Plot a Cone on a Stereonet
Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green BayFirst-time Visitors: Please visit Site Map and Disclaimer. Use "Back" to return here.
Cones and Small Circles
Conical structures are relatively rare in geology and the need to plot small circles on the stereonet is fairly uncommon, but it's good training in understanding the stereographic projection. Shatter cones and conical folds are the most important structures requiring knowledge of cones and small circles.
In general terms, a cone is any surface that is swept out by a line that always passes through one fixed point. Thus cones need not be circular although most geological conical structures are at least approximately circular. A circular cone with its center at the center of a sphere cuts the sphere in a small circle. We can define the cone in terms of the trend and plunge of its axis and the angular radius or apical half-angle of the cone.
Example
Plot a small circle (cone) whose axis trends 290 degrees, plunges 50 degrees, and has an angular radius of 25 degrees.
Plotting Without A Stereonet
Strictly speaking, you can do any stereonet construction graphically. This is one of the simpler constructions to do without a net.
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1. Mark the trend of the cone axis. 2. Rotate the axis trend until it is horizontal. Mark off the plunge angle and the angular radius angles as shown. Points A and B are the endpoints of the diameter of the small circle. 3. Construct a circle through the end points of the diameter. Note that its center does not coincide with the projection of the cone axis. 4. Rotate the overlay to its original position. |
Plotting On A Stereonet
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1. Mark the trend of the cone axis. 2. Rotate the axis trend until it is lies along a vertical great circle. Count off the plunge angle and the angular radius angles as shown. 3. Construct a circle through the end points of the diameter. Note that its center does not coincide with the projection of the cone axis. 4. Rotate the overlay to its original position. |
Circles That Cross The Primitive Circle
It's perfectly possible for small circles to cross the primitive circle. Geometrically, that means that part of the cone surface is above the horizontal. However, unless you're using an extended stereonet, there is no way to measure or plot points on the exterior portion of the circle. We have to find some way to bring that part of the small circle inside the stereonet.
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Created 17 March 1999, Last Update 17 March 1999
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