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):

• Make sure you set your data format first (Data -> Set Data Format) before you enter data.
• Save your entered data file so you can replot it if necessary.
• In order to plot poles to planes, you need to have the program calculate them first (Operations -> Poles).
• To contour data use the standard 1% option (Plot -> 1% Area Contour), but you can also do the Kamb plot for comparisons sakes.
• You can ask the computer for a statistically computed great circle girdle estimate or the average orientation for a simple bullseye population (Plot -> Cylindrical Best Fit or Plot Mean Vector).
• You can also visually pick your own girdle by using Plot -> Pick Great Circle.
• You can't print plots directly from the program. You need to save the plot (it will be in a vector based Mac format known as pict), and then open it in Adobe Photoshop or Illustrator, or some other program, and plot it from there. At this stage you can also label and alter the image.

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