PRACTICAL ASSESSMENT OF CRYSTALLOGRAPHIC PREFERRED ORIENTATION STRENGTH

Quantifying finite strain is an aspiration of many geological studies, but in practise the extractable data often fall short of this goal. Instead, the relative differences in deformation intensity between specimens is simpler to assess and can be nearly as insightful . Some studies have used the strength of a crystallographic preferred orientation (CPO) as a proxy for deformation intensity. Complications of differing lithologies and the assumption that the strain producing mechanism is also responsible for CPO development notwithstanding, the stronger, more organized CPO have been interpreted to record greater strains than those with weaker distributions. Many published works have quantified CPO strength using an eigenvector-based method, e.g. intensity, cylindricity or uniformity statistic, which relates strength to the relative length of three mutually perpendicular eigenvectors defined by the distribution of the crystal directions. The orthogonality of the eigenvectors, however, means that the measures should not be applied to CPOs with two, variably inclined distributions or crossed girdles, such as quartz c-axis pole figures, which has been commonplace.

In order to quantify the potential effects of inappropriately applying eigenvector-based methods to CPO strength determinations we model a series of pole figures representing commonly observed quartz c-axis distributions: random, single point maxima, double point maxima, single girdle, and crossed girdles with various opening angles. The strength of these pole figures was quantified using the abovementioned eigenvector-based methods in addition to the L2-norm of the density distribution of the data. The results show a direct correlation between the type of distribution and value of strength measure, which varies with quantification method. While differences in strength may be expected when comparing point maxima to crossed-girdle pole figures, significant differences in strength were also noted between crossed-girdle distributions with different opening angles. All eigenvector-based methods show a negative correlation between strength measure and interlimb angle. The same is not noted when quantifying CPO strength using the density L2-norm and as such this method may be the most robust for comparison of relative CPO strength.