The relationship between magmatic tiling, fluid flow and crystal fraction

Tiling of crystals in magmatic rocks is used to indicate flow in the magmatic state and also as an indicator of shear sense. The status of tiling as a kinematic indicator is often regarded with caution due to a poor understanding of the dynamics involved in its development. By considering a simple numerical model involving both rotation and translation of pairs of crystal objects under different homogeneous steady state flow conditions (i.e. 0≤W_k≤1.5), the dynamics of crystal tiling is studied in detail. A consistent relationship between tiling proportions (i.e. dextral versus sinistral) and W_k is observed. For pure shear the relationship is 50/50 whereas for simple shear one sense dominates accounting for 70% of the tiling. A similar relationship is observed for low and high crystal fractions and a wide variety of object aspect ratios. Through application of the statistics of proportions it is shown that approximately 60 observations are required for a shear sense determination, whereas for accurate estimation of W_k at least 200 observations are required. The density of tiling varies with crystal fraction and it may be possible to use the frequency of occurrence of tiling to estimate the crystal fraction at the time of tiling. It is concluded that a few observations of crystal tiling is a highly unreliable shear sense indicator.