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:
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:
You can link to a bigger version of these images by clicking on them.
Excellent reference: Ramsey, J. G., & Huber, M. I., 1983, The Techniques of Modern Structural Geology Volume 1: Strain Analysis; Academic Press, ISBN 0-12-576921 - 0