Geophysical Insights hosting the 2018 Oil & Gas Machine Learning Symposium in Houston on September 27, 2018
Introduction to Machine Learning for Multi–Attribute Interpretation and AASPI attributes - A 1-day, DGS Continuing Education course in Denver, CO on September 18th
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

Amplitude -> E_gauss, E_mean, E_max_azimuth, and E_min_azimuth

Attribute Description:  The E_gauss, E_mean, E_max_azimuth and E_min_azimuth are additional curvature attributes that can be used to complement geologic information extracted from E_pos and E_neg attributes (refer to Curvatures -> Amplitude -> E_max, E_min, E_pos, and E_neg attributes description section).

Interpretation Use:  The E_gauss, E_mean, E_max_azimuth, and E_min_azimuth attributes offer additional measurements of volumetric curvature. They can be used to support the stratigraphic features, faults, and fractures that were identified by E_pos and E_neg attributes (Chopra and Marfurt, 2007). Attribute results are better analyzed in plan view or draped over a horizon displays.

Recommended color palette:  For the E_gauss and E_max_azimuth attributes a divergent color scheme is suggested. The midpoint color is white to emphasize the progression outward two different dark hues. In the examples below, the dark hues were set to blue and red to better highlight geologic features. 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: e_gauss (b) and e_max_azimuth (c).

Figure 1. Color bar examples of seismic amplitude (a) and output attributes: e_gauss (b) and e_max_azimuth (c).

Examples:

  Figure 2. Time slice displays of seismic amplitude (a) and output attributes: e_gauss (b) and e_max_azimuth (c).

Figure 2. Time slice displays of seismic amplitude (a) and output attributes: e_gauss (b) and e_max_azimuth (c).

Recommended color palette:  For the E_mean and E_min_azimuth attributes a divergent color scheme is suggested. The midpoint color is white to emphasize the progression outward two different dark hues. In the examples below, the dark hues were set to blue and red to better highlight geologic features. We suggest using the histogram of values to guide setting color value thresholds.

  Figure 3. Color bar examples of seismic amplitude (a) and output attributes: e_mean (b) and e_min_azimuth (c).

Figure 3. Color bar examples of seismic amplitude (a) and output attributes: e_mean (b) and e_min_azimuth (c).

Examples:

  Figure 4. Time slice displays of seismic amplitude (a) and output attributes: e_mean (b) and e_min_azimuth (c).

Figure 4. Time slice displays of seismic amplitude (a) and output attributes: e_mean (b) and e_min_azimuth (c).

Computation: The E_gauss, E_mean, E_max_azimuth, and E_min_azimuth attributes are computed using this workflow:

Input data → Estimates of reflector dip → Estimates of coherent energy gradients through measurements of similarity → Curvature amplitude data

The process can be summarized as follows (AASPI documentation):

  1. ake the Inline Dip, Crossline Dip, and seismic amplitude volumes as input data (refer to Filter Dip Components -> Inline Dip, Crossline Dip, and Confidence attribute description section)
  2. Run a similarity computation (refer to Similarity attributes description section)
    1. Computing the covariance matrix from the complex trace signal
    2. Decomposing the covariance matrix into its corresponding kth eigenvalue and vth eigenvectors. Then normalize the eigenvectors to be unit length
    3. Estimating a scaled principal component, where the scale is the inner product or correlation of the eigenvector
  3. Generate estimates of inline and crossline coherent energy gradient
  4. Use the inline and crossline energy gradients to solve the coefficients of the quadratic surface:
e_gauss - 06.png

where,

e_gauss - 07.png
e_gauss - 08.png

and the azimuth of the maximum and minimum curvatures are respectively (Chopra and Marfurt, 2007):

e_gauss - 09.png

References