Leastsquares Joint Imaging of Primaries and Multiples

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Least-squares Joint Imaging of Primaries and
Multiples

• Morgan Brown
• Stanford University
• 2002 SEG, Salt Lake City

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A Stack of the Primaries...
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and a Stack of the Multiples
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CMP gathers are also consistent
primaries multiples
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What information can multiples add?

• At least redundant
• Related AVO behavior
• Similar structural image
• Different illumination
• Near offsets
• Shadow zones

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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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The Gameplan

• Imaging
• NMO for Multiples
• Constraint/Integration
• Regularized least-squares inversion
• Synthetic Real data tests

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NMO for multiples - kinematics
R
S
t
t
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NMO for multiples - kinematics
Building a pseudo-primary
t
R
S
t
t
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NMO for multiples - kinematics
Building a pseudo-primary
t
R
S
t
t
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NMO for multiples - kinematics
Building a pseudo-primary
t
R
S
t
t
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NMO for multiples - kinematics
Building a pseudo-primary
t
R
S
t
t
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NMO for multiples - kinematics
Building a pseudo-primary
t
R
S
t
t
Dx
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NMO for multiples - kinematics
NMO for primary
NMO for multiple 1
Effective RMS velocity
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NMO for multiples - kinematics
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Modeling Amplitudes Assumptions

• Constant AVO WB reflection.
• Free surface R.C. -1.
• Ignore geometric spreading.
• Ignoring primary AVO multi (-r)iprim
• AVO more later.

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Forward Modeling Equation
d
m0
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Forward Modeling Equation
(-r)NMO1
m1
d
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Forward Modeling Equation
(-r)2NMO2
m2
d
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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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Least-squares objective function
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Least-squares objective function
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Image Simplicity and Crosstalk
Ideally, the simplest model...
N2R2m2
N1R1m1
N0m0


m0
m1
m2
d
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Model Simplicity and Crosstalk
but this problem is underdetermined.
N2R2m2
N1R1m1
N0m0


m0
m1
m2
d
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Discriminating between crosstalk and signal
Self-consistent, flat primaries
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Discriminating between crosstalk and signal
Inconsistent, curved crosstalk
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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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Dm Modeling AVO of multiples

• No explicit AVO modeling
• Model relative primary/multiple AVO dependence.
• Dm differences at different offsets.

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Dm Modeling AVO of multiples
Mult(h) prim(hp) (-r)
hp
R
S
t
h
t
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Dm Modeling AVO of multiples
In constant velocity
hp
R
S
t
h
t
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Dm Modeling AVO of multiples
In constant velocity
Curves hp(t)
m1
m0
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Synthetic Data Results
Raw primaries
Raw mult. 1
Raw mult. 2
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Synthetic Data Results
Est. primaries
Est. mult. 1
Est. mult. 2
x(-r)
x(-r 2)
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Synthetic Data Results
Raw primaries
Est. primaries
Difference
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Synthetic Data 2 Results
Est. primaries
Raw primaries
Difference
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Real Data Results
Raw primaries
Est. primaries
Difference
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Strengths

• Good separation.
• ...at near offsets
• without a prior noise model
• Amplitude-preserving process
• General integration framework

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Weaknesses

• 1-D earth.
• Amplitudes - Incomplete Modeling?
• Parameter sensitivity
• e1, e2, r, velocity.
• Multiples coherent across offset.
• NMO stretch.

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The Future

• Migrationtougher battle, richer spoils
• Different illumination
• Amplitudes?
• Converted waves (PS,PSP).
• Tall operator.
• One image, many datasets.
• Prior wavefield separation.

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Acknowledgements

• ExxonMobil, WesternGeco for data.
• Biondo Biondi, Bob Clapp, Antoine Guitton.