The Rigid Grain Net (RGN): An alternative method for estimating mean kinematic vorticity number (Wm)

The use of porphyroclasts rotating in a flowing matrix to estimate mean kinematic vorticity number (Wm) is important for quantifying the relative contributions of pure and simple shear in penetratively deformed rocks. The most common methods, broadly grouped into those that use tailed and tailless porphyroclasts, have been applied to many different tectonic settings; however, attempts have not been made to unify the various methods. Here, we propose the Rigid Grain Net (RGN) as an alternative graphical method for estimating Wm. The RGN contains hyperbolas that are the mathematical equivalents to the hyperbolic net used for the porphyroclast hyperbolic distribution (PHD) method. We use the RGN to unify the most commonly used Wm plots by comparing the distribution of theoretical and natural tailless porphyroclasts within a flowing matrix. Test samples from the South Tibetan detachment, Tibet yield indistinguishable results when the RGN is compared with existing methods. Because of its ease of use, ability for comparing natural data sets to theoretical curves, potential to standardize future investigations and ability to limit ambiguity in estimating Wm, the RGN makes an important new contribution that advances the current methods for quantifying flow in shear zones.