Lab 3 Stereonets

September 20, 2012

Last week we learned how Brunton compasses can be used to measure the orientations of

linear or planar structures in the field. This week we'll be using a stereonet to plot these data.

Stereonets are tools used by geologists to visualize three dimensional data in two dimensions.

They can be employed for a variety of analytical purposes as well. Seismologists also use

stereonets for plotting certain types of earthquake data.

Equipment: cardboard backing, thumbtacks, tape, blank stereonets, tracing paper, scissors,

erasers

Part 1 Building your stereonet

1.1 Cut a piece of cardboard slightly larger than 8.5"x11". This will be the backing for your

stereonet.

1.2 Tape a blank stereonet mesh on one side of the cardboard. Label the North direction, and

the azimuthal orientations in 10 degree increments, clockwise around the stereonet.

1.3 Push a thumbtack through the very center of the stereonet. Then remove the thumbtack

and push it through the cardboard from the back side. This thumbtack will be used to position

and rotate your stereonet drawings.

1.4 Using scotch tape, tape down the back of the thumbtack so it doesn't fall out.

1.5 Break off a small piece of eraser. This can be stuck on the business end of the thumbtack

for protection.

1.6 For each of the problems below, you will cut a piece of tracing paper, slightly larger than the

stereonet itself.

1.7 Push it onto the thumbtack and secure with the eraser.

1.8 Trace the outline (the outer radius) of the stereonet on the tracing paper. Note the

locations of North, South, East, and West.

Part 2 Getting to know your stereonet

A stereonet is a projection of 3D data into two dimensions. This is a familiar concept: it's

something we do any time we create a 2D map of our spherical planet. There are many

different projections that are used in cartography. For stereonets, most geologists use a

projection called a Lambert equal-area projection. The essence of this type of projection is that

it preserves areas at the expense of angles and shapes. Angles and shapes are especially

distorted near the poles. Check this out in the Figure below, where Earth is plotted using an

equal area projection.

http://www.mgaqua.net/AquaDoc/Projections/Projections_Azimuthal.aspx

Stereonets can be either upper hemisphere or lower hemisphere projections. An upper

hemisphere projection would be a convex surface (think of a globe). A lower hemisphere

projection would be a concave surface (think of the inside of a spherical bowl. As geologists, we

typically use lower hemisphere projections. This works better because most of the things we're

plotting are beneath our feet. In the lab, we have a globe that's been cut in half. Use this to

visualize what a lower hemisphere projection would represent.

Part 3 Plotting planes, lines, and poles on a stereonet

A three-dimensional plane, projected on a stereonet, loses one of its dimensions. Thus, it

becomes a two dimensional curve or line. The following procedure explains how to plot a

plane, as represented by a strike and a dip measurement, on your stereonet.

Position your tracing paper so North on the tracing paper is parallel to North on the

stereonet. We'll refer to this as the "home" position.

Mark the location of the strike by measuring the appropriate number of degrees

clockwise around the outer circumference of the stereonet.

Rotate the tracing paper until your strike mark is aligned with the North direction on the

stereonet.

To project the dip, you will now count along the E-W line from the outer radius towards

the center of the stereonet,. In your field notes you have indicated the direction of dip

(generally either North or South). Make sure you count from this direction! Make a

mark on your tracing paper at the appropriate dip angle.

Note that each of the curves that intersect the E-W line is a great circle that intersects

the North and South poles of the stereonet. Each of these great circles represents a

plane that would cut the spherical shape in half. With your tracing paper still oriented

such that the Strike is still pointing North-South, draw a line following the great circle

corresponding to your dip angle.

A dipping structure will be revealed as a curved line. The more vertical the structure,

the straighter the line. A structure dipping 90 degrees will appear to be a straight line

passing through the center of the stereonet.

For each of the problems below, create a new plot. Make sure to label all of your work!

3.1 Plot the following 3 planes on your stereonet. Next to each curve, note its orientation. (3

pts)

A. 135/26 N

B. 220/85 S

C. 264/40 S

The intersection of two planes is a line. As we noted earlier, everything plotted on a stereonet

loses one dimension. Therefore the intersection of two planes appears as a point. The

stereonet can be used to calculate the orientation of this line. We will record this information

as a trend and plunge.

To measure the trend and plunge of a line, rotate the point until it is on the EW axis of

the stereonet.

A line running from the midpoint of the stereonet through the point of interest, will now

intersect the outer radius of the stereonet in either the East or West direction.

Mark this point on the outer radius of the stereonet, and rotate the tracing paper to the

home orientation to measure the azimuth of the trend.

The dip is measured by counting along the EW axis, from the outer radius of the

stereonet towards the point of interest (just as you did when you plotted the dip of the

planes.)

These data are recorded in the standard trend and plunge format (XXX / XX) where the

first three digits are the azimuthal direction of the trend (0-360) and the second two

digits are the dip (0-90).

Fossen (2010)

This procedure is often used in geologic mapping to determine the orientation of a fold

axis from its two limbs. (We'll learn more about these terms later in the semester.)

3.2 Calculate the trend and plunge of the lines corresponding the intersection of planes: (3 pts)

1. A and B

2. B and C

3. A and C

All planes have a unique line with an orientation that is perpendicular to the plane. This line is

called the pole to the plane. One way to illustrate this is to use your hand to represent the

plane, and stick a pencil through your fingers to represent the pole. Since the pole to the plane

uniquely defines the orientation of the plane itself, we will sometimes plot these poles to

reduce the amount of data plotted on our stereonets. The following procedure describes how

to plot the pole of a plane:

Once you have plotted the plane itself, rotate the tracing paper so that the strike of the

plane is oriented N-S. If you have just finished plotting the plane, your tracing paper will

already be in this position.

The pole to the plane will plot on the E-W axis, 90 degrees away from the dip angle.

Simply count off 90 degrees from where the plane intersects the E-W axis and make a

mark. This is the pole to the plane.

3.3 Using your data from last week's Brunton compass lab, plot the orientations of stops 1 and

3, and the poles to these planes (2 pts)

Part 4 More practice

4.1 Plot the two orientations from stop 2. Calculate the trend and plunge of the line

corresponding to the intersection of these planes. Thinking back to this "outcrop" what

architectural feature does this line represent? (3 pts)

4.2 Plot the two orientations from stop 4. Again, calculate the trend and plunge of the line

corresponding to the intersection of these planes. (3 pts)

4.3 Plot the three orientations from stop 5 and the poles to these planes. Calculate the

orientations of all intersections between these planes. There will be three. (6 pts)

Homework: Homework can be submitted by in person or by email (pskemer@wustl.edu) and is

due before the start of lab next week.