3D Stereonet
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Multivariate Cluster Analysis of Oriented 

Discontinuity Data:  Three-D Stereonet

The characterization of discontinuous rock requires measuring and characterizing discontinuities (joints) and identifying sets or families of joints based on their orientation or some combination of other attributes.

Consider a lower hemisphere stereonet with 4 joint normals (poles), each pole from a different depth along an imaginary vertical borehole.
Each pole is plotted on an individual stereonet, and the stereonets are stacked with spacing proportional to the spacing between the discontinuities along the borehole.
Thus the concept of a "three dimensional stereonet.
Consider this contrived data set, .
Conventional cluster analysis might determine three joint sets in this manner.
If we use both orientation and spacing as a parameter in the cluster analysis, we may get this type of clustering.
Shown here in a conventional view.
As an example, a seemingly cut and dry example of a sandstone with 3 mutually orthogonal joint sets.
Conventional clustering analysis shows wide variability on the sub-vertical discontinuities.
Clustering on basis of orientation, position, and roughness of the discontinuity results in 6 sets, including 5 sub-vertical sets.  Sets 6 and 3 are distinguished by their high roughness values, and from each other by their orientation and position. Sets 1,4,5 are distinguishable by their moderate roughness values, and are distinguished from each other by their position and orientation.

 
REFERENCES:

Maerz, N. H., and Zhou, W., 2000.  Discontinuity data analysis from oriented boreholes. Pacific Rocks;  Proceedings of the Fourth North American Rock Mechanics Symposium, Seattle, Washington, July 31- Aug.1, 2000, pp. 667-674.

Maerz, N. H., and Zhou, W., 1999.   Multivariate analysis of bore hole discontinuity data.  Rock Mechanics for Industry, Proceedings of the 37th US Rock Mechanics Symposium, Vail Colorado, June 6-9, 1999., v. 1, pp. 431-438.