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

Structural -> Maximum and Minimum Curvature

Attribute Description:

Maximum (kmax) and minimum (kmin) curvatures define the curvature anomalies in magnitude yet, still, captures the folding axis that contains geological information. This is done by fitting two circles tangent to a surface.  The circle with the minimum radius is the maximum curvature (kmax) and the circle which is perpendicular to the first circle is the minimum curvature (kmin).

Interpretation Use:

These attributes reveal faults, flexures, anticlines, and synclines.  The maximum curvature has the larger absolute value and the minimum the smaller absolute value.  For this reason, the minimum curvature can define the elevation change along the long axis of a valley or ridge which is identified by maximum curvature. These attributes are also very good at defining upthrown and downthrown portions of fault systems.

Recommended Color Palette:

Colorbar for curvatures often includes two color themes such as blue and red or black and red to mark the anomalies. The less anomalous value along the zero value is marked by white or being transparent in the middle.

  Figure 2: Colorbar example for curvatures

Figure 2: Colorbar example for curvatures

Gaussian - 02.png

Example:

  Figure 1: Maximum (upper) and minimum (lower) curvatures

Figure 1: Maximum (upper) and minimum (lower) curvatures

Max and Min - 04.png

Computation:

At any point on the mapped surface, two radiuses are derived (Figure 4) by fitting two circles to the perpendicular planes. The reciprocal of the radius of each circle is called apparent curvature. Within the infinite plane combinations, the circles with the two planes that have the minimum and maximum radiuses, then produce the maximum curvature (kmax) and minimum curvature (kmin).

In order to capture the curvature information, the mapped plane is first defined by fitting a quadratic surface using least-square based calculation.
 

Max and Min - 05.png

Gaussian (kGauss) and mean (kmean) curvatures are then derived from the quadratic surface. After that, KGauss and kmean can further formulate the most-positive and most-negative principal curvatures (k1 and k2).

For more details on how kGauss and kmeank1 and k2 were derived, please refers to principal curvatures computation section.

After k1 and k2 are derived, the maximum and minimum curvatures (kmax and kmin) are defined by the largest and smallest principal curvatures in magnitude, regardless of the curving direction. The derivation of kmax and kmin is conceptually equivalent to the step described above that looks for the most representative circles on the two planes.

Max and Min - 06.png

and

Max and Min - 07.png
  Figure 4: Two fitting circle at point P on mapped surface

Figure 4: Two fitting circle at point P on mapped surface

Reference