Basic Stereographic Operations
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All operations and computer examples on this page can be performed
with the free (unlicensed version) of Cauldron 2
Obtaining a Stereographic Net For Manual Examples
Launch Cauldron 2 and do not enter any data. First visit the 'Style Tab'.
Check the 'net on' box.
You may wish to adjust/play with some other variable on this page -choose equal angle or equal area.
It is assumed on this page that the 'Pole for net' option is set to the traditional 'north-south' one. Be aware, however that many
of the colour and all the line thickness variables effect only the screen version of the plot.
Next go to the 'Print' tab. Here you can adjust line thicknesses and colours for printing (but it will not
show on the screen). Finally click "Print now".
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Basic Entry/Plotting operations
Manual Plotting Preliminaries
To plot stereographic data manually you need a net (here you have to choose which
projection you wish to use: equal area for contouring and statistical work, equal
angle for most angular or tectonic work). Usually a drawing pin/thumb tack is placed
point upwards thorugh the centre and a sheet of tracing paper placed over the net.
First, trace the
circular outline of the plot, mark North and put a tick every 10 degrees on round
the circumference. The plot on the tracing paper can now be rotated on the pin so that the
underlying net can have any orientation
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To manually plot a direction
Suppose we wish to represent the orientation of a tunnel sloping down 35 degrees
on a bearing of 157.
- Start with the plot circle upright, so that the N which you have marked
on the plot circle aligns with the 'north' at the top of the underlying net.
- Put a light pencil tick on the circumference at the point
157 degrees clockwise from north.
- Rotate the tracing paper so that that tick is over the east (90 degree) point on the net beneath. Count 35 degrees in from the
edge along the straight east west line. Depending on how your net is drawn that
may be three thick (10 degree lines) and 2 and a half thin (2 degree) divisions.
- Mark this point carefully in a permanent fashion.
- Rerotate the tracing paper so that its north coresponds to that on the net's north below.
To plot a direction using Cauldron 2
There are many ways of entering data (including clicking on the plot circle). The most straight
forward is as follows:
- Select the enter tab
- Using the Select Format control (top left on tab) choose
"bearing of pole".
- Using the Select Data Type control (directly below the
Select format control) select 'point' -if it is not already selected.
- Make sure that the box next to the word "Visible" is checked.
- If you wish: to select the type of mark used to plot
the point, click on the arrows level with the work "Mark".
- If you wish: to select the colour used to plot the mark click on the
Colour (lwr) button.
- If you wish:If you wish to leave a comment with the point, so you can remember its
significance later, then type some brief text in the remark box.
- Enter the bearing (degrees clockwise from north =157 in the above example)in the bearing box
- Enter the dip in the dip box (angle to the horizontal =35 in our example).
- Finally click on the enter button
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To manually plot a Plane
To plot a bedding plane that dips 30 degrees towards a bearing of 236 degrees"
- As before, start with the plot circle aligned with the net.
- Lightly pencil the point 236 degrees clockwise from north at the edge of the plot circle.
- Rotate the plot so that this mark lies over the west (or east) point of the underlying grid.
- Count thirty degrees in towards the centre of the circle. This will bring you over
one of the great circles that run North South on the underlying grid.
- Trace this line onto the tracing paper.
- Return your plot so that it again aligns with the grid beneath.
To Plot a Plane Using Cauldron 2
Except in the selection of format and data type this is almost identical to the proceedure for
plotting a direction:
- Select the enter tab
- Using the Select Format control (top left on tab) choose
"bearing of dip".
- Using the Select Data Type control (directly below the
Select format control) select 'Great Circle'.
- Make sure that the box next to the word "Visible" is checked.
- If you wish: to select the colour used to draw the plane, click on the
Colour (lwr) button.
- If you wish:If you wish to leave a comment with the plane, so you can remember its
significance later, then type some brief text in the remark box.
- Enter the bearing (degrees clockwise from north =236 in the above example)in the bearing box
- Enter the dip in the dip box (angle to the horizontal =30 in our example).
- Finally click on the enter button
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Plotting Poles
When a large number of planes are to be represented it often is more convenient
to plot poles rather than great circles. A pole to a plane is that direction
which is at right angles to the any line drawn on that plane. If you consider
a plane dipping thirty degrees east then the pole to it is inclined to the
vertical by thirty degrees towards the west.
A bed which dips 34 degrees towards a bearing of 155 degrees has a pole which is is inclined at an angle of
90-34=56 degrees to the horizontal towards a bearing of 155+180 = 235 degrees. A joint plane which dips 80 degrees
towards a bearing of 305 degrees has a pole which is inclined by 90-80=10 degrees to the horizontal towards
305+180 = 485 (subtracting 360) =125 degrees.
Cauldron represents planes internally
by their poles. It also can store things on the 'upper hemisphere'. This dodge is
useful for representing overturned beds.
Directions within a plane
A plot of a plane and its pole
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Ploting Poles With Cauldron 2
If you have entered a plane using the instructions for the previous example
(plotting poles) then simply change the 'type' control to
"2:Pole" and reclick the Enter button. This will enter a second data point, identical to the
first, except that the pole will be plotted rather than the plane.
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The Intersection of two planes
Many basic operations revolve around the problem of finding the orientation
of the intersection of two planes. The trick is to remember that when you plot a
a plane as a great circle each point on the great circle is a direction within
the plane. One way of describing the problem of finding the intersection of
two planes is thus to find the one direction that they have in common.
This is, of course, represented by the point where the two lines cross on the
stereoplot. Sometimes it is also useful to consider the intersection as being
the direction normal to the poles of the two planes.
Finding the Intersection between Two Planes using Cauldron 2
- Enter the two planes as explained above . In fact it doesn't really
matter if you plot them as planes or poles.
- Go to the 'Edit' Tab. Here you will find a list box with the details of the two planes
which you have entered.
- Click on first one and then the other. As you click on the information in the list box, the
plane in the plot circle will turn green. This is called 'picking'. Cauldron remembers the last
two points picked.
- Now go to the 'Calcs' tab. Note that the angle between the planes is shown.
- Click on the "Intersection of 2" button. This adds not one but two new points!
- Return to the 'edit' page to examine the results. The two new points have the comment "circle intersection".
The 'dip' value is misleading, however, as it indicated the angle to (vertically) down. Recall
that we use a 'lower hemisphere' projection, so that the centre of the plot represents 'down'. One of the
new points is 180 degrees to the other, has a 'dip' of over 90 and can be ignored here.
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Finding the Apparent Dip
When a planar structure is viewed from any direction except normal to its true
dip the amount of dip appears diminished. When, for example, bedding plane is exposed
in a vertical cliff face the observed dip is refered to as Apparent Dip. Just as
a line may be thought of as a set of points, so a plane plotted as a great circle
may be thought of as the set of direction within that plane. So if we plot a bed dipping
40 degrees to the Southeast (135 degrees) and we would like to find the apparent
dip on an east west cliff then we could plot the east west cliff as a vertical
line goind straight across the plot from west to east. The point where it crosses
the bedding plane represents the apparent dip. This is the one direction common to
both planes. In other words the bedding plane is
represented by a great circle on the plot. So is the vertical cliff. The
point on the plot at which they cross represents the direction that the bedding plane traces
on the outcrop
-the apparent dip.
Finding Apparent Dips Using Cauldron
There are many ways to determine apparent dip using Cauldron. A direct qnd quick way is to display
the bedding plane as a great circle and then (on the style tab) click the 'net on'
option and select the 'down' option in the 'pole for net' box.
The net consists of straight lines representing vertical planes.
In this diagram the green line represents a bedding plane of interest (dipping 54.9 degrees towards
128.2 degrees). The red lines have been highlighted at 20 degree intervals representing cliff bearings
of 60 to 200 degrees. The length of each line gives the apparent dip in this direction. If we examine
the thick pink line (on a bearing of 90 degrees) we can measure it as about 48 degrees (each concentric
circle here represents 5 degrees). Cauldron lets us do better, however. First pick a plane (by clicking
on the list box under the edit tab. Since it is green you can see that we have already clicked the plane
in the diagram. Now switching to the 'Calcs' tab you find a box labelled "apparent dip on selected
plane". By typing 90 in the text box and clicking on the 'find' button the value 48.251 apears for
the apparent dip of our bed on a east-west trending cliff
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Plotting 'Apparent Dip' Measured on an Inclined Exposure
If the exposed rock face on which a bedding plane is exposed is not vertical, then how do you plot
the direction of 'apparent dip'? It turn out there are two situations -depending on what you measure.
- If you measure the angle to the bedding in the plane of the exposure, this is called the 'pitch'.
For example, if you pencil in the strike direction on the rock and use (you compas as) a potractor to
measure the angle between the strike and the bed, then you have measures the pitch. The pitch can have
any reasonable value (generally we would write it being in the range 0-90).
- If you measure the angle to the bedding in the vertical plane, this is called the 'plunge'. Here you
place you compass-clinometer on edge (use it as a clinometer and, with one edge on the trace of the bedding,
measure the angle that it makes with the vertical.
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Plotting a bedding-exposure lineation from a Pitch measurement
Manually:
- Plot the exposure plane as you would a bedding plane.
- Turn the net underneath so that the pole of the net is aligned
with the end (horizontal direction or strike) of the exposure.
- If the pitch is 20 degrees, find the small circle that is 20 degrees
from the end of the exposure plane.
- Where the great circle and the small circle cross is the direction representing the
trace of the bedding on the exposure: "the apparent dip".
Using Cauldron
- Plot the exposure plane as you would a bedding plane.
- Create a small circle centred on the 'strike' direction of the exposure. e.g. if the
exposure dips towards a beaing of 118 (amount is not important). The strike direction
is either 118-90=28 degrees or 118+90=208 degrees -choose the direction that the pitch
was measured from. The diameter
of the small circle should be the amount ot the pitch e.g. 20 degrees.
- In the Edit tab select both the great circle and the small cricle.
- Under the Calcs tab click the 'intersection of 2' option. This will create two
new data points representing the two directions along the bedding-exposure lineation.
One will be in the upper hemisphere so you generally want the lower one.
- You can read off the details in the list box under the Edit tab.
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Plotting a bedding-exposure lineation from a Plunge measurement
Manually
- Plot the exposure plane as you would a bedding plane.
- Find one of the Great circles on the net which is a stright line (N-S or E-W).
Count in from the edge of the circle the amount of the plunge (e.g. 20 degrees).
- Rotate the net so that this point is directly underneath the exposure great circle
(in the direction of the plunge). Mark this with a check on the exposure great circle.
- This check is at the direction of the bedding-exposure lineation: the apparent dip.
Using Cauldron:
- Plot the exposure plane as you would a bedding plane.
- Create a small circle about the vertical with a diameter of 90 - the plunge
amount. i.e. if the plunge is 20 use a diameter of 70.
- In the Edit tab select both the great circle and the small cricle.
- Under the Calcs tab click the 'intersection of 2' option. This will create two
new data points because there are two directions with the plunge specified.
- You can read off the details in the list box under the Edit tab. Hint: click
on the two new points to decide which is the correct one.
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Finding the True dip from two apparent dips
More common than the above example is wanting to finds the true dip from the apparent on two or more
exposures. Simply plot the two apparent dips as points. Next rotate the tracing paper so
that they both lie on the same great circle. Trace this great circle. Rotating
this you will be able to read off the amount and bearing of its maximum dip.
Cauldron can perform the same function with more accuracy. Simply plot the two bedding-exposure lineations
(apparent dips), select them under the 'edit' tab and use the 'intersection of 2' function. This will produce the
two points normal to the apparent dip directions. This is also the pole to the true dip. You can convert
one of these new points into a plane (great circle) using the 'make pick into' function under the
edit tab(you must select it first).
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Finding the true dip knowing its bearing and one case of Apparent dip
A variation on this problem is the case where you know one apparent dip
and the bearing of the true dip. If the true dip is on a bearing of say 135
degrees then you know that the strike direction is 135-90=45 degrees thus the
apparent dip on a bearing of 45 is 0. Now you know the apparent dip in two
direction so the problem is the same as the previous one.
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Making the most of Many Apparent Dip Measurements
In real situations you may have several readings of apparent dip and want to find the best estimate
of the true dip. Cauldron's 'Fit Plane' functions (under the calc tab) will do this either to your apparent dips entered as the
only visible data on the plot (on visible data version of function) or entered in their own set, which you then click on
(select) under the sets tab.
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Copyright: The copyright (2001) of this page is owned by Dr Nigel Stuart of Resource
Dynamics, Alberta, Canada. You are welcome to use, reproduce it in part or in whole.
Should you reproduce it in part please ensure that credit/blame for authorship is given.
A link to the Resource Dynamics home page would be appreciated.