# G321 Structural Geology 013004 Pre-Lab 3. Stereographic Projections

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```					G321 Structural Geology
01/30/04
Pre-Lab 3. Stereographic Projections and Stereonets

Stereographic Projections
Thus far you have been introduced to the basics of topographic and geologic maps
and the geometric information they commonly illustrate. An alternative means of
conveying information about the geometric arrangement of geologic elements is through
the use of stereographic projections and stereonets. While maps provide for analysis of
the spatial distribution of certain geometric elements it is somewhat limited in the total
amount of data that can be shown and therefore analyzed. Stereonets allow large
amounts of geometric data to be analyzed at once for a variety of purposes, but does not
allow for the spatial distribution of elements (i.e. the distance between them) to be
incorporated. Additionally, the use of stereonets can be very useful in quickly making
some of the geometric calculations that you have already had occasion to learn (e.g. Lab
2: true dip from two apparent dips).
Spherical stereographic projections were first used by astronomers to chart the
locations of stars and other celestial bodies. The directions to these objects were plotted
as white dots on the surface of the spherical projection with the earth at the center.
Geologists subsequently adopted the use of stereographic projections for use in
crystallography (i.e. map the directions to the various crystal faces). Similarly, structural
geologists have used the method to show the orientations of the linear and planar features
measured from rocks during field exercises. The spherical projection of a line or a plane
that passes through the center of the sphere will intersect the surface of the sphere at two
points or along a circle, respectively. These intersections are their projections.
For ease of use and portability spherical projections can be made into a two
dimensional plane. Such two dimensional projections are constructed by passing
projection lines from a point source through the sphere to the projection plane. The plane
must be oriented such that the unique projection line that passes through the center of the
sphere is perpendicular to the projection plane. The projection plane can have any
orientation such as polar or equatorial projections. A stereographic projection, that which
is typically utilized by geologists, is a
special type of projection where the
point source is located at the top, or
zenith, of the sphere and lines are
through the equatorial projection plane.
Projected lines and points are projected
from the lower half of the sphere and
therefore, this is called a lower
hemisphere projection.
The use of stereographic projections
is enhanced through the incorporation of
a coordinate grid system. For geometric
analysis of lines and planes we typically
use a stereonet that preserves angular
Figure 1        relationships and is therefore, called an
equal-angle projection (also known as
Wulff net). Such stereonets are
constructed with a coordination system
equivalent to that of latitude and longitude
on a globe and where grid lines are
separated by 2°. Every ten degrees is a
thicker reference line for easier
management of the stereonet. The
outermost circle on the stereonet is known
as the primitive circle. Those that connect
the north and south ends of the net (i.e.
similar to lines of longitude) are known as
great circles while those that are
perpendicular to the great circles and
terminate at the primitive circle are known
as small circles.
Figure 2       While equal-angle nets are useful in the type of analyses you will learn in this lab
(e.g. determining the apparent dip angle from a true strike and dip) they are not useful in
the statistical treatments of orientation data (e.g. determining paleo-stress fields) where
an equal-area projection net would be appropriate.

Plotting Geometric Data
When working with stereonets by hand it is common to overlay a piece of
transparency or tracing paper over the net with a thumbtack stuck through the center.
This allows you to rotate the sheet of paper you are working on and to preserve the
original net. Second, mark the location of the north direction on the overlay, this will be
used as a reference mark as you plot your planar and linear data.
Planar features should have an attitude given in strike and dip, or dip and dip
direction. Most Americans use the former convention so we will limit our descriptions
here to this method. We will further limit our nomenclature to the right-hand rule
convention (i.e. the strike direction with the plane dipping down to the right (see lab 1).
To plot the orientation of a dike (i.e. a planar feature) that has an attitude of 300° 50°
begin by rotating the overlay counterclockwise the specified (i.e. 300°) number of strike
degrees. Note that you could have achieved the same thing by rotating the graph
clockwise 60° but to be consistent for now always rotate the number of strike degrees
counterclockwise. The sheet of paper is now oriented such that the line of strike is north-
south with respect to the stereonet grid below the overlay. Since we are using the right-
hand rule, the plane is automatically dipping to the east or to the right of the strike line.
Count the number of degrees the plane is dipping in from the east and draw a great circle
at that point. This line is the trace of the plane on the surface of the sphere and it is
known as the cyclographic trace.
An alternative method for plotting the orientation of a planar feature is to plot its pole.
This method of plotting planar features is particularly useful if a large amount of such
data is to be plotted. The pole to a plane is a line that is oriented exactly perpendicular to
the center of the plane and that intersects the surface of the lower hemisphere on the
cyclographic                N
Strike line
trace

N
N
Rotate aroun
50o

d3
o          00

underside of the plane. To plot the pole to a plane you would orient the overlay such that
the strike of the plane is vertical (N-S) on the graph as in the example above. At this
point you have two options for plotting the pole. First, you could count the number of
degrees the plane is dipping from the east and then an additional 90° through the center of
the stereonet where you will place a dot representing the intersection of the pole with the
surface of the sphere. Alternatively, you could subtract the dip angle from 90° and count
in the difference from the west.
N
Strike line
N
N
Rotate ar

o
90                                Figure 3
40o          50o
oun
d3
o          00

Figure 4
Plotting lineation data when given in trend and plunge follows a similar procedure to
that of planar features. Let a mineral lineation (e.g. the alignment of hornblende) have a
trend and plunge of 040° 60°. Begin by rotating the overlay 040° counterclockwise such
that the direction 040 is oriented north on the grid. Next, count in the appropriate number
of degrees (in this case 60°) from the north and put a dot there.
o
0
tate 4                                    N
Ro
N

60
o

Figure 5
In many instances you will observe that lineations will be within a plane, typically a
foliation plane. When this is the case it is often more accurate to measure the lineation in
terms of rake from the strike line. If we are using the right-hand rule, then the rake will
be given in degrees from the strike end given. When plotting such a lineation you first
need to plot the planar feature and then you may plot the lineation and simultaneously
determine its trend and plunge. Thus, once you have the plane plotted keep the strike line
oriented north-south and count along the cyclographic trace the number of degrees rake
to the lineation and mark it with a dot. You may then rotate the overlay until the dot lies
on either an east-west or north south line. Here you can count in the number of degrees
to the dot. This is the plunge. At the same time put a small mark on the primitive circle
and rotate the overlay back so that the north on the overlay matches the underlying grid.
Where the tick mark is (i.e. in azimuth degrees) is the trend of the lineation.
N
Me
as
ure

N
Rake
300 50
o

of 138

32o
o

o

Lineation: 32oo
090

Figure 6

Geometric Problem Solving
Now that you have learned the basics of stereonets and attitude plotting, it is time to
turn our attention to some of the utilities that stereonets can provide. First and foremost,
is the determination of apparent dip angles from a plane with known strike and dip. Let
us assume that we have a bedding plane that is oriented 340° 50° and we want to know
the apparent dip for a line that trends 110°. With the plane already plotted and the
overlay orient with north up (i.e. the same as the underlying grid) place a small tick mark
on the primitive circle at 110° and rotate the overlay until this tick mark is parallel to a
north-south or east-west line. Next, count the degrees in from the primitive circle to the
cyclographic trace of the bed on the line to which you rotated the tick mark. This is the
apparent dip in that direction (~42° in this case).
N                                   N

42o

o
110

Figure 7.

In lab 2 you learned how to graphically determine the true dip from two apparent
dips. This is also possible using stereonets. The first step is to plot the apparent dip and
dip directions as you would lineations. Next, rotate the overlay until the two apparent
dips are on the same great circle. Draw the cyclographic trace along that great circle and
measure the angle from either the east or west edge of the stereonet (i.e. from the same
half of the stereonet the trace is located). This is the true dip angle of the plane. Next,
rotate the overlay back so that north aligns with north again and measure the strike of the
plane at the end where the plane dips off to right. In the example give the two apparent
dips were 30° towards 305° and 40° towards 230°. The true strike and dip of the plane
were 253° 51°.
N                                                              N
N

51o

253oo
51

Figure 8.
In many instances in geology it is important to be able to remove the rotational effects
of folding or faulting. One such example is where paleo-current information is measured
as a lineation from an inclined bed. Here, you can see that in order for that information to
be meaningful one must restore the bed to its originally horizontal orientation to
determine the true original orientation of the paleo-current. In this example we will take
a bedding plane with an attitude of 300° 50° and a lineation that is in the bedding plane at
42° 070°. We will be rotating this plane about its strike line so the first step is to rotate
the overlay until the strike line is oriented north south. Next, take note of the position of
the lineation and what small circle it is on. Now, trace the lineation up along the small
circle the number of degrees the bedding plane is dipping (50° in this case). If, for some
reason the amount of rotation is greater than the number of degrees the lineation is below
the primitive circle add or subtract 180° to the position of the intersection of the lineation
with the primitive circle and begin counting down the small circle on the opposite side.
In other words, note that a lineation has two ends and as you pass through the horizontal
the end that was pointing down will now be pointing up and vise versa.

N

N
50
o

00

o
42
o

3

50 o

Lineation: 42oo
070
Figure 9.

Introduction to the program “StereoNett”

StereoNett (Nett is German and means nice) is a program to display and evaluate
orientations. It is written by Johannes Duyster from the Ruhr University, Bochum,
http://homepage.ruhr-uni-bochum.de/Johannes.P.Duyster/stereo/stereo1.htm .

How to use “StereoNett”

1. Once you have downloaded the program you start it and open a new file file>new.

2. Before you begin to enter the field data, you need to check the following:
- go to view and check text
- go to options>projection and check equal-area if you wish to plot your
data on a Schmidt-net and equal-angle if you need the Wulff-net.
- Make sure that under options>hemisphere>Lower is checked because this
is the hemisphere we usually need for our projections.
3. You start to enter your collected field data into the new sheet:
- You type in the dip direction! of the strike of a plane or of the trend of a
lineation into the first white box in the left top corner.
- Into the second white box you type in the dip angle of a plane or the
plunge of a lineation.
- Check “linear” for lineation data and “planar” for planes.
- You can type in a comment into the white long box to the right, e.g.
“aplitic dike, 15 cm wide”, but this is not necessary.
- Click “add”: Your planar or linear feature appears in the big white box
underneath and you have entered your first datum.
- If you click on the white box with the cross on it, you can change the
symbol (shape, color, filling) for the orientation you gave it to better
distinguish different orientation data. Further, if you like to see the great
circle to the pole you need to check the white box next to great circle.
- Should you like to change a datum you already typed in, you go to the list
in the big white box, click on the orientation you want to change, make the
you click on modify.

4. Once you are done with entering your data you go to view and check Stereogram
to see your plotted data in the Stereogram. For switching between text and
Stereogram you can also use the buttons on the top.

5. The Stereogram now shows in symbols the planes as poles and the lineations. If
you checked under data>symbols the white box next to great circle, you will see
the measurement as a great circle and its pole.

6. The legend next to the stereogram shows you the total number of measurements
(Num total) and the distribution of the different symbols used for different
structures.

7. You can now analyze your plot and save and print it out under file.

This is just a first introduction to the program StereoNett, so that you can use it for
simple data plots. It has some more functions you could use to analyze structural data.
If you like to know more about them or you have questions how to use the program,