Stereonet analysis part 2

Contouring and interpreting orientation data.

In trying to document the character of structural elements it is not uncommon to have hundreds of orientation readings. Trying to interpret such data plotted as raw orientations (scatter plots) on a stereonet, without further data treatment is difficult and susceptible to bias. In order to guide interpretation it is standard treatment to contour the orientation data. The resulting contours show data density patterns. Perhaps think of it as a crude cluster analysis. Minor sub-populations and subtle patterns hidden by the 'noise' will often be 'brought out' or highlighted by such data treatment. On the other hand biased sampling may produce clusters or patterns that do not reflect reality, especially if your sample size is small (less than 30 readings). Properly done, contoured stereonets are extremely useful and can tell you such things as: joint set orientation, cylindrical or non cylindrical fold form, interlimb angle, fold curvature, conjugate fault geometry, rotation axes for faults, degree of structural obliquity, deformational vorticity, and more.

Contouring data is basically a way of mapping the density distribution of data. It greatly aids in the visual interpretation of data clouds. Two major 'cloud' patterns often found are: a) a bullseye distribution, and b) a girdle distribution.

A bullseye pattern can be thought of as even dispersion around some average orientation; i.e. as a population or set. A dike swarm, joint set or a simple fault population can often exhibit such a pattern. The amount of spread is also a function of how well behaved the populations is (the natural variation, or dispersion) and the amount of measurement error. Some fractures are much more planar, others anastomose. Often the distribution of scatter around the mean approaches a normal distribution, and standard deviations are typically in the range of 5-15 degrees. In addition, the noise, the other portion of the data is neglected, and an interesting question that can be asked is what percentage of your total data set does not belong to the defined set.

As an example, the above is a series of stereonet contour plots of poles to fractures in a variety of different rock types from a USGS study (http://pubs.usgs.gov/of/2002/ofr02-013/html/bedrock.html). The details can be found by following the link. Since many of the fractures are subvertical they are also show a form of circular histogram (rose diagram) for the fracture strike azimuths. A key and important finding here is that different fracture sets are vound in different rocks. Another component of such analysis is to identify domains that you develop plots for. In this case the domains are determined by rock type.

A great-circle girdle distribution pattern is often due to some differential tectonic or strain rotation of a planar element, such as occurs with folding. Remember that if it is a cylindrical fold the girdle defined by contours of poles to the folded surface should follow a great circle whose pole is itself the fold axis. Sometimes small-circle girdle distributions can also be found, indicating conical fold forms. Additional information about the fold form exists in how and where the data is concentrated along the great circle best fit. If measurements of the strikes and dips are representative of the fold surface as a whole then distinct clusters likely represent fold limbs (longer portions that should be representatively sampled more). If limbs are well defined then an interlimb angle can be estimated. If the fold style is very angular, then the fold limbs should be well defined. Otherwise for rounded forms there should be more a distribution along the girdle. If the one cluster from the one limb is better developed than another, this may reflect the asymmetry of the fold. It could also reflect that more measurements were taked from one fold than the other, and so one must be cautious in making these types of interpretations.

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, http://www.geo.cornell.edu/geology/faculty/RWA/programs.html). 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.

This is another plot of bedding from Spitsbergen, from Triassic strata involved in a thin-skinned fold-thrust belt. The black lines are the great circle plots of the bedding. The black dots are poles to bedding. The blue lines are contour lines in increments of 3% per 1 percent area. The red box and great circle are the programs statistical best-fit pole girdle and the pole to that girdle, which is the best estimate of the fold axis. The purple line and rectangle is a hand-picked estimate of the equivalent girdle and fold axis. These are relatively upright and tight folds, with subhorizontal axes.

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.


Procedure for hand contouring orientation data on a stereonet: While you won't be required to hand plot and contour data you should know what is involved (i.e. what the black box computer is doing for you).

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

2) Second, construct a counting circle. The counting circle has a radius one tenth that of the stereonet you are using. As a result it includes within it 1% of the entire stereonet's area. Note that you need two counting circles whose centers are separated by a line equal in length to the diameter of the stereonet you are using. This is so that when you are counting on the stereonet's margin and part of the counting circle is outside of the stereonet you can count the 'missing' portion which actually lies diametrically opposed on the other side of the stereonet.

3) Overlay a counting grid on the stereonet with the plotted data. The grid spacing is not necessarily fixed, but must be < the radius of the counting circle. Try to think of why this is so.

4) Position the counting circle with its center at a grid intersection. Count all the data points within the counting circle and put that number at that intersection. Repeat for every intersection until the all the grid intersections within the stereonet have been 'counted'. Remember to count the data points on the other side when part of your counting circle falls outside of the stereonet (i.e. use both counting circles). You are basically asking over and over the question - " how many data points fall within this 1% area of the stereonet projection, hence this can be considered a data density map." Since you are mapping data density you are free to place the counting circle center anywhere if you want to get a better control on the density distribution.

5) Transform the count numbers into percentages (count # / total number of data points * 100).

6) Contour these percentage areas following the normal rules of contouring a continuum (the continuum representing the presumed infinite population of possible structural element orientations which has been sampled, and represents, a continuous, smooth surface). You will need to decide on a contour interval. Look at your percentage values and their pattern and decide which interval will serve the best.

7) The fun part - interpret the data. Pick out different populations or girdles. You can also compare your hand plot versus a computer plot (after calculating poles chose the contour option.


Kamb plots are where the departure from a random distribution of points is mapped. As the number of data points goes up the Kamb and standard 1% data density plots look more and more alike. I encourage you to use such plots, especially if n<100 or so. They can greatly aid in preventing overinterpretation of the data (something humans are demonstrably prone to). Their disadvantage is simply that this is not the conventional approach, and you may have to explain their use to some people.


Hints on using Allmendinger's software (available on computers in Cart Lab):


Readings from pre-Pennsylvanian strata near Turner falls Oklahoma

This data uses the right hand rule (ask if you are unfamiliar).

strike dip
270 20
334 15
270 80
280 78
270 15
270 32
270 75
307 46
296 64
315 60
280 72
278 32
275 82
271 81
276 74
300 12
282 14
316 74
326 60
301 4
330 34
315 60
304 70
330 32
278 83
278 78
296 12
316 38
292 42
300 62
320 60
315 32
310 66
286 70
298 64
345 20
275 78
245 10
312 64
276 78
274 74
245 1
285 10
305 68
320 48
312 58
315 65
286 70
300 80
335 32
285 82
280 80
320 40
282 14
306 66
314 88
311 66
300 71
286 70
345 35
314 15
275 82
264 80
266 4
292 80
280 68
245 10
292 42
284 20
300 14
282 14
326 60
330 30
300 72
335 32
278 83
276 78
328 38
292 42
320 60
291 74
276 78
264 82
245 10
330 30
312 64
286 70
330 32
240 18
286 70
330 32
278 32
296 72
252 22
264 70
218 30
216 68
266 40
266 6
298 60
270 19
124 67
207 6
266 6
266 40
220 38
266 40
201 38
252 22
216 32
215 20
234 14
248 68
120 40
90 20
90 28
90 30
80 44
74 40
42 25
28 40
100 72
120 26
92 22
10 45
20 40
30 48
28 40
80 44
100 72
84 70
74 40
112 27
42 72
60 18
106 78
114 46
98 24
141 22
117 46
119 40
174 26
167 28
132 24
122 20
134 68
134 50
129 71
134 63
142 64
114 68
115 80
141 84
121 87
132 16
120 18
137 80
136 28
112 18
132 21
128 20
121 40
130 74
138 68
134 68
129 70
109 68
120 80
145 86
140 40
115 75
115 72
138 52
130 74
105 74
16 18
140 80
120 15
84 20
136 49
125 40
124 50
138 58
90 30
60 38
120 24
120 60
130 74
124 70
120 80
120 75
136 80
120 58
112 68
134 16
104 204
134 30
172 18
120 58
105 65
140 70
135 65
137 17
115 75
170 85
112 32
100 32
120 40
128 45
120 40
134 68
126 78
130 74
138 74
115 75
117 84
140 55
140 83
32 30
112 56
84 20
111 20
132 32
118 22
162 58
137 80
124 16
121 40
121 5
108 68
130 72
129 71
115 75
145 86
142 55
120 15
140 54
110 50
123 46
122 24
126 20
132 68
105 76
119 72
148 85
134 16
136 50
112 10
141 44
128 58
146 68
124 22
120 40
126 45
118 18
118 45
132 68
114 74
118 76
120 80
38 55
40 34


Bedding for Pennsylvanian conglomerates and sandstones, Turner Falls, Oklahoma

bedding strike dip
288 20
278 13
328 20
219 28
265 14
307 22
316 12
296 20
68 38
282 15
320 18
305 30
290 20
330 48
298 55
280 15
315 21
315 26
307 22
315 60
284 24
316 12
296 20
282 15
318 21
80 20
8 55
113 20
112 18
117 11
124 60
119 36
120 15
60 38
120 50
123 48
125 85
120 22
120 24
118 40
117 11
101 18
120 15
118 40
126 63
60 38
110 22
120 20


Fault planes from near Turner Falls, Oklahoma.

 

fault strike dip
0 60
314 88
284 28
357 80
268 80
280 64
54 84
282 14
214 45
214 84
280 64
268 87
82 80
276 74
245 10
244 68
134 44
112 68
248 68
248 68
52 84
114 32
42 72
70 34
42 72
106 70
58 86
52 60
74 85
28 30
65 75
42 72
112 18
136 28
108 38
130 74
100 34
108 40
110 72
100 80
60 38
10 30
84 20
186 90