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

• Objective

• Overview

– Complex trace analysis

– Noise in attributes

– Multiscale analysis

– The Gaussian Pyramid

• Proposed method

– Theory

– Results

• Conclusion

Outline

• To improve the commonly used seismic attributes by:

– Improving noise robustness

– Preserving small-scale seismic features

Objective

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

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.

• 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

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

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

• 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

Results: Dip attribute

Original Multiscale with Mean Fusion

Multiscale with Median Fusion Multiscale with Weighted Mean Fusion

Original

Multiscale with

Mean Fusion

Multiscale with

Median Fusion

Multiscale with

Weighted Mean

Fusion

Results Dip Attribute

Original Multiscale with Median Fusion

Results: Dip Angle

Multiscale AttributeOriginal AttributesTime Section 187 from New Zealand Dataset

Results: Most positive Curvature

Multiscale AttributeOriginal Attributes

Results: Most negative curvature

Multiscale AttributeOriginal Attributes

• 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

You can download the code to reproduce these results from here:

Code:

ghassanalregib.com/publications/

Thank You

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http://www.ghassanalregib.com/