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

Principal Components (PC) Filtered Data, Alpha-Trimmed Mean Filtered Data, Lum (lower-upper-middle) Filtered Data, and Mean Filtered Data

Attributes Description:

The Principal Components (PC) Filtered Data, Alpha-Trimmed Mean Filtered Data, Lum Filtered Data, and Mean Filtered Data are structure-oriented attributes filters that reduce noise while preserving structural and stratigraphic discontinuities from seismic data. Another advantage of these filter attributes is that they can enhance the ability of coherence, curvature, or other AASPI structural attribute computations at uncovering thin or small structural and stratigraphic details.

Interpretation Use:

The Principal Components (PC) Filtered Data, Alpha-Trimmed Mean Filtered Data, Lum Filtered Data, and Mean Filtered Data attributes can enhance the ability of coherence, curvature, or other AASPI structural attribute computations at uncovering thin or small structural and stratigraphic details. Note that the Alpha-Trimmed Mean and Mean Filtered Data filters work best in areas where the data has random incoherent noise but might misestimate the amplitude. Also, the Alpha-Trimmed Mean filter is relatively insensitive to spikes in the data. The PC Filtered Data filter diminishes random noise and better preserve lateral variations in signal amplitude. The structured-oriented filter attributes can be also useful for providing more information sensitive to stratigraphy or structural features (Chopra and Marfurt, 2007). Attribute results can be analyzed in different ways, from a plan view, vertical transects, or draped over a horizon display.

Recommended color palette:

For the PC Filtered Data, Alpha-Trimmed Mean Filtered Data, Lum Filtered Data, and Mean Filtered Data 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. Or any color scheme that works well with normal seismic amplitude data. 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: alpha-trimmed meanfiltered data (b) and Lum filtered data (c).

Figure 1. Color bar examples of seismic amplitude (a) and output attributes: alpha-trimmed meanfiltered data (b) and Lum filtered data (c).

  Figure 2. Time slice displays of seismic amplitude (a) and output attributes: alpha-trimmed mean filtered data (b), Lum filtered data (c), mean filtered data (d), and PC filtered data (e).

Figure 2. Time slice displays of seismic amplitude (a) and output attributes: alpha-trimmed mean filtered data (b), Lum filtered data (c), mean filtered data (d), and PC filtered data (e).

Computation:

The PC Filtered Data, Alpha-Trimmed Mean Filtered Data, Lum Filtered Data, and Mean Filtered Data attributes use seismic amplitude data (time or depth domain) or other attributes (e.g., impedance; AASPI Documentation) as input. Then, the process follows this workflow:

Input data → Estimates of reflector dip → Estimates of similarity → Filtered data

The dip component attributes are computed using a Kuwahara algorithm with an overlapping window method (Luo et al., 2002) to avoid smearing of faults, fractures, and other discontinuities (refer to Filter Dip Components -> Inline Dip, Crossline Dip, and Confidence attribute description section). Note that in case of noise, the following structure-oriented filters can be applied during the computation of the Inline Dip and Crossline Dip attributes: i) Lower-Upper-Middle (LUM), ii) Multistage Median-based Modified Trimmed-Mean (MSMTM), iii) Alpha-Trimmed Mean, and iv) Mean (refer to Filter Dip Components -> Inline Dip, Crossline Dip, and Confidence attributes description section). Then after, the computation of similarity is conducted (refer to Similarity attributes description section).

The structure-oriented filters are computed as follows:

  1. PC Filtered Data. For a laterally shifted Kuwahara window, the principal component filtered data are given by (Marfurt, 2006):

    where m is the analysis point, μ denotes the input seismic data, v1(t) is the first eigenvector and u1(t) its corresponding first principal component. The process iterates for all J traces in the analysis window.
  2. Alpha-Trimmed Mean Filtered Data. For all J samples falling within a window of analysis, the alpha-trimmed mean is given by (Al-Dossary and Marfurt, 2007):

    where , the Eq. 6 is replaced by the median filter. . In this case, the samples are ordered using index k (e.g., If α = 0, the Eq. 6 is replaced by the mean filter.
  3. Lum Filtered Data. The Lum filter calculates the median by the following steps (Al-Dossary and Marfurt, 2007):
    1. Sort the samples in the window of analysis as shown above for the case α = 0.5. Then, the user defines lower and upper order statistics
    2. Compare the value of the center sample of the window dc with these two order statistics. To smooth the output, the process takes the median of the lower order (d(k)), upper order (d(N-k+1)), and the center sample:
  4. Mean Filtered Data. The filter is a running sum window that outputs the average of all the samples that fall within an analysis window at its center (Al-Dossary and Marfurt, 2007):

References

  • AASPI Documentation, http://mcee.ou.edu/aaspi/documentation/Volumetric_Attributes-sof3d.pdf
  • Chopra, S. and K. J. Marfurt, 2007, Seismic attributes for prospect identification and reservoir characterization: SEG Geophysical development series, 11, 187 – 218.
  • Al-Dossary, S., and K. J. Marfurt, 2007, Lineament-preserving filtering: Geophysics, 72, P1 – P8.
  • Marfurt, K., 2006, Robust estimates of 3D reflector dip and azimuth: Geophysics, 71, P29 – P40.
  • Marfurt, K., R. L. Kirlin, S. L. Farmer, and M. S. Bahorich, 1998, 3-D seismic attributes using a semblance-based coherency algorithm: Geophysics, 63, 1150 – 1165.