Strain analysis is the quantification of magnitudes
and histories of strain using measurements on natural strain markers.
Techniques vary greatly given the type of natural strain marker.
Ramsey & Huber (1983) provide an excellent compilation of
different approaches. For this lab we will do a center-to-center
technique known as the Fry method, which was discussed in class.
The idea is simple. Think of the distance from the center of any
one grain to another neighbor grain as a vector, with orientation
and magnitude. If we were to take all these vectors for all the
grains and their nearest neighbors, and plot them with their tails
at the origin the average vector length in some directions would
be different because of the way the grains have been deformed.
However, the plot would be a solid mass of vectors, and it would
be difficult to see anything. If instead we plot the vector head
as a simple point we would have an array of points that would
represent the average center to center vectors. __By graphically
looking at enough center-to center distances for grain neighbors
the cloud of points forms an ellipse whose orientation and long
and short axis is a direct measure of the finite strain ellipse
in that plane.__

See the diagram below for an image of how the center to center distances, marked by red lines, change through 3 steps of pure shear deformation.

The basic steps of the hand-hewn analysis are:

- Mark all the centers on an overlay sheet. You don't have to agonize about what is the exact center of any given grain, as this inaccuracy comes out in the statistical wash.
- Mark a center point in the middle of another overlay sheet (what will be your Fry plot), and superimpose it on one of the centers, and then mark all the other centers on that sheet.
- Translate, do not rotate, this Fry plot to another grain center and repeat the process above. Keep doing this until all the grain/particle centers on the base sheet have been covered.
- Draw in by eye the best-fit ellipse and measure the long and short axis of the your estimated finite strain ellipse.

Of course, if you have the grain center coordinates this can be done mathematically.

A basic assumption of the Fry method is that whatever grains whose centers are being used to mark the deformation originally had a non-random distance relationship. It works best for very well sorted clastic textures. The first time I tried this lab we used a deformed amygdeloidal bomb from pyroclastics down in South Carolina. Even though the amygdules were clearly deformed ( elliptical in cross section) the results did come out well at all. One good possibility is that the gas vesicles had more of an initial random, center to center distance distribution. Another basic assumption is that the grains were well sorted (i.e. that the grains started out with a common center to center distance).

For more details read the section from Ramsey & Huber (1983). The return on your investment in this type of strain analysis is pretty high. There is also a fair bit of description on the web. One example is a site where you can practice and create a plot - http://www.geolsoft.com/Fry1.jpg

Conduct a center-to-center technique on either of the two images below. The first image is of a deformed quartz specimen from the Augusta Fault Zone. This was originally a quartz vein that was severely deformed in the mylonite zone. Syndeformational recrystallization was thorough. However, as you can see the grains are not equant, but have a preferred long axis direction. You may want to revisit your lecture notes and readings on mechanisms of deformation at the atomic lattice scale and thin section deformation textures. The Augusta Fault Zone for at least the later part of its history was a low-angle normal fault, and thus the shearing was likely during a retrogressive history (one of decreasing Temperature). The second image is of a well sorted Jurassic sandstone from Utah as seen in a thin section with crossed nicols. The original image was distorted in Adobe Illustrator a certain amount and in certain directions to create the image you have here. Your Fry plot should tell you how it was deformed by delineating the strain ellipse.

Your **final products** should include:

- a copy of the image.
- a copy of the marked centers you have identified.
- a Fry plot.
- your estimate of the ratio of the long to short axes of the strain ellipsoid.
- a description of the significance of your results given the context provided. What are your basic assumptions as to the predeformation geometry? Is this a measure of the the total strain the rock has seen and why or why not? One to two paragraphs should suffice here.

**Methodology:**

- You can complete the lab manually, by marking centers, then displacing an overlay to mark other centers, until you have done all the points.
- You can also do it in Illustrator, probably just as easily, by using the layers option and displacing all the points in one layer over another layer which has the centers marked.
- You can also obtain (or write your own software) and input your centers to get your results. If you have as input the relative x,y positions of the centers then you can actually complete this in Excel (although it is a bit awkward).
- One of the biggest challenges here will be
**picking centers**. Because of undulose extinction and various stages of recrystallizaton some of the grains are not well defined. I have chosen this sample exactly because it is a more typical sample that one might work with, and will make you aware of some of the issues that can be related to using this technique. Note that this technique has a statistical aspect to it and in order to work you have to have a significant number of centers to plot the relative positions of. In this way, picking the exact center of the grain is not crucial, but gets washed out if you have enough centers. - Remember it is not the grains far away from
a given center that determine the shape of the final ellipse.
It is the neighboring grains.
__So when you make this plot you don't have to plot all the grains, just the ones that are 3-4 times the average grain diamater away.__ - Using the larger image will help.

*You can link to a bigger version
of these images by clicking on them.*