Multiscale Fusion for Seismic Geometric Attribute Enhancement · 2017-09-22 · Multiscale Fusion...
Transcript of Multiscale Fusion for Seismic Geometric Attribute Enhancement · 2017-09-22 · Multiscale Fusion...
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Multiscale Fusion for Seismic
Geometric Attribute Enhancement
26 September, 2017
Motaz Alfarraj*, Haibin Di, and Ghassan AlRegib
Center for Energy and Geo Processing,
Georgia Institute of Technology, Atlanta, GA
{ motaz, haibin_di, alregib}@gatech.edu
www.ghassanalregib.com
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• Objective
• Overview
– Complex trace analysis
– Noise in attributes
– Multiscale analysis
– The Gaussian Pyramid
• Proposed method
– Theory
– Results
• Conclusion
Outline
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• To improve the commonly used seismic attributes by:
– Improving noise robustness
– Preserving small-scale seismic features
Objective
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ถ𝑧(𝑡)𝐶𝑜𝑚𝑝𝑙𝑒𝑥 𝑡𝑟𝑎𝑐𝑒
= ถ𝑥(𝑡)𝑅𝑒𝑎𝑙 𝑡𝑟𝑎𝑐𝑒
+ 𝑖 ถ𝑦(𝑡)𝑄𝑢𝑎𝑑𝑟𝑎𝑡𝑢𝑟𝑒 𝑡𝑟𝑎𝑐𝑒
= 𝐴 𝑡 𝑒𝑖𝜃 𝑡
• Various attributes can be derived from complex seismic traces such as:
1. Instantaneous amplitude: 𝐴 𝑡 = 𝑥2(𝑡) + 𝑦2(𝑡)
2. Instantaneous phase: 𝜃 𝑡 = arg 𝑧 𝑡 = Im ln 𝑧(𝑡)
3. Instantaneous Frequency: f 𝑡 =1
2𝜋Im
𝑧′(𝑡)
𝑧(𝑡)
4. Cosine of the phase: cos(𝜃 𝑡 )
5. Phase dip:
• Temporal Frequency: 𝑓𝑡 =𝑑𝜃
𝑑𝑡
• Spatial Frequency: 𝑓𝑥 =𝑑𝜃
𝑑𝑥
• Dip: 𝛾 = −arctan𝑓𝑥
𝑓𝑡
Complex trace analysis
Illustration of a complex trace
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Noise in attributes
Seismic Inline Dip Attribute
• Noise is traditionally overcome using:
– Larger processing windows. • Might produce low resolution attributes (blurry).
– Post-processing techniques such as spatial filtering • Might compromise small-scale features such as small faults.
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• Multiscale analysis methods refer to the representation of an image at different resolution levels, each of
which comprises features of the same scale in terms of size.
• Salient image structures occur at multiple scales
• Multiscale analysis has been used for a wide verity of applications such as: – Coding
– Compression
– Detection
• An example is The Gaussian Pyramid
Multiscale analysis
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The Gaussian Pyramid
Blur and
downsample
Blur and
downsample
Input SectionScale 0
Scale 1
Scale K-1
Full resolution
1/2 resolution
1/4 resolution
1/8 resolution
2D Gaussian Kernel
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The proposed method
Fusio
n
Multiscale-fused
attribute
Compute
attribute
Scale 0
ResizeCompute
attribute
Blur and
downsample
Scale 1
ResizeCompute
attribute
Blur and
downsample
Scale K-1
Input Section
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• Scale-space filtering as opposed to spatial/temporal filtering
– 𝐴𝑀𝑒𝑎𝑛 𝑚,𝑛 =1
𝐾σ𝐴𝑖[𝑚, 𝑛]
– 𝐴𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑𝑀𝑒𝑎𝑛 𝑚,𝑛 =1
𝐾σ𝛼𝑖𝐴𝑖[𝑚, 𝑛]
– 𝐴𝑀𝑒𝑑𝑖𝑎𝑛 𝑚,𝑛 = 𝑚𝑒𝑑𝑖𝑎𝑛 𝐴0 𝑚,𝑛 ,… , 𝐴𝐾−1[𝑚, 𝑛]
Multiscale Fusion
𝑀𝑒𝑎𝑛 =1
34 + 9 + 7 = 6.67
𝑀𝑒𝑑𝑖𝑎𝑛 = 𝑚𝑒𝑑𝑖𝑎𝑛 4,9,7 = 7
𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑀𝑒𝑎𝑛 =1
63 × 4 + 2 × 9 + 1 × 7 = 6.17
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Results: Dip attribute
Original Multiscale with Mean Fusion
Multiscale with Median Fusion Multiscale with Weighted Mean Fusion
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Original
Multiscale with
Mean Fusion
Multiscale with
Median Fusion
Multiscale with
Weighted Mean
Fusion
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Results Dip Attribute
Original Multiscale with Median Fusion
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Results: Dip Angle
Multiscale AttributeOriginal AttributesTime Section 187 from New Zealand Dataset
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Results: Most positive Curvature
Multiscale AttributeOriginal Attributes
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Results: Most negative curvature
Multiscale AttributeOriginal Attributes
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• Multiscale fusion improves seismic attributes in two aspects:
– Reducing noise present in these attributes
– Persevering small-scale features
• The proposed method can be extended to other seismic attribute such as coherence.
Conclusion
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You can download the code to reproduce these results from here:
Code:
ghassanalregib.com/publications/
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Thank You
For more information about the center, please visit:
http://www.ghassanalregib.com/