**Lab objectives:**

- understand the geometry of the stereographic projection.
- understand the projections uses in structural analysis.
- be able to plot by hand strike and dip and trend and plunge on a stereonet.
- be able to use a program to plot and contour orientation data.
- be able to interpret the patterns on such plots.

**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. *

**Some stereonet facts:**

- In contrast to mineralogy, structural geologists use lower hemisphere plots. Typically, it is as if you are looking into a hemispheric bowl sitting on the ground, and oriented along a N-S axis.
- There are an assortment of different types of stereonets (equal angle, equal area, polar). You should know which one you are using and why. One can recognize them by their distinct appearance.
- Great circles look like lines of longitude, and represent where planes with a north-south strike but incrementally varying dips intersect the outer hemisphere surface.
- Small circles look like lines of latitude, and represent where cones with a north-south horizontal axis and incrementally increasing apical angles intersect the outer hemisphere.
- You can plot two types of features on a stereonet, a line (e.g. trend and plunge) and a plane (e.g. a strike and dip). A line plots as a point and a plane plots as a great circle.
- All elements plotted pass through the center of the hemisphere, and their projection reflects where the plane or line intersects the outer hemispheric surface. This means that information about relative position is not represented in the plot, only information about relative orientation.
- Planes are often represented by plotting their pole, which is the line perpendicular to that plane.
- More complex structural features can be represented
by plots of multiple elements. Some examples are:
- a) a fault plane, with the direction (line) of movement on it.
- b) a cylindrical fold, often viewed as a great circle distribution of poles to the layering being folded.
- c) a conical fold, often expressed as a small circle distribution of poles to the layering being folded.
- d) an angular unconformity, expressed as the difference between the orientation of the bedding above and below.
- e) a population of joints or any other structural feature, often expressed as a data cloud with dispersion around some average value.

- You can also use a stereonet to:
- find the intersection between two planes (e.g. the fold axis if folding is cylindrical).
- find the angle between two lines, two planes or a line and a plane.
- to find the restored orientation of a geologic feature such as a cross bed once it is rotated about some axis.
- bisect the angle between two planes (e.g. if you are trying to model kinematic axes or principal stresses associated with conjugate faults).

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.

This part needs to be done with pencil and tracing paper, with a stereonet projection underneath.

**A)** Plot the
following two planes: 320 - 45W and 65 -60E. 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.

trend ___________ plunge _______________

**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.e. the pole.

**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.

acute 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.

trend ___________ plunge _______________

**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. Its strike and dip is
______________________ .

**G)** On a new sheet
of paper plot the following two lines. 220 20 and 352 45. Label
each one clearly.

**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.

strike ______________________ dip __________________________

**I)** Determining
the angle between the two lines by counting along the common great
circle in degree increments from one to the other line.

acute angle ___________________

**J)** On a new page,
plot the following line 186 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?

form _________________________