c) Equal-area stereonets are used in structural geology because they present b ) The north pole of the stereonet is the upper point where all lines of longitude. Background information on the use of stereonets in structural analysis The above is an equal area stereonet projection showing great circles as arcuate lines. Page 1. mm. WIDTH. Blunt. TUT. HT. T itillinn.

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In other words, they provide the best projection for analyzing the direction and the vectors of structural forces. Small circles represent half of a conical surfaces with the apex at hemisphere center. Also, every plane through the origin intersects the unit sphere in a great circle, called the trace of the plane.

InEdmond Halleymotivated by his interest in star chartspublished the first mathematical proof that this map is conformal. No map from the sphere to the plane can be both conformal and area-preserving. Computers now make this task much easier.

To plot the pole rotate the great circle representing the plane so that it’s strike line is oriented N-S, then count 90 degrees along the equator passing through the middle point of the stereonet. This part needs to be done with pencil and tracing paper, with a stereonet projection underneath.

Most figures are made using an xtereonet area projection, but sometimes and equal angle projection is used as well.

For example, from intersection point 3 upwards towards NW direction of the great circle intersection of plane A. An example of such a plane is shown in red here. What is the form that results?

## Stereographic projection for structural analysis

These orientations can be visualized as in the section Visualization of lines and planes above. Retrieved from ” https: Angles are slightly distorted and make the circles appear as ellipses. To find the sttereonet rotate the intersection point stedeonet the vertical equatorial plane and count up from the intersection point to the nearest periphery point in degrees along the equatorial plane – that is your plunge angle.

The stereographic projection presents the quadric hypersurface as a rational hypersurface. The foliation of a rock is a planar feature that often contains a linear feature called lineation. Note that stedeonet line plots as point – the point of intersection with the lower wtereonet.

In practice, the projection is carried out by computer or by hand using a special kind of graph paper called a stereographic netshortened to stereonetor Wulff net. It is believed that already the map created in by Gualterius Lud [2] was in stereographic projection, as were later the maps of Jean RozeRumold Mercatorand many others.

If it were, then it would be a local isometry and would preserve Gaussian curvature. In geometrythe stereographic projection is a particular mapping function that projects a sphere onto a plane. Cahill Butterfly Dymaxion Quadrilateralized spherical cube Waterman butterfly. The projection that is usually chosen for this, is the Lambert Azimuthal Equal-Area Projection with equatorial aspect See: In this example a projection point exists one sphere radius directly above the center.

The point 1 and 2 are best fit line points for the poles that lies about the center of the diagram. Together, they describe the sphere as an oriented surface or two-dimensional manifold. Two points P 1 and P 2 are drawn on a transparent sheet tacked at the origin of a Wulff net.

### Equal Area (Schmidt) Stereonet

So the projection lets us visualize planes as circular arcs in the disk. They are hemisphere surface paths from one line equa rotated about another line the pole of rotationboth passing through the hemisphere center.

Planes are lines are drawn on steronets as they intersect at the bottom of the sphere Figure 1. This facilitates an elegant and useful notion of infinity for the complex numbers syereonet indeed an entire theory of meromorphic functions mapping to the Riemann sphere.

The set of all lines through the origin in three-dimensional space forms a space called the real projective plane. Wikimedia Commons has media related stereinet Stereographic projection. E Find the acute bisector of the two plane. The steeper the dip the less curved the great circle is and the closer to the center, and the shallower the dip of the plane the more curved and the closer to the outside margin of the stereonet plot the great circle is.