1. Least-squares Joint Imaging of Primaries and Multiples
Morgan Brown
Stanford University
2002 SEG, Salt Lake City
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2. A Stack of the Primaries...
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3. …and a Stack of the Multiples
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4. CMP gathers are also consistent
primaries multiples
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5. What information can multiples add?
At least redundant:
Related AVO behavior
Similar structural image
Different illumination:
Near offsets
Shadow zones
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6. How to exploit the information?
Constraint on existing information
Integrate additional information
Three requirements:
Image self-consistency
Consistency with data
Simplicity of images
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7. The Gameplan Imaging: “NMO for Multiples” Constraint/Integration:
Regularized least-squares inversion
Synthetic & Real data tests
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8. NMO for multiples - kinematics
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9. NMO for multiples - kinematics
Building a pseudo-primary t’ S R 1 t’ t
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10. NMO for multiples - kinematics
Building a pseudo-primary t’ S R 2 t’ t
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11. NMO for multiples - kinematics
Building a pseudo-primary t’ S R 3 t’ t
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12. NMO for multiples - kinematics
Building a pseudo-primary t’ S R 4 t’ t
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13. NMO for multiples - kinematics
Building a pseudo-primary t’ S R t’ t Dx
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14. NMO for multiples - kinematics
primary
NMO for
multiple 1
Effective
RMS velocity
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15. NMO for multiples - kinematics
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16. Modeling Amplitudes: Assumptions
Constant AVO WB reflection.
Free surface R.C. = -1.
Ignore geometric spreading.
Ignoring primary AVO: multi (-r)i*prim
AVO: more later.
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17. Forward Modeling Equation
NMO0 d m0
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18. Forward Modeling Equation
(-r)*NMO1 d m1
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19. Forward Modeling Equation
(-r)2*NMO2 d m2
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20. Forward Modeling Equation
Ni :adjoint of NMO
for multiple i.
Ri : (-r)iI.
mi : pseudo-primary
panel i.
d : input CMP gather.
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21. Least-squares objective function
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22. Least-squares objective function
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23. Image Simplicity and Crosstalk
Ideally, the “simplest” model...
N0m0 +
N1R1m1 +
N2R2m2
“inverse” d m0 m1 m2
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24. Model Simplicity and Crosstalk
…but this problem is underdetermined.
N0m0 +
N1R1m1 +
N2R2m2
“inverse” d m0 m1 m2
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25. Discriminating between crosstalk and signal
Self-consistent,
flat primaries
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26. Discriminating between crosstalk and signal
Inconsistent,
curved
crosstalk
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27. Model Regularization suppresses crosstalk
Dm= Difference between pseudo-primary panels.
Penalizes inconsistent crosstalk events.
Dx= Difference along offset. Penalizes curving events.
e1,e2 = Scalar regularization parameters.
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28. Dm: Modeling AVO of multiples
No explicit AVO modeling
Model relative primary/multiple AVO dependence.
Dm differences at different offsets.
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29. Dm: Modeling AVO of multiples
From forward model
Mult(h) ~ prim(hp) * (-r) hp S R t’ h t
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30. Dm: Modeling AVO of multiples
In constant velocity: hp S R t’ h t
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31. Dm: Modeling AVO of multiples
In constant velocity:
Curves:
hp(t) - - m0 m1
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32. Synthetic Data Results
Raw primaries
Raw mult. 1
Raw mult. 2
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33. Synthetic Data Results
Est. primaries
Est. mult. 1
Est. mult. 2
x(-r)
x(-r 2)
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34. Synthetic Data Results
Raw primaries
Est. primaries
Difference
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35. Synthetic Data #2 Results
Raw primaries
Est. primaries
Difference
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36. Real Data Results Raw primaries Est. primaries Difference
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37. Strengths Good separation…. Amplitude-preserving process
...at near offsets
…without a prior noise model
Amplitude-preserving process
General integration framework
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38. Weaknesses 1-D earth. Amplitudes - Incomplete Modeling?
Parameter sensitivity…
…e1, e2, r, velocity.
Multiples coherent across offset.
NMO stretch.
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39. The Future Migration…tougher battle, richer spoils
Different illumination
Amplitudes?
Converted waves (PS,PSP).
“Tall” operator.
One image, many datasets.
Prior wavefield separation.
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40. Acknowledgements ExxonMobil, WesternGeco for data.
Biondo Biondi, Bob Clapp, Antoine Guitton.
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