STATISTICAL SYMMETRY OF LATTICE PREFERRED ORIENTATIONS: APPLICATIONS TO QUARTZ AND OLIVINE

We introduce and apply a new method for analyzing the symmetry of lattice preferred orientation (LPOs) in deformed rocks. The symmetry of LPOs can be used to interpret the symmetry of the deformation, such as pure shear vs. simple shear, plane strain vs. flattening vs. constriction, and the sense of shear in noncoaxially deformed rocks.

At present, the symmetry of LPOs are analyzed empirically, by comparison with experimental results and inspection for asymmetry in pole figures. Our analysis focuses on finding the set of statistically significant 2-fold rotation axes in the LPO. Using synthetic olivine examples, we show that an LPO created by simple-shear deformation contains one 2-fold rotation axis, perpendicular to the shear direction and parallel to the shear plane. In contrast, an LPO created by coaxial flattening deformation (Sx=Sy>Sz) has a great circle distribution of rotation axes, with the pole of the great circle equivalent to the maximum shortening direction.

To estimate the two-fold rotation symmetry elements of an LPO data set, we search a grid of rotation axis orientations in the lower hemisphere of a stereonet, and rotate the LPO distribution around this axis to create a second, rotated LPO distribution. The original and rotated distributions are compared in orientation distribution space using a Kolmogorov-Smirnov test to measure the probability that the distributions are similar, save for random variation. This analysis allows us to use the full crystal orientations, rather than specific crystal axes, to measure the symmetry of the entire LPO dataset.

We apply our symmetry method to both olivine and quartz using synthetic, experimental, and natural samples. Our synthetic examples show the conditions under which deformation symmetry can be inferred from the texture symmetry, and allow us to provide recommendations for how to best sample LPOs. We also compare our results with other measures of LPO strength, such the M-index. We show how the symmetry patterns of quartz, in particular, can be easily misinterpreted and provide new results for enigmatic quartz textures in the Moine Thrust Zone rocks of Northwest Scotland.