The stereonet or stereographic projection is the most important visualization tool for orientation data in structural geology. Most figures are made using an equal area projection, but sometimes and equal angle projection is used as well. In most cases it is preferable to use a projection that optimises equal area, because it makes it easier to assess the spatial distribution of structures. The projection that is usually chosen for this, is the Lambert Azimuthal Equal-Area Projection with equatorial aspect See: Snyder , p. In geology this is usually referred to a Schmidt Net , after Walter Schmidt. Angles are slightly distorted and make the circles appear as ellipses.

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Background information on the use of stereonets in structural analysis. It is helpful to understand the 3-D geometry that is being represented on the 2-D stereonet projection plane.

The diagrams below attempt to show you that geometry in three stages, each more complex. It may take some timeand focus to understand the geometry. This is the basic 3D geometry we will start with. A horizontal plane passes through a sphere, of which the lower hemisphere is shown, or considered opposite to mineralogy where the upper hemisphere is considered. Where the lower hemisphere intersects the horizontal plane is the outward trace of the stereonet plot. Cardinal directions are shown.

Planes and lines whose orientation is being plotted all pass through the center. An example of such a plane is shown in red here. What is plotted on the stereonet is a projection of where a given line or plane intersects the lower hemisphere surface. We can now consider how two lines the ones in green plot. The one line is formed by the intersection of the N-S vertical plane and the red plane of interest, and the other by the E-W vertical plane and the red plane of interest.

These could be though of as the apparent dips of the red plane in a N-S and E-W vertical cross section respectively. There are different methods by which the points of intersection with the lower hemisphere are projected onto the stereonet. In this example a projection point exists one sphere radius directly above the center.

A line is drawn from that projection point to the lower hemisphere intersection point light green dashed lines. Where that line passes through the stereonet project plane is where the line plots the dark green dot.

Note that a line plots as point - the point of intersection with the lower hemisphere. If we repeat this operation for all the points of intersection of the plane with the hemisphere then a curved line, a great circle trace, is formed on the streonet. Planes plot as great circle traces. 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.

The above is an equal area stereonet projection showing great circles as arcuate lines connecting the North and South Points and small circles as arcuate lines in a latitudinal type position. The great circles represent north-south striking planes with dips in 10 degree increments.

Those labeled with dip amounts on the left side, dip to the west. If the same plane was rotated about a vertical axis in the stereonet center, they would then retain their dip, but have a different strike.

The numbers in the upper right quadrant represent potential strike line positions from degree, in 10 degree increments see below diagram. Small circles represent half of a conical surfaces with the apex at hemisphere center. They are hemisphere surface paths from one line being rotated about another line the pole of rotation , both passing through the hemisphere center.

The above diagram shows the same plane in two positions. The blue plane position is where North has been rotated so that the great circles all have a strike of N45W In this case the North position is designated in blue. In this position it is easy to trace out the great circle with the appropriate dip, here 50 degrees to the NE.

The green represents the plane's orientation when North is rotated back to its standard top-of-the-stereonet position. The open and filled red stars represent two lines solid 58, open 37 and the dashed red great circle represents their common plane with a strike of SE. The green stars and great circle represent that line rotated 35 degrees counter clockwise so that the filled star is on the equatorial plane where you can count its plunge as about 58 degrees.

The blue represents the position where you can count the plunge of the open star as about 37 degrees. In the above diagram two planes are plotted, one red, one blue. The strike and dips are given to the left. The green point represents their common line, i. The trend and plunge is given as 89 Remember the convention is that the first number represents the trend direction and the second represents the plunge amount.

Some structural elements whose orientations can be plotted on a stereonet are: bedding, cross beds, joints, foliations, fault planes, veins, dikes, fold axes, fault striae, slickensides, boudin axes, long axes of inequant objects such as fossils, parting lineations, shatter cone axes and more.

The first part of your stereonet lab will explore the mechanics of manually plotting elements on a stereonet, while the second part will focus using computer programs to contour data and make analysis. Remember it is always good to know what the black box software program is doing for you. You will need the following materials in order to proceed with this and the subsequent stereonet exercises: a an equal-angle stereonet taped on to cardboard or other stiff backing , b a tack, which can be pushed up through the center of the stereonet so that the point is showing, c onion skin paper, which is used as an overlay for plotting the structural features, d colored pencils to help differentiate the various elements plotted.

The onion skin overlay permits you to rotate the points being plotted with respect to the underlying, fixed reference frame. As you start plotting points you will see why this is necessary. Part 1 - Plotting and manipulating elements on a stereonet. This part needs to be done with pencil and tracing paper, with a stereonet projection underneath.

A Plot the following two planes: - 45W and 65 E. Label each one clearly. B Determine the trend and plunge of the intersection. To find the plunge rotate the intersection point to 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 plunge direction is evident as the quadrant your associated periphery point lies in and the angle along the hemisphere periphery from underlying N to the periphery point is your trend.

C Plotting the poles to each of those planes and label them. 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. The point you arrive represents a line perpendicular to the plane you started with, i. D Finding the angle between the poles and thus between the two planes.

In order to do this, rotate the two pole points until they fall on the same great circle. Then count along that great circle in degree increments moving from one point pole to the other.

That is the angle desired. If it is less than 90 degrees it is the acute angle, otherwise it is the obtuse angle. E Find the acute bisector of the two plane.

Along the common great circle containing the two poles count in degree increments half of the angle found in D above. Mark that point. This is the bisector. It could represent a principal stress for a conjugate fault pair. F Now rotate the bisector point and the intersection point of the two lines to a common great circle and draw and label that great circle..

That great circle is the bisecting plane. G On a new sheet of paper plot the following two lines. H Determining the strike and dip of the common plane those two lines define. To do this rotate the two lines until they fall on one great circle. The strike and dip of that great circle is that of the common plane. I Determining the angle between the two lines by counting along the common great circle in degree increments from one to the other line.

J On a new page, plot the following line 40 and then find the family of lines points on the stereonet that is 20 degrees away. You can do this by simply rotating the point representing the line on to any great circle, and then count along that great circle 20 degrees in both directions and mark those points which will be two lines 20 degrees either side of the first.

Repeat this on another nearby great circle. What is the form that results?

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## Schmidt net

Equal Angle projection preserves the geometry of projected shapes. The area on the surface of the sphere, represented by a projected region, depends on its location. The projected area of a given circle increases towards the equator of the projection see below for illustration. Equal Area projection distorts geometrical shapes such as small circles circles with centers not coincident with that of the sphere.

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## Stereonet Equal Angle / Equal Area Projection Comparison in Dips

The Schmidt net is a manual drafting method for the Lambert azimuthal equal-area projection using graph paper. It results in one lateral hemisphere of the Earth with the grid of parallels and meridians. The method is common in the geophysical sciences. In the figure, the area-preserving property of the projection can be seen by comparing a grid sector near the center of the net with one at the far right of the net. The two sectors have the same area on the sphere and the same area on the disk.

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