Mauricio D' Sacchi

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Signal Analysis and Imaging Group Department of
Physics University of Alberta
Filter-Bank Strategies for Efficient Computation
of Radon Transforms for SNR Enhancement

• Mauricio D. Sacchi

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Outline

• Radon Transforms for Noise Signal modeling
• Filter Banks
• Filter Banks Radon Transforms
• Examples
• Summary

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Hybrid Radon Transform (Trad, Sacchi, Ulrych,
JSE 2001)
v
p
d
Inverted m Sparse Inversion
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Hybrid Radon Transform (Trad, Sacchi, Ulrych,
JSE 2001)
Recovered model of hyperbolic events

• Recovered Model of linear events

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Hybrid Radon Transform (Trad, Sacchi, Ulrych,
JSE 2001)
Linear and Hyperbolic RT
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Hybrid Radon Transform (Trad, Sacchi, Ulrych,
JSE 2001)
Simultaneous signal and noise focusing
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Hybrid Radon Transform (Trad, Sacchi, Ulrych,
JSE 2001)
Solution
Model of linear noise
Model of signals with hyperbolic/parabolic moveout
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Hybrid Radon Transform (Trad, Sacchi, Ulrych,
JSE 2001)
Algorithm CG Preconditioning Updates for
high res.
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Hybrid Radon Transform (Trad, Sacchi, Ulrych,
JSE 2001)
Algorithm CG Preconditioning Updates for
high res.
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Filter banks Analysis and Synthesis
s(t)
2
L
L
2
x(t)
x(t)
2
H
H
2
d(t)
x(t)x(t)
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Cosine Filters
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Filter Banks 3 Levels Decomposition
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Analysis Signal Linear Noise
N0512 N1256 N2128
N364
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Analysis Signal Linear Noise
N0512 N1256 N2128
N364
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Analysis Signal Linear Noise
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Proposed Algorithm
IRT Inverse Radon Transform Linear and
Hyperbolic FLRT Forward Linear RT FHRT
Forward Hyperbolic
FHRT
IRT
FLRT
FHRT
IRT
Linear Noise
FLRT
N0512 N1256 N2128
N364
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Analysis Signal Linear Noise at Level 3
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Analysis Signal Linear Noise at Level 3
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Radon Transform at Level 3
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Synthesis from Radon Transform at Level 3
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Radon Transform at Level 3
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Synthesis from Radon Transform at Level 3
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Summary of results at level 3
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Synthesis at Level 1 Modeled Noise
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Final Subtraction at Level 1
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Field Data Example

• 3 Levels decomposition
• High Resolution Hyperbolic Linear Radon
  Transform
• Hybrid RT (Trad, Sacchi and Ulrych, JSE 2001)
• Sparseness in Radon panels is introduced via
  pre-conditioning

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Field Example
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Data at level 3
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Radon at level 3 - low pass decompostion
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Data from Radon at level 3
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Radon at level 3 - high pass decompostion
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Data from Radon at level 3
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Linear noise from level 3 back at level 1
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Final Subtraction
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Cost

• Improvement for 3 levels decomposition

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Summary - Discussions

• High Resolution Time Domain Hybrid Radon
  Transforms are expensive to compute
• The use of Radon de-noising methods with Filter
  Banks leads to a simple and efficient strategies
  for linear noise attenuation

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Summary - Discussions

• We have exploited differences in
• Frequency content
• Moveout signature
• to estimate a model of linear noise that is
• then subtracted from the data
• Important applications Time domain Radon noise
  attenuation of 3D shots and hybrid gathers
  (x-spreads)

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Acknowledgments

• SAIG Sponsors
• CGGVeritas
• ConocoPhillips
• Encana
• ENI SPA AGIP
• Divesco
• Fugro
• Norsk Hydro
• Statoil
• Faculty of Science, University of Alberta
• Natural Sciences and Engineering Research Council
  of Canada (NSERC)