Dr. Tom Smith presenting on Machine Learning at the 3D Seismic Symposium on March 6th in Denver
What is the "holy grail" of Machine Learning in seismic interpretation? by Dr. Tom Smith, GSH Luncheon 2018
Using Attributes to Interpret the Environment of Deposition - A Video Course. Taught by Kurt Marfurt, Rocky Roden, and ChingWen Chen
Dr. Kurt Marfurt and Dr. Tom Smith featured in the July edition of AOGR on Machine Learning and Multi-Attribute Analysis
Rocky Roden and Ching Wen Chen in May edition of First Break - Interpretation of DHI Characteristics using Machine Learning

Homogeneity, Energy, Contrast, Dissimilarity, Entropy, Mean, and Variance

Attribute Description: 

The Homogeneity, Energy, Contrast, Dissimilarity, Entropy, Mean, and Variance attributes are statistical measures to classify seismic textures using gray-level co-occurrence matrices (GLCM). The GLCM represent the joint probability of gray-levels for pixel values (e.g., amplitudes) in a 2D sub-region of the seismic data (Chopra and Alexeev, 2006). These attributes are described as follows: i) homogeneity is a measure of the overall smoothness of a seismic image, ii) energy is a measure of textural uniformity in a seismic image, iii) contrast is a measure of the seismic image contrast or the amount of local variation present in a seismic image, iv) dissimilarity is a measure of the seismic image contrast weighted by the absolute value of gray-level differences from the GLCM diagonal, v) entropy is a measure of disorder or complexity of the seismic image, vi) mean, and vii) variance is a measure of the dispersion of the difference between the reference pixel and its neighbors (see Chopra and Alexeev, 2006; Chopra and Marfurt, 2007; Yenugu et al., 2010).

Interpretation Use: 

The Homogeneity, Energy, Contrast, Dissimilarity, Entropy, Mean, and Variance attributes can be used to characterize stratigraphic features by tabulating how often different combinations of amplitude brightness values (e.g., gray levels) occur within an analysis window (Chopra and Marfurt, 2007). Attribute results are better analyzed in plan view or draped over a horizon displays.

Recommended color palette: 

For the texture attributes a grayscale gradient color scheme is suggested. The color progression could begin with white (to highlight useful geological features) and finish with black (to denote shadow areas), or vice-versa. We suggest using the histogram of values to guide setting color value thresholds.

  Figure 1. Color bar examples of seismic amplitude (a) and output attributes: entropy (b), energy (c), dissimilarity (d).

Figure 1. Color bar examples of seismic amplitude (a) and output attributes: entropy (b), energy (c), dissimilarity (d).

  Figure 2. Color bar examples of seismic amplitude (a) and output attributes: contrast (b), homogeneity (c), mean (d).

Figure 2. Color bar examples of seismic amplitude (a) and output attributes: contrast (b), homogeneity (c), mean (d).

  Figure 3. Color bar examples of seismic amplitude (a) and output attribute: variance (b). 

Figure 3. Color bar examples of seismic amplitude (a) and output attribute: variance (b). 

Examples:

  Figure 4. Time slice displays of seismic amplitude (a) and output attribute: entropy (b), energy (c), dissimilarity (d).

Figure 4. Time slice displays of seismic amplitude (a) and output attribute: entropy (b), energy (c), dissimilarity (d).

  Figure 5. Color bar examples of seismic amplitude (a) and output attributes: contrast (b), homogeneity (c), mean (d).

Figure 5. Color bar examples of seismic amplitude (a) and output attributes: contrast (b), homogeneity (c), mean (d).

  Figure 6. Color bar examples of seismic amplitude (a) and output attribute: variance (b).

Figure 6. Color bar examples of seismic amplitude (a) and output attribute: variance (b).

Computation:

The texture attributes are computed along the inline and crossline dip components. In addition to supplying these attributes, the input volume to be analyzed in terms of GLCM is also supplied. The latter can be a seismic amplitude (time or depth), spectral components, or any other attribute (AASPI documentation). The data is first reformatted from its original bit format to a user-defined number of integer gray levels. Then, the GLCM volume is given by:

HEC - 07.png

where amd are the integer-valued scaled seismic data at the (p,q) (p + Δp,q + Δq) and locations and the delta function is 0 and otherwise. From the GLCM, the texture attributes are defined as follows:

  1. Homogeneity attribute
  2. Energy attribute
  3. Contrast attribute
  4. Dissimilarity attribute
  5. Entropy attribute
  6. Mean attribute
  7. Variance attribute

References

  • AASPI documentation, http://mcee.ou.edu/aaspi/documentation/Volumetric_Attributes-glcm3d.pdf
  • Chopra, S. and V. Alexeev, 2006, Texture attribute application to 3D seismic data: 6th International Conference and Exposition on Petroleum Geophysics, 874 – 879.
  • Chopra, S. and K. J. Marfurt, 2007, Seismic attributes for prospect identification and reservoir characterization: SEG Geophysical development series, 11, 113 – 116.
  • Yenugo, M., K. J. Marfurt, and S. Matson, 2010, Seismic texture analysis for reservoir prediction and characterization: The Leading Edge, 29, 1116 – 1121.