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A description of the systematic errors associated with the measurement of the vorticity number from poryhroclasts in natural systems is presented and discussed. We show that strong biases and systematic errors could derive both from some erroneous physical (i.e. no slip across clast/matrix boundary, homogeneity within the matrix) as well as geometrical assumptions (i.e. the radius ratio and angular measurements carried out in two dimensions on outcrop surfaces and thin section). By comparing natural datasets of porphyroclast shape preferred orientation (SPO) with different theoretical curves plots, we suggest that at least one of the Jeffery physical assumptions can be tested when applying vorticity techniques. The comparison of different possible sources of systematic errors indicates that, for medium-to-low vorticity numbers (Wm , 0.8), vorticity data are strongly biased and that a minimum systematic error of 0.2 should be taken into account. Finally, we use data from natural shear zones from the Southern Variscan Belt in Sardinia to test and discuss the starting assumptions of the Jeffery model. One of the main challenges of modern structural geology is to try to obtain information about the rheology and kinematics of flow occurring in the deepest crust and upper mantle. Several microstructure fabrics (e.g. fabric asymmetry) associated with mylonites represent potentially important sources of information to obtain kinematic data as well as for estimation of deformation parameters (see Passchier & Trouw 2005 for a review). In particular, porphyroclast systems have been shown to be a sensitive indicator of flow parameters and can be used to constrain the relative ratio of combined pure and simple shear (i.e. the vorticity of the flow). Several theoretical and practical studies indicate that syn-kinematic recrystallization of mantles (sor d-shaped tails) around porphyroclasts and shape preferred orientation (SPO) of porphyroclasts may store information on the amount of shear strain. With the aim of developing a vorticity gauge, theoretical and experimental models for study of the rotation and behaviour of elliptical porphyroclasts in a fluid have been proposed and developed. The first attempt began with the pioneering works of Jeffery (1922) and Eshelby (1957) that found solutions for rigid objects immersed in a viscous and linear-elastics fluid, respectively. Bretherton (1962), Ghosh & Ramberg (1976) and Bilby & Kolbuszewski (1977) further adapted the basic Jeffery analytical solution to material science and structural geology. Subsequent investigations used the previous theoretical calculation to develop efficient strain and vorticity gauge techniques capable of quantifying the flow parameters within shear zones (Passchier 1987; Wallis 1992; Simpson & De Paor 1993; Holcombe & Little 2001). Three main analytical techniques (Passchier 1987; Wallis 1995; Holcombe & Little 2001) are commonly employed to characterize flow within shear zones using rigid porphyroclats (Jessup et al. 2007). All these techniques use the measurement of the axial ratio of porphyroclast R (the shape factor; Fig. 1) and the angle of long axis porphyroclast with respect to foliation or stretching direction h (Fig. 1) and the distribution of the cross-plotted curves to define the mean vorticity number Wm. These curves define a threshold number Rc, below which the porphyroclasts continuously rotate and above which they record stable sink position. However, as many authors (Passchier 1987; Marques & Coelho 2001) have already noted, the Jeffery model assumes: (1) rigid particles immersed in a non-confined viscous flow, (2) a perfect coupling on matrix/particle interface and (3) no interference between particles during deformation. Use of the Jeffery model implies that these physical assumptions are met, and/or need to be, at least preliminarily, tested. Although techniques to estimate the vorticity of flow have become routinely used on sheared rocks in a variety of tectonic settings (e.g. Klepeis et al. 1999; Xypolias & Doutsos 2000; Xypolias & Koukouvelas 2001; Bailey & Eyster 2003; Law et al. 2004; Carosi et al. 2006, 2007; Iacopini et al. 2008; Sarkarinejad et al. 2008, 2010; Frassi et al. 2009; Larson & Godin 2009), relatively few detailed analysis of error sources have been proposed and a critical discussion From: Prior, D. J., Rutter, E. H. & Tatham, D. J. (eds) Deformation Mechanisms, Rheology and Tectonics: Microstructures, Mechanics and Anisotropy. Geological Society, London, Special Publications, 360, 301–318. DOI: 10.1144/SP360.17 # The Geological Society of London 2011. Publishing disclaimer: www.geolsoc.org.uk/pub_ethics at University of Aberdeen on November 19, 2012 http://sp.lyellcollection.org/ Downloaded from