Stereonet 8

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In Python, stereonet are veeery simple to do thanks to Joe Kington (a geologist!). Joe created a stereonet module for matplotlib called mplstereonet. We are going to explore this module in this tutorial.

The upper faces of an isometric crystal are plotted in the stereonet above. These faces belong to forms {100}, {110}, and {111}. Note that the faces (111) and (110) both have a Φ angle of 45o. The ρ angle for these faces is measured along a line from the center of the stereonet (where the (001) face plots) toward the edge. For the (111) face the ρ angle is 45o, and for the (110) face the ρ angle is 90o. In Lab, your lab instructor will show you how to construct a stereonet for plotting crystal faces. This will consist of a stereonet mounted on a piece of cardboard with a thumbtack through the center. You can then place a sheet of tracing paper on the stereonet and rotate it around the thumb tack. The following rules are then applied: All crystal faces are plotted as poles (lines perpendicular to the crystal face. Thus, angles between crystal faces are really angles between poles to crystal faces. The b crystallographic axis is taken as the starting point. Such an axis will be perpendicular to the (010) crystal face in any crystal system. The [010] axis (note zone symbol) or (010) crystal face will therefore plot at Φ = 0o and ρ = 90o. Positive Φ angles will be measured clockwise on the stereonet, and negative Φ angles will be measured counter-clockwise on the stereonet. Crystal faces that are on the top of the crystal (ρ 90o) will be plotted as "+" signs. Place a sheet of tracing paper on the stereonet and trace the outermost great circle. Make a reference mark on the right side of the circle (East). To plot a face, first measure the Φ angle along the outermost great circle, and make a mark on your tracing paper. Next rotate the tracing paper so that the mark lies at the end of the E-W axis of the stereonet. Measure the ρ angle out from the center of the stereonet along the E-W axis of the stereonet. Note that angles can only be measured along great circles. These include the primitive circle, and the E-W and N-S axis of the stereonet. Any two faces on the same great circle are in the same zone. Zones can be shown as lines running through the great circle containing faces in that zone. The zone axis can be found by setting two faces in the zone on the same great circle, and counting 90o away from the intersection of the great circle along the E-W axis. To plot symmetry axes on the stereonet, use the following conventions: = 2-fold axis = 3-fold axis = 4-fold axis = 6-fold axis = axis = axis = axis

There are two types of stereonets available in Leapfrog Geo: equatorial stereonets and polar stereonets. The process of creating a stereonet is the same for both types; you can change the type of stereonet by clicking the Options button in the stereonet window. Both Fisher and Bingham statistics are available for stereonets.

Organising the stereonet tab and the Scene View tab so they are displayed side-by-side can be useful in working with the data as you can select data in the stereonet or in the scene window. This is described further in Using the Scene Window with the Stereonet below.

If you have activated the Statistics option in the Stereonet Options window, the program will compute a variety of statistics. A summary of these will be included with the stereonet plot in a legend. In the topics below is a summary of the methods used to compute these directional statistics.

Stereonets are a graphical tool representing the hemisphere of a globe, used for presentation, analysis and interpretation of three-dimensional directional data such as planes and lines. A stereonet allows the stereographical projection of three-dimensional information onto a two-dimensional plane (usually as a piece of paper or computer image) and is used as a tool applied to a range of geological problems including the removal of structural tilt. Stereonets involve the projection of lines or planes onto a sphere; two alternative projections are commonly used, the upper and lower hemisphere respectively, with use depending on the discipline of interpretation. See example to the left.

In trying to document the character of structuralelements it is not uncommon to have hundreds of orientation readings.Trying to interpret such data plotted as raw orientations (scatterplots) on a stereonet, without further data treatment is difficultand susceptible to bias. In order to guide interpretation it isstandard treatment to contour the orientation data. The resultingcontours show data density patterns. Perhaps think of it as a crude clusteranalysis. Minor sub-populations and subtle patterns hidden bythe 'noise' will often be 'brought out' or highlighted by suchdata treatment. On the other hand biased sampling may produceclusters or patterns that do not reflect reality, especially ifyour sample size is small (less than 30 readings). Properly done,contoured stereonets are extremely useful and can tell you suchthings as: joint set orientation, cylindrical or non cylindricalfold form, interlimb angle, fold curvature, conjugate fault geometry,rotation axes for faults, degree of structural obliquity, deformationalvorticity, and more.

Contoured stereonet plot of poles to bedding from deformed Jurassic shales, Revneset, Spitsbergen. the different colors represent contoured data density with a 3% interval. The strongest concentration is greater than 15% of the data in a 1% area. Note the great circle girdle pattern evident here. The great circle shown is a computer best-fit solution generated by the program (Allmendinger, ). One could speculate that two limbs are evident in the two bullseye, and that the one limb is better represented and thus the folds may be asymmetric. Both limbs would be shallowly dipping (remember that the poles are at 90 degrees and so the poles plunge steeply, and here the NE dipping limb readings are more prevalent.

Part two of the stereonet analysis lab is to take the data provided below and a) create scatter plots, b) create contour plots, c) interpret your plots as fully as possible. The assignment is purposefully open ended. See what you can get out of the data and don't hesitate to come see me for feedback. The data was acquired by students during a field trip in 2000, and are from the west end of the Arbuckle mountains near Turner Falls and along thruway 35. You should be familiar with the basic geology a bit from your air photo interpretation exercise. There is a major Pennsylvanian angular unconformity, and you have readings from above and below this unconformity. You also have the strikes and dips of fault planes in the area.

1) First plot all the data on a equal-areastereonet. Plot the data as poles to create a scatter plot.Make sure you have the right stereonet. Equal angle stereonetshave distorted areas and so a symmetrical, bullseye data populationwill appear distorted. If you are dealing with planar data, plotit as poles (since you can not contour great circles).

2) Second, construct a counting circle. Thecounting circle has a radius one tenth that of the stereonet youare using. As a result it includes within it 1% of the entirestereonet's area. Note that you need two counting circles whosecenters are separated by a line equal in length to the diameterof the stereonet you are using. This is so that when you are countingon the stereonet's margin and part of the counting circle is outsideof the stereonet you can count the 'missing' portion which actuallylies diametrically opposed on the other side of the stereonet.

4) Position the counting circle with its centerat a grid intersection. Count all the data points within the countingcircle and put that number at that intersection. Repeat for everyintersection until the all the grid intersections within the stereonethave been 'counted'. Remember to count the data points on theother side when part of your counting circle falls outside ofthe stereonet (i.e. use both counting circles). You are basicallyasking over and over the question - " how many data pointsfall within this 1% area of the stereonet projection, hence thiscan be considered a data density map." Since you aremapping data density you are free to place the counting circlecenter anywhere if you want to get a better control on the densitydistribution. 2b1af7f3a8