TESTING THE UTILITY OF THE PORPHYROCLAST HYPERBOLIC DISTRIBUTION METHOD OF KINEMATIC VORTICITY ANALYSIS

Kinematic vorticity (W_k) is a dimensionless measure of rotation relative to finite stretching and is essential for complete understanding of flow in ductile shear zones. Values range from 0 to 1; with pure shear dominated values of 0.0-0.4, general shear values of 0.4-0.95, and 0.95-1 being simple shear dominated deformations. The porphyroclast hyperbolic distribution (PHD) method is a widely used technique for measuring W_k based on measuring the acute angle between the extensional and stable eigenvectors as defined by the orientations of back rotated sigma porphyroclasts. PHD analyses have been used to estimate thinning and displacement along shear zones and could be useful in discerning flow paths and strain symmetries of mylonites. In an effort to test the utility of the PHD, ultramylonites from the Santa Catalina Mtns, Arizona, and Virgin Mtns, Nevada were analyzed. Lineation parallel and normal planes of samples were examined to investigate strain symmetry. The data set used to analyze the PHD is comprised of 54 thin sections from 7 different samples. Ultramylonites from the Santa Catalina Mtns record a single general shear deformation and may be triclinic as indicated by lineation parallel W_k's of 0.57 and lineation normal W_k's of 0.30. Virgin Mtns ultramylonites are the product of strain partitioning with zones of pure and general shear, the latter of which exhibit a rolling lineation with the transport direction orthogonal to the direction posited by other workers. Bootstrapping statistics and a computational sieving process were used to analyze the PHD data set. Average standard deviations of the bootstrapped data sets yielded a 1 σ standard error of ±8.3 for a W_k value measured in % simple shear. The error expressed as % simple shear converts to W_k values between ±0.01 for simple shear and ±0.13 for pure shear. Sieving results imply that back-rotated porphyroclasts may not orient parallel to the extensional eigenvector. The PHD method is useful for discerning between deformations that are pure shear, general shear, or simple shear dominated but is not accurate enough to report precise W_k values. The PHD performed on multiple sections can be used to identify zones of monoclinic vs triclinic shear.