features: ◮ incorporates neighboring CMP gathers W I T

  15. CRS stacking: a CRS stack simplified explanation Mann et al. Features inherited from conventional stack: Motivation CRS stack ◮ normal ray concept Stacking parameters ◮ assumption of reflector continuity What about 3D? Practical aspects ◮ analytical traveltime approximation (2nd order) Conclusion ◮ coherence analysis yields stacking parameters Acknowledgments ◮ stack yields simulated zero-offset section Additional features: ◮ incorporates neighboring CMP gathers ◮ yields additional stacking parameters W I T

  16. CRS stacking: a CRS stack simplified explanation Mann et al. Features inherited from conventional stack: Motivation CRS stack ◮ normal ray concept Stacking parameters ◮ assumption of reflector continuity What about 3D? Practical aspects ◮ analytical traveltime approximation (2nd order) Conclusion ◮ coherence analysis yields stacking parameters Acknowledgments ◮ stack yields simulated zero-offset section Additional features: ◮ incorporates neighboring CMP gathers ◮ yields additional stacking parameters ◮ increases the coverage W I T

  17. CRS stacking: a CRS stack simplified explanation Mann et al. Features inherited from conventional stack: Motivation CRS stack ◮ normal ray concept Stacking parameters ◮ assumption of reflector continuity What about 3D? Practical aspects ◮ analytical traveltime approximation (2nd order) Conclusion ◮ coherence analysis yields stacking parameters Acknowledgments ◮ stack yields simulated zero-offset section Additional features: ◮ incorporates neighboring CMP gathers ◮ yields additional stacking parameters ◮ increases the coverage ◮ improves reflector continuity and S/N ratio W I T

  18. CRS stacking: a CRS stacking parameters simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion Acknowledgments W I T

  19. CRS stacking: a CRS stacking parameters simplified explanation Mann et al. Motivation CRS stack CRS stacking operator usually parameterized Stacking parameters in terms of wavefield attributes What about 3D? Practical aspects Conclusion Acknowledgments W I T

  20. CRS stacking: a CRS stacking parameters simplified explanation Mann et al. Motivation CRS stack CRS stacking operator usually parameterized Stacking parameters in terms of wavefield attributes What about 3D? + vivid geometrical interpretation Practical aspects Conclusion Acknowledgments W I T

  21. CRS stacking: a CRS stacking parameters simplified explanation Mann et al. Motivation CRS stack CRS stacking operator usually parameterized Stacking parameters in terms of wavefield attributes What about 3D? + vivid geometrical interpretation Practical aspects Conclusion + useful for inversion, smoothing, . . . Acknowledgments W I T

  22. CRS stacking: a CRS stacking parameters simplified explanation Mann et al. Motivation CRS stack CRS stacking operator usually parameterized Stacking parameters in terms of wavefield attributes What about 3D? + vivid geometrical interpretation Practical aspects Conclusion + useful for inversion, smoothing, . . . Acknowledgments – unfamiliar parameters W I T

  23. CRS stacking: a CRS stacking parameters simplified explanation Mann et al. Motivation CRS stack CRS stacking operator usually parameterized Stacking parameters in terms of wavefield attributes What about 3D? + vivid geometrical interpretation Practical aspects Conclusion + useful for inversion, smoothing, . . . Acknowledgments – unfamiliar parameters Aims in the following: W I T

  24. CRS stacking: a CRS stacking parameters simplified explanation Mann et al. Motivation CRS stack CRS stacking operator usually parameterized Stacking parameters in terms of wavefield attributes What about 3D? + vivid geometrical interpretation Practical aspects Conclusion + useful for inversion, smoothing, . . . Acknowledgments – unfamiliar parameters Aims in the following: ◮ operator expressed in more familiar terms W I T

  25. CRS stacking: a CRS stacking parameters simplified explanation Mann et al. Motivation CRS stack CRS stacking operator usually parameterized Stacking parameters in terms of wavefield attributes What about 3D? + vivid geometrical interpretation Practical aspects Conclusion + useful for inversion, smoothing, . . . Acknowledgments – unfamiliar parameters Aims in the following: ◮ operator expressed in more familiar terms ◮ demonstrate relation between these parameters W I T

  26. CRS stacking: a CRS stacking parameters simplified explanation Mann et al. Motivation CRS stack CRS stacking operator usually parameterized Stacking parameters in terms of wavefield attributes What about 3D? + vivid geometrical interpretation Practical aspects Conclusion + useful for inversion, smoothing, . . . Acknowledgments – unfamiliar parameters Aims in the following: ◮ operator expressed in more familiar terms ◮ demonstrate relation between these parameters ◮ clear distinction between model and data space W I T

  27. CRS stacking: a CRS stacking operator simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion Acknowledgments W I T

  28. CRS stacking: a CRS stacking operator simplified explanation Mann et al. Hyperbolic representation: Motivation CRS stack x 2 + ∆ m 2 t 2 ( ∆ m , x ) = [ t 0 + 2 p ∆ m ] 2 + Stacking parameters v 2 v 2 What about 3D? NMO CMO Practical aspects Conclusion Acknowledgments W I T

  29. CRS stacking: a CRS stacking operator simplified explanation Mann et al. Hyperbolic representation: Motivation CRS stack x 2 + ∆ m 2 t 2 ( ∆ m , x ) = [ t 0 + 2 p ∆ m ] 2 + Stacking parameters v 2 v 2 What about 3D? NMO CMO Practical aspects Conclusion Acknowledgments midpoint displacement m − m 0 ∆ m W I T

  30. CRS stacking: a CRS stacking operator simplified explanation Mann et al. Hyperbolic representation: Motivation CRS stack x 2 + ∆ m 2 t 2 ( ∆ m , x ) = [ t 0 + 2 p ∆ m ] 2 + Stacking parameters v 2 v 2 What about 3D? NMO CMO Practical aspects Conclusion Acknowledgments midpoint displacement m − m 0 ∆ m p horizontal slowness W I T

  31. CRS stacking: a CRS stacking operator simplified explanation Mann et al. Hyperbolic representation: Motivation CRS stack x 2 + ∆ m 2 t 2 ( ∆ m , x ) = [ t 0 + 2 p ∆ m ] 2 + Stacking parameters v 2 v 2 What about 3D? NMO CMO Practical aspects Conclusion Acknowledgments midpoint displacement m − m 0 ∆ m p horizontal slowness v CMO curvature-moveout velocity W I T

  32. CRS stacking: a CRS stacking operator simplified explanation Mann et al. Hyperbolic representation: Motivation CRS stack x 2 + ∆ m 2 t 2 ( ∆ m , x ) = [ t 0 + 2 p ∆ m ] 2 + Stacking parameters v 2 v 2 What about 3D? NMO CMO Practical aspects x 2 t 2 4 t 0 p ∆ m + 4 ∆ m 2 p 2 Conclusion = 0 + + v 2 Acknowledgments NMO � �� � � �� � conventional stack dip dependent ∆ m 2 + v CMO � �� � curvature dependent midpoint displacement m − m 0 ∆ m p horizontal slowness v CMO curvature-moveout velocity W I T

  33. CRS stacking: a simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion Acknowledgments Time W I T Distance

  34. CRS stacking: a simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion m 0 Acknowledgments Time W I T Distance

  35. CRS stacking: a simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion m 0 Acknowledgments Time Time W I T Distance Offset

  36. CRS stacking: a simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion m 0 Acknowledgments P P 0 t 0 0 Time Time W I T Distance Offset

  37. CRS stacking: a simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion m 0 Acknowledgments P P 0 t 0 0 Time Time W I T Distance Offset

  38. CRS stacking: a simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO W I T Distance Offset

  39. CRS stacking: a simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO W I T Distance Offset

  40. CRS stacking: a simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO W I T Distance Offset

  41. CRS stacking: a simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO P 0 W I T Distance Offset

  42. CRS stacking: a simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO P 0 W I T Distance Offset

  43. CRS stacking: a simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 W I T Distance Offset

  44. CRS stacking: a simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 W I T Distance Offset

  45. CRS stacking: a simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  46. CRS stacking: a simplified explanation Mann et al. Depth Motivation CRS stack Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  47. CRS stacking: a m 0 simplified explanation Mann et al. Depth Motivation CRS stack Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  48. CRS stacking: a m 0 simplified explanation Mann et al. Depth Motivation CRS stack Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  49. CRS stacking: a m 0 simplified explanation Mann et al. α Depth Motivation CRS stack Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  50. CRS stacking: a m 0 simplified explanation Mann et al. α Depth Motivation CRS stack NIP Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  51. CRS stacking: a m 0 simplified explanation Mann et al. α Depth Motivation CRS stack NIP Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  52. CRS stacking: a m 0 simplified explanation Mann et al. α Depth Motivation CRS stack NIP Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  53. CRS stacking: a m 0 simplified explanation Mann et al. α Depth Motivation CRS stack NIP Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  54. CRS stacking: a m 0 simplified explanation Mann et al. α Depth Motivation CRS stack NIP Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  55. CRS stacking: a m 0 simplified explanation Mann et al. α Depth Motivation CRS stack NIP Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  56. CRS stacking: a m 0 simplified explanation Mann et al. α Depth Motivation CRS stack NIP Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  57. m 0 CRS stacking: a simplified explanation Mann et al. α R N Depth Motivation CRS stack NIP Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  58. m 0 CRS stacking: a simplified explanation Mann et al. α R N Depth Motivation CRS stack NIP Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  59. m 0 CRS stacking: a simplified explanation Mann et al. α R N Depth Motivation CRS stack NIP Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  60. m 0 CRS stacking: a simplified explanation Mann et al. α R N Depth Motivation CRS stack NIP Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  61. m 0 CRS stacking: a simplified explanation Mann et al. α R N Depth Motivation CRS stack NIP Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  62. m 0 CRS stacking: a simplified explanation Mann et al. α R N Depth Motivation CRS stack NIP Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  63. m 0 CRS stacking: a R NIP simplified explanation Mann et al. α R N Depth Motivation CRS stack NIP Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Time Time NMO 2p P 0 v CMO W I T Distance Offset

  64. m 0 CRS stacking: a R NIP simplified explanation Mann et al. α R N Depth Motivation CRS stack NIP Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Data space Time Time NMO 2p P 0 v CMO W I T Distance Offset

  65. m 0 CRS stacking: a R NIP simplified explanation Mann et al. α R N Depth Model space Motivation CRS stack NIP Stacking parameters What about 3D? Practical aspects Distance Conclusion m 0 Acknowledgments P P 0 t 0 0 v Data space Time Time NMO 2p P 0 v CMO W I T Distance Offset

  66. CRS stacking: a Relations between parameters simplified explanation Mann et al. Motivation CRS stack Stacking parameters What about 3D? Practical aspects Conclusion Acknowledgments W I T

  67. CRS stacking: a Relations between parameters simplified explanation Mann et al. Motivation CRS stack Parameterization in terms of. . . Stacking parameters What about 3D? traveltime wavefront slowness and Practical aspects derivatives properties velocities Conclusion � Acknowledgments ∂ t � sin α p � ∂ m v 0 m = m 0 , x = 0 � cos 2 α ∂ 2 t ∂ t � v CMO � ∂ m , ∂ m 2 v 0 R N m = m 0 , x = 0 � cos 2 α ∂ m , ∂ 2 t ∂ t � v NMO � ∂ x 2 v 0 R NIP m = m 0 , x = 0 W I T

  68. CRS stacking: a Relations between parameters simplified explanation Mann et al. Motivation CRS stack Parameterization in terms of. . . Stacking parameters What about 3D? traveltime wavefront slowness and Practical aspects derivatives properties velocities Conclusion � Acknowledgments ∂ t � sin α p � ∂ m v 0 m = m 0 , x = 0 � cos 2 α ∂ 2 t ∂ t � v CMO � ∂ m , ∂ m 2 v 0 R N m = m 0 , x = 0 � cos 2 α ∂ m , ∂ 2 t ∂ t � v NMO � ∂ x 2 v 0 R NIP m = m 0 , x = 0 v 0 : near surface velocity W I T

  69. CRS stacking: a Relations between parameters simplified explanation Mann et al. Motivation CRS stack Parameterization in terms of. . . Stacking parameters What about 3D? traveltime wavefront slowness and Practical aspects derivatives properties velocities Conclusion � Acknowledgments ∂ t � sin α p � ∂ m v 0 m = m 0 , x = 0 � cos 2 α ∂ 2 t ∂ t � v CMO � ∂ m , ∂ m 2 v 0 R N m = m 0 , x = 0 � cos 2 α ∂ 2 t � v NMO � ∂ h 2 v 0 R NIP x = x m , h = 0 v 0 : near surface velocity W I T

  70. CRS stacking: a Relations between parameters simplified explanation Mann et al. Motivation CRS stack Parameterization in terms of. . . Stacking parameters What about 3D? traveltime wavefront slowness and Practical aspects derivatives properties velocities Conclusion � Acknowledgments ∂ t � sin α p � ∂ m v 0 m = m 0 , x = 0 � cos 2 α ∂ 2 t ∂ t � v CMO � ∂ m , ∂ m 2 v 0 R N m = m 0 , x = 0 � cos 2 α ∂ m , ∂ 2 t ∂ t � v NMO � ∂ x 2 v 0 R NIP m = m 0 , x = 0 v 0 : near surface velocity W I T

  71. CRS stacking: a CRS operator simplified explanation Mann et al. Offset Midpoint Midpoint e m i M T O Offset Motivation f f s i d Time e t p o i n t CRS stack Time Stacking parameters What about 3D? Practical aspects Conclusion Acknowledgments CMP gather and section at offset 500 m W I T

  72. CRS stacking: a CRS operator simplified explanation Mann et al. Offset Midpoint Midpoint e m i M T O Offset Motivation f f s i d Time e t p o i n t CRS stack Time Stacking parameters What about 3D? Practical aspects Conclusion Acknowledgments CMP gather and section at offset 500 m Displayed ranges: offset up to 3.5 km, midpoint ± 5 km W I T

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