The western Idaho shear zone (WISZ) is a Late Cretaceous, mid-crustal exposure of intense shear localized in the Cordillera of western North America. This shear zone is characterized by transpressional fabrics, i.e., downdip stretching lineations and vertical foliations. Folded and boudinaged late-stage dikes indicate a dextral sense of shear. The vorticity-normal section is identified by examining the three-dimensional shape preferred orientation of feldspar populations and the intragranular lattice rotation in quartz grains in deformed quartzites. The short axes of the shape preferred orientation ellipsoid gather on a plane perpendicular to the vorticity vector. In western Idaho this plane dips gently to the west, suggesting a vertical vorticity vector. Similarly, sample-scale crystallographic vorticity axis analysis of quartzite tectonites provides an independent assessment of vorticity and also indicates a subvertical vorticity vector. Constraints on the magnitude of vorticity are provided by field fabrics and porphyroclasts with strain shadows. Together these data indicate that the McCall segment of the WISZ displays dextral transpression with a vertical vorticity vector and an angle of oblique convergence ≥60°. North and south of McCall, movement is coeval on the Owyhee segment of the WISZ and the Ahsahka shear zone. Together, the kinematics of these shear zones are consistent with northeast-southwest–directed convergence. Plate motion in this orientation acting on a curved plate boundary could have produced pure shear–dominated transpression in the Owyhee (α = 40°) and McCall (α = 60°) segments of the WISZ, while causing reverse-sense shearing (α = 90°) in the Ahsahka shear zone.


Clear constraints on the vorticity of a high strain zone are fundamental to understanding the deformation history of that zone. Vorticity is a tensor quantity (e.g., Malvern, 1969) and therefore has both direction and magnitude. In structural geology both the orientation and the magnitude of vorticity provide constraints on the kinematics of deformation. First, the orientation of maximum spin defines a vorticity vector, i.e., the axis of maximum rotation (e.g., Tikoff and Fossen, 1995). Two-dimensional kinematic vorticity analysis typically assumes that the vorticity vector is oriented normal to the section in which data are gathered, that is normal to the lineation-parallel, foliation-normal surface. Field fabrics, however, may not be reliable indicators of vorticity orientation, as shown theoretically by Lin et al. (1998) and others. Second, kinematic vorticity is a measure of the relative amounts of the coaxial versus noncoaxial components acting in a shear zone (e.g., Means et al., 1980). This approach is used because most shear zones lack fabric elements that provide quantitative information about the rates of rotation, but those same fabric elements can be used to distinguish between coaxial versus noncoaxial components of rotation (e.g., Passchier, 1987; Simpson and De Paor, 1993; Bailey et al., 2004; Jessup et al., 2007; Xypolias, 2010; Iacopini et al., 2011; Li and Jiang, 2011).

The utility of a vorticity analysis is its ability to constrain the type of deformation undergone by a shear zone and make predictions of other quantities such as finite strain, infinitesimal strain, and the principal directions of motion, known as flow apophyses. The flow apophyses define the relative motion of the shear zone walls with respect to each other. At the plate boundary scale, flow apophyses characterize how the plate on one side of a shear zone moves relative to the other, i.e., relative plate motion. Strike-slip plate boundaries, such as the San Andreas fault, are dominated by simple shear. Obliquely convergent boundaries, such as the Alpine fault zone in New Zealand, include components of pure shear (e.g., Little et al., 2005). Defining the relative plate motion, which is related to vorticity, is central to understanding the role of an ancient shear zone in the greater tectonic history of the region. Mean vorticity (Wm) is a common measure of vorticity used in the structural geology community and it varies from zero (100% pure shear) to one (100% simple shear; e.g., Xypolias, 2010).

Transpression is a three-dimensional (3D) kinematic model often used to describe the flow of material at the plate tectonic scale (e.g., Sanderson and Marchini, 1984). Although there are many forms of transpressional deformation, for the purposes of this paper we refer to transpression as a volume-constant, monoclinic system with shortening orthogonal to the shear zone, vertical elongation, and no elongation parallel to the shear direction. For transpressional deformation, the angle of oblique convergence is used to quantify the relative plate motion (i.e., vorticity) of a system (e.g., Sanderson and Marchini, 1984; Fossen and Tikoff, 1993; Fig. 1). An angle of oblique convergence (α) of 0° describes a strike-slip plate boundary (Wm = 1), while an angle of 90° describes a purely convergent system (Wm = 0). Transpressional and transtensional models of deformation are ideal for plate-scale tectonics because they are the only deformations characterized by straight and parallel flow lines in the horizontal plane (e.g., Fossen and Tikoff, 1998; Tikoff and Teyssier, 1998).

We present the results of a vorticity analysis of deformed rocks within the western Idaho shear zone (WISZ; Fig. 2). We use this shear zone because (1) it has been modeled as a transpressional shear zone (e.g., Giorgis and Tikoff, 2004; Giorgis et al., 2005; Davis and Giorgis, 2014); (2) it has a primary bend in its orientations (Braudy et al., 2016; Schmidt et al., 2016), which should correspond to different kinematics (Benford et al., 2010); and (3) it is locally well exposed. In this contribution, we quantitatively constrain both the orientation of the vorticity vector and the kinematic vorticity number for deformation in this shear zone. First, we use 3D shape preferred orientation (SPO) of feldspar populations to estimate a vorticity vector and kinematic vorticity number. Second, we use a statistically robust technique to determine the orientation of bulk vorticity vector by averaging the crystallographic rotation axes calculated from individual deformed grains (Michels et al., 2015, following Bestmann and Prior, 2003; Reddy and Buchan, 2005). The WISZ records a vertical vorticity vector and transpressional deformation (this study), while the simultaneous and kinematically linked Ahsahka shear zone records thrust motion and a horizontal vorticity vector (Schmidt et al., 2016). Using the vorticity vector and the kinematic vorticity number studies together, we conclude that the majority of strain in the WISZ accumulated under transpressional conditions with an angle of oblique convergence of ∼60° in the McCall region.


The WISZ near McCall, Idaho, deforms a series of granitic units on the western edge of the Idaho Batholith in the Late Cretaceous (Manduca et al., 1993; Giorgis et al., 2008). The Blue Mountain terrane is west of the shear zone and on the basis of paleomagnetic data, is thought to have traveled hundreds of kilometers northward to its present location (Hillhouse et al., 1982). Fabrics in the WISZ indicate dextral transpression (McClelland et al., 2000). Foliation, defined by aligned micas, amphiboles, and stretched quartz grains, strikes north-south and dips steeply to the east near McCall (Fig. 2). South of the Sage Hen area on West Mountain (Fig. 3), the foliation is oriented ∼020, and dips steeply eastward. Lineation, also defined by aligned amphiboles and stretched quartz, pitches steeply downdip to the east. Removal of the effects of tilting due to Miocene and Holocene Basin and Range extension yields a subvertical foliation and lineation (Tikoff et al., 2001). The WISZ extends from the Owyhee Mountains south of Boise (Benford et al., 2010) to north of Riggins and is ideally located to accommodate some of the Late Cretaceous northward translation of terranes in the Cordillera (Fig. 2; e.g., Wyld et al., 2006; Wright and Wyld, 2007).

While there is general consensus that the WISZ is a transpressional structure (Lund and Snee, 1988; McClelland et al., 2000; Tikoff et al., 2001), there are few published constraints on the vorticity of this structure. In Giorgis and Tikoff (2004) we used potassium feldspar SPO fabrics to determine an angle of oblique convergence of 45°. More rigorous analysis, however, suggests that these fabrics are consistent with a wide variety of vorticity values (Davis and Giorgis, 2014). Strain analysis of the strontium isotopic gradient suggests that this shear zone records a large amount of contraction (Giorgis et al., 2005). The Giorgis et al. (2005) study, however, only provided information about the contractional component of deformation, not the strike-slip component, and therefore offers no insight into the vorticity of the system.


Shear sense indicators in the WISZ can be difficult to interpret. Symmetric or domainal shear sense indicators are found on surfaces perpendicular to foliation and parallel to lineation (e.g., Manduca et al., 1993). In contrast, asymmetric shear sense indicators are found on surfaces perpendicular to both foliation and lineation (McClelland et al., 2000). However, for an individual outcrop, the sense of shear can be ambiguous. Furthermore, because the finite strain is so high in this zone, almost all contacts have been rotated into parallelism to the overall trend of the shear zone, with the major contacts often reactivated as normal faults (e.g., Tikoff et al., 2001).

A few critical outcrops provide unambiguous evidence for dextral offset. For example, small outcrops of the Little Goose Creek complex show evidence for north-south–oriented localized structures with clear dextral separation (McClelland et al., 2000). This outcrop is unusual, however, because the WISZ typically exhibits distributed, rather than localized, shearing. An exposure of the Sage Hen orthogneiss, located just south of Cascade, exhibits clear dextral shearing during distributed deformation (Fig. 4). In this location, one mafic dike is folded and another is boudinaged on a subhorizontal, glacially polished surface. These dikes are not sheared into parallelism with the main fabric, unlike most other features in the WISZ. Consequently, we interpret that the two mafic dikes intruded late in the deformation history and only record a small proportion of the overall finite strain. The asymmetric boudin pods show right step-over morphology and provide an unambiguous dextral shear sense.

The orientations of the folded dike and boudinaged dike are also consistent with dextral transpression (Fig. 4). At this location, the strike of WISZ foliation is north-south, the boudinaged dike has a trend of ∼340, and the folded dike has a trend of ∼060. Using the kinematic model of Tikoff and Fossen (1993) for dextral transpression along a north-south–oriented shear zone, shortening in the entire northeast-southwest quadrants (000–090 and 180–270) is predicted and elongation is possible for some orientations in the northwest-southeast quadrants (090–180 and 270–360). This prediction is consistent with the field observations. In contrast, sinistral transpressional deformation will result in shortening only in the northwest-southeast quadrants; thus, the finite strain field recorded by the dikes is incompatible with any sinistral component of deformation. A contraction-only deformation (pure shear with vertical elongation and horizontal shortening) will result in shortening only in the horizontal plane. Note that with more boudinaged and/or folded dikes it might be possible to more precisely constrain the vorticity of deformation in addition to the sense of shear (e.g., Kuiper and Jiang, 2010). With a small set of observations, however, we come to the more limited conclusion that this outcrop is consistent with dextral transpression (or dextral simple shear) kinematics characterizing the deformation in the WISZ.


Populations of Rigid Clasts

The orientation of the vorticity vector corresponds with the axis about which rotation occurs due to the simple shear component of deformation (e.g., Tikoff and Fossen, 1995). A plane oriented normal to this vector, i.e., the vorticity-normal section, contains the maximum amount of rotation in the deformation. Data to constrain the 2D mean vorticity (Wm) of deformation in a monoclinic system should be collected in this plane (e.g., Xypolias, 2010). Numerical modeling of oblate spheroidal objects, such as feldspar porphyroclasts, suggests that the short axis of these objects should gather in the vorticity-normal section for a contractional monoclinic deformation (Passchier, 1987). Although it is difficult to measure the orientation of a single feldspar in the field or hand sample, it is possible calculate the SPO of a population of feldspars by gathering measurements on three orthogonal planes (e.g., Robin, 2002).

The presence of large (1–3 cm) K-feldspar porphyroclasts is the defining characteristic of a portion of the Little Goose Creek Complex (Fig. 3; e.g., Manduca et al., 1993). In thin section, the mean grain size of the matrix surrounding these porphyroclasts is an order of magnitude smaller than the porphyroclasts (<1 mm) and they are rarely mantled with strain shadows (Giorgis and Tikoff, 2004). SPO measurements of the population of K-feldspar porphyroclasts, in three mutually perpendicular planes (∼50 K-feldspar porphyroclasts per plane), were gathered at 23 stations across the WISZ (Giorgis and Tikoff, 2004). A 3D SPO ellipsoid was calculated for each station using the method of Robin (2002); particular attention was paid to the short axes. The short axes of these SPO ellipsoids collect in a shallow west-dipping plane (Fig. 5). After correction for the effects of post-Miocene rotation on normal faults (∼15° of westward tilting; Giorgis et al., 2006), the short axes of these SPO ellipsoids collect in a subhorizontal plane (Fig. 5). The pole to that plane is nearly vertical.

We suggest that the pole to the plane defined by the short axis of the SPO ellipsoids represents the vorticity vector for the deformation. Numerical models demonstrate that the short axes of the ellipsoid describing the SPO of a population of feldspars should collect in the vorticity-normal section (Giorgis and Tikoff, 2004). It is well documented that rigid objects will continue to rotate about the vorticity vector due to the simple shear component of deformation (e.g., Jezek et al., 1994). Thus, the long axis of an individual rigid clast becomes attracted to the vertical direction because it is a fabric destination (Fossen et al., 1994) or attractor (Passchier, 1987). However, the rigid object keeps rotating around a vertical axis (in the horizontal plane). A population of rigid objects is therefore expected to have both short and intermediate SPO axes in the horizontal plane. In the case of the WISZ, the rigid K-feldspar porphyroclasts typically have a tabular geometry (i.e., the length of the maximum and intermediate axes are approximately equivalent), making the short axis of the SPO the most reliable indicator for vorticity analysis.

If this interpretation is correct, the vorticity-normal section is horizontal for the WISZ, which implies that the vorticity vector is vertical and subparallel to the stretching lineation (Fig. 5). Vertical foliation, vertical stretching lineation, and a vertical vorticity vector are all consistent with monoclinic transpression (e.g., Sanderson and Marchini, 1984; Fossen and Tikoff, 1993).

Crystallographic Vorticity Analysis


Crystallographic vorticity axis (CVA) analysis is a new quantitative method for identifying the position of grain-scale vorticity axes (one vorticity axis per grain) in geologically deformed aggregates (Michels et al., 2015). Specifically, CVA analysis uses rotational statistics to calculate the position of a rotational axis that matches the intragranular dispersion of crystallographic orientations in a single deformed grain. In Michels et al. (2015) it was demonstrated that the preferred orientation from a specimen-representative population of crystallographic vorticity axes can be used to track the position of the bulk vorticity vector in monoclinic shear zones (i.e., flow fields ranging from subsimple shear to pure shear–dominated transpression). The major advantage of this method is that it provides an objective quantitative determination of the vorticity vector orientation, independent of any presumptions about the relationship between vorticity and fabric elements such as lineation, foliation, and crystallographic texture.


Crystallographic orientation maps were collected by means of electron backscatter diffraction analysis of three oriented quartzite samples from a metasedimentary screen in the WISZ near West Mountain. Analyzed sample surfaces were cut parallel to the macroscopic stretching lineation and perpendicular to the trace of foliation (i.e., map x-direction parallel to direction of lineation and map y-direction normal to the foliation plane). Data were acquired at the University of Wisconsin–Madison Department of Geoscience, using a Hitachi S3400N variable pressure scanning electron microscope (tungsten filament; 20 kV and 25 Pa conditions) equipped with an Oxford Instruments Nordlys II detector. Matrices of orientation maps were collected for each sample at step sizes ranging from 10 to 20 µm using a 3-step-overlap between maps. Map matrices were stitched together and processed to reduce noise (minimum nearest neighbor of 6) using the Channel5 (Oxford Instruments; www.oxford-instruments.com) software suite. On an average, the processed maps comprise 81% indexed solutions with a mean angular deviation <1°.

Grain detection analyses were conducted using the free and open source software toolbox MTEX (4.0; http://mtex-toolbox.github.io/) (Hielscher, 2007; Schaeben et al., 2007; Hielscher and Schaeben, 2008; Bachmann et al., 2010a) for MATLAB (MathWorks; http://www.mathworks.com). Grain sets were constructed from electron backscatter diffraction orientation maps (e.g., Bachmann et al., 2010b) using a 10° misorientation threshold for grain boundary identification. Grains sets were filtered to identify subsets in which each grain encompasses >3 orientation solutions. The filtered grain sets comprise our selection of specimen-scale representative orientation data used for subsequent grain-scale CVA analysis and characterization of sample-scale quartz lattice preferred orientation. In the WISZ samples, we calculate grain-scale crystallographic vorticity axes using the method described in Michels et al. (2015). We define the bulk vorticity axis as the axis that matches the maximum orientation density of CVAs based on nonparametric kernel density estimation using a 1° resolution and a de la Valée Poussin kernel with a 10° half-width (e.g., Michels et al., 2015).


Quartzite samples in the WISZ were gathered from the Sage Hen metasedimentary screen on West Mountain (Fig. 3; Braudy et al., 2016). This screen contains pelite, marble, and quartzite, and is found in the western portion of the Payette River tonalite. Both the metasedimentary screen and the surrounding tonalite are deformed along the eastern margin of the WISZ. Proterozoic detrital zircon ages from the quartzites clearly require a sedimentary source (Braudy et al., 2016).

Sample-scale representative populations of quartz grains were analyzed, such that CVA was calculated for each quartz grain with a grain boundary that encompasses three or more orientation solutions. For direct comparison with regional data, we rotate the vorticity axes into a geographic reference frame based on the orientation of foliation and lineation measured in the field (Fig. 6). In the specimen reference frame, the bulk vorticity axes from the samples plots near the specimen x direction (i.e., at the edge of the outer circle in a specimen equal area projection). In a geographic reference frame, the bulk vorticity axes plunge downdip in the steeply oriented WISZ foliation.

The results of our CVA analyses indicate that the vorticity vector in each sample is close to parallel with the long axis of the stretching lineation. The subparallel relationship between vorticity and lineation defies the kinematic geometry necessary for simple shear–dominated deformation (lineation is always perpendicular to the vorticity vector in simple shear). Alternatively, these vorticity results are entirely consistent with pure shear–dominated transpression (parallel vertical stretching lineation and vertical vorticity vector). If post-Miocene fault movements are restored, these CVAs have subvertical orientations.

Quartz Crystallographic Preferred Orientation

We present the following methods and data to (1) provide crystallographic texture context for the samples from which we calculate our CVA analyses; and (2) set the foundation for a discussion about quartz crystallographic preferred orientation (CPO) interpretation in pure shear– versus simple shear–dominated monoclinic transpressional deformation.


To quantitatively characterize the quartz crystallographic orientation texture in the WISZ samples, we compute an orientation density function using the mean crystallographic orientations of quartz grains (one orientation per grain) in each sample. The orientation density function is calculated using 1° resolution and a symmetrized, antipodal kernel density estimation with a de la Valée Poussin kernel and a 10° half-width. The density function is normalized to multiples of uniform density and provides a measure by which we characterize and identify the patterns of quartz CPOs in the samples (Fig. 6).


We present quartz crystallographic texture data (Fig. 6) in both the specimen (i.e., acquisition) reference frame and the kinematic reference frame (i.e., vorticity-normal section) in order to discuss the potential pitfalls of interpreting deformation conditions from quartz CPO patterns that developed as a result of pure shear–dominated transpression (see Discussion). In all the samples, quartz c-axes form a clustered distribution centered about a direction that is subparallel to the bulk stretching lineation in the fabric and the calculated bulk CVA orientation, and quartz a-axes form a symmetric girdle of clusters normal to it. In a vorticity-normal reference frame (i.e., a projection centered about the preferred CVA orientation), the concentration of quartz c-axes plots at the center of an equal area projection (Fig. 6), with a girdle of a-axes clusters that traces a great circle arc along the outer edge of the plot.

In simple shear and wrench-dominated transpression, the X-Z fabric ellipsoid reference frame is identical to the vorticity-normal (i.e., kinematic) reference frame, and serves as the most appropriate framework in which to interpret kinematics and CPO patterns. For this reason, when the specific deformation geometry is unknown or assumed, the fabric X-Z plane is commonly selected for microstructural investigation and analysis. However, in pure shear–dominated transpression, the vorticity-normal surface is, instead, coincident with the Y-Z plane of the fabric ellipsoid reference frame, with the vorticity axis parallel to the X-direction of the fabric ellipsoid. This orientation raises the question of which reference frame is most suitable interpreting the kinematic significance of quartz texture data for transpressional deformation. In the following n, we present an independent assessment of quartz slip systems based on a misorientation axis analysis in the crystallographic reference frame. In the Discussion, we explore some ramifications of reference frame selection for data analysis and potential pitfalls of quartz texture interpretation in transpressional systems.

Misorientation and Slip-System Analysis of Quartz


Misorientation analysis provides a complimentary type of texture characterization to the CPO analysis described here, and intragranular misorientations can be used to constrain dominant slip systems during deformation independent of information about the orientations of foliation and lineation. A crystallographic misorientation is the 3D rotation between any two selected crystal orientations. Each misorientation rotation can be described by an axis of rotation and an angular magnitude of rotation about that axis. For each quartz grain in the WISZ samples, we calculate the misorientation between every measured lattice orientation within the grain and the mean intragranular orientation for that same grain. We consider the distribution of misorientation axes in the crystal reference frame in order to assess the predominant crystal slip mechanisms. In this manner, the relationship between the preferred low-angle misorientation axes and crystallographic axes can be used to determine the active quartz slip system (e.g., Nicolas and Poirier, 1976; Lloyd and Freeman, 1994; Lloyd et al., 1997; Neumann, 1996; Fig. 6), independent from interpretations made in the specimen, kinematic, or geographic reference frame.


Intragranular misorientation axes in all three samples exhibit a preferred association with quartz c-axis orientations (i.e., low-angle misorientation axes form a cluster centered about the quartz c-axis) (Fig. 6). This result indicates that the quartz c-axis is the main rotational axis about which lattice deformation occurs to accommodate intracrystalline slip. This crystallographic relationship with misorientation axes is characteristic of the prism <a> slip ({m}<a> slip) system in quartz (Fig. 6). However, the distribution of quartz c-axes in the specimen reference frame forms a cluster that is subparallel to the stretching lineation (i.e., fabric attractor; Passchier, 1987) with <a> axes normal to it (Fig. 6). This latter association between quartz c-axes and stretching lineation is characteristic of prism [c] slip ({m}[c] slip) in quartz for simple shear–dominated deformation.

The results of quartz CPO pattern interpretation for the WISZ samples vary depending on the reference frame in which they are considered. Specifically, when viewed in the typical X-Z fabric reference frame, the CPO matches patterns developed during prism [c] slip at temperatures >650 °C; whereas, when viewed in a vorticity-normal projection, the CPO pattern matches those developed by dominantly prism <a> slip at lower temperatures (> 500 °C). However, intragranular misorientation axes from the WISZ samples indicate that prism <a> slip dominated during crystal-plastic deformation. This result suggests that plotting CPO in fabric reference frame is not always appropriate. The CPO plotted in the fabric reference plane would (erroneously) suggest that prism [c] slip was active in the WISZ. However, prism <a> slip is the dominant slip system. The main reason is that for pure shear–dominated transpressional deformations, the X-Z (finite strain) plane is not coincident with the vorticity-normal plane (the Y-Z finite strain) plane. Our data suggest that a vorticity-normal kinematic perspective may be a more useful way to interpret CPO data.


Fabric Orientation

In transpression the orientation of the maximum stretching direction is a function of the vorticity of deformation (e.g., Fossen and Tikoff, 1993). In pure shear–dominated transpression, i.e., transpression with a high degree of contraction, the maximum stretching direction is always vertical. In wrench-dominated transpression, i.e., transpression with a high degree of strike-slip motion, the maximum stretching direction starts out horizontal and will switch to vertical at very high strain. The boundary between pure shear–dominated and wrench-dominated transpression occurs at Wm = ∼0.8 or an angle of oblique convergence (α) of ∼20° (e.g., Fossen and Tikoff, 1993).

Assuming that the vertical stretching lineation observed in the field is a good proxy for the maximum stretching direction, the WISZ is characterized by either very high strain wrench dominated transpression, or pure shear–dominated transpression. Although porphyroclast-based strain analyses in the Little Goose Creek Complex do not provide very precise results (Davis and Giorgis, 2014), they indicate that strains are not high enough to produce a vertical lineation in a wrench-dominated transpressional deformation. This result suggests that the kinematics recorded by the finite strain fabric of the WISZ are pure shear–dominated transpression (Wm <0.8 or α >20°).

Porphyroclast Hyperbolic Distribution Method

The porphyroclast hyperbolic distribution (PHD) method seeks to estimate the vorticity of a shear zone by defining the zone of back rotation (Simpson and De Paor, 1993). This is a 2D approach that assumes that porphyroclasts are elliptical in cross section with no initial preferred orientation to their long axes. In simple shear all porphyroclasts rotate in the same direction, i.e., clockwise for dextral simple shear zone, and there is no zone of back rotation. In pure shear, grains will rotate either clockwise or counterclockwise depending on the orientation of their long axis and the aspect ratio of the grain. This approach is typically used in plane strain shear zones that exhibit some combination of pure and simple shear (e.g., Simpson and De Paor, 1993; Bailey et al., 2004).

Transpression is also a mixture of pure and simple shearing. However, the elongation component of pure shear is located orthogonal to the maximum vorticity plane (e.g., vertical). The 2D numerical modeling based on Ghosh and Ramberg (1976) shows that the shortening component of the pure shear in transpression creates domains of clockwise versus counterclockwise rotation (Giorgis et al., 2004). Therefore in transpression, the relative size of the clockwise versus counterclockwise rotational domains is a function of the relative percentage of pure shear to simple shear. This ratio can be characterized as either the angle of oblique convergence (i.e., oblique flow apophysis) or the kinematic vorticity number. However, the relationship between the angle of oblique convergence and the kinematic vorticity number is different from that of 2D general shear (Tikoff and Fossen, 1995). In our simplified analysis, we assume that the angle of the oblique flow apophyses separates the clockwise versus counterclockwise rotational domains.


The PHD analysis is based on measurements of the aspect ratio, orientation of the long axis, and sense of rotation of σ-type porphyroclasts. Typically, these data are collected in thin section. The feldspars of the Little Goose Creek Complex, however, are too large for thin section analysis. In addition, most do not have strain shadows to provide information about the sense of rotation of that grain. The data from this study were measured directly from the outcrop surfaces oriented perpendicular to foliation and lineation gathered over a 2-km-wide traverse across the shear zone (Figs. 3 and 7). By applying this method at the map scale rather than the thin section scale, we assume that deformation in the WISZ is homogeneous. Regional scale shear zones may subdivide into anastomosing networks of localized shear zones at the outcrop scale (e.g., Huddleston, 1999). Field observations in the McCall area of the WISZ, however, show no evidence for a penetrative system of localized, anastomosing shear zones at the outcrop scale, which suggests that our assumption of a homogeneous system is tenable.


The data are presented on a polar plot showing aspect ratio, orientation, and sense of rotation (Fig. 7B). Ideally, the σ-porphyroclasts with a counterclockwise sense of rotation will form a domain that is clearly separated from clockwise domain. Instead, we observe two overlapping populations (Fig. 7B). Therefore we evaluate these data by investigating every possible orientation of the convergent flow apophysis and tabulate how many observations are consistent with that orientation (Fig. 7C). For example, a convergent flow apophysis oriented at 5° to the shear zone boundary would suggest that all of the clasts measured in this study should have a clockwise sense of rotation. There are 79 clasts that agree with this interpretation, but the remaining 100 clasts, i.e., the clasts with a counterclockwise sense of rotation, disagree (Fig. 7C). This analysis suggests that a convergent flow apophysis oriented in the range of 60°–120° is consistent with the greatest number of observations. Orientations >90° indicate sinistral transpressional kinematics. Given the dextral nature of the WISZ, we therefore interpret these data to indicate an angle of oblique convergence in the range of 60°–90° (Fig. 8).


Orientation of Vorticity Vector

In this study we derive vorticity vectors in two different ways. The first is based on the orientation of short axes of fabric ellipsoids calculated from populations of oblate rigid clasts. These short axes fall on a great circle, the pole to which we interpret as a vorticity vector. The nearly vertical vorticity vector is subparallel to the stretching lineations. Field-based SPO analysis requires exposures with fracture and/or foliation surfaces that are nearly orthogonal. The rugged, glaciated region just north of McCall provides these types of outcrops in the Little Goose Creek Complex. Farther south, suitable outcrops are not available, and we are unable to apply this same technique. Rather, we apply the CVA approach to quartzites in the WISZ on West Mountain. CVA analysis has not yet been experimentally validated, and only a few consistency arguments have been demonstrated in support of the method thus far (Michels et al., 2015; Schmidt et al., 2016). We note that our results provide a new type of consistency argument in that the results of CVA analysis match vorticity axis orientations derived from our analysis of fabric ellipsoids. Specifically, the crystallographic approach records the same kinematics as the field SPO data, i.e., a nearly vertical vorticity vector parallel to the stretching lineation. Moreover, both approaches suggest a nearly, but not quite, vertical vorticity vector. In both cases the vorticity vector consistently plunges steeply to the north and is not exactly parallel to the mean stretching lineation. This could imply some triclinic component to the deformation, suggesting that the monoclinic approach taken here may be oversimplifying the kinematics of the WISZ.

Relationship Between Vorticity and CPO of Quartz

Prior work has attempted to establish the relationships between deformation and quartz crystallographic textures in naturally deformed rocks. In many cases, crystallographic patterns in quartzitic tectonites can be compared with results from experimental deformation studies (e.g., Green et al., 1970; Tullis et al., 1973) and numerical models (e.g., Etchecopar, 1977; Lister et al., 1978) to adequately establish the relationship between crystallographic texture, strain symmetry, and finite strain axes (e.g., reviews by Schmid and Casey, 1986; Law 1990). The vorticity-normal section is regarded as the critical reference frame in which to interpret crystallographic patterns. For simple shear–dominated systems, the vorticity-normal reference frame is always perpendicular to the long axis of the finite strain ellipsoid (i.e., the fabric attractor and direction of the macroscopic stretching lineation). In addition, when the kinematic reference frame is unknown, workers often assume a simple shear–controlled relationship between vorticity and lineation; the vorticity vector is assumed to lie in the foliation plane, perpendicular to lineation. However, in the case of pure shear–dominated transpression, lineation and vorticity are parallel, and the vorticity-normal reference frame is centered about the vorticity vector and the fabric attractor. Therefore, without proper identification of the vorticity vector orientation (parallel to lineation in pure shear–dominated transpression), interpretations of quartz CPO that are based on a presumed simple shear–type relationship between lineation and quartz c-axes CPO may lead to incorrect conclusions about the dominant active slip system and the kinematics of the deformation history.

Viewed in the fabric reference frame, the quartz CPO patterns in the WISZ samples closely match the predicted pattern for prism [c] slip in simple shear (Fig. 6). That is, the parallel relationship between quartz c-axes maxima and the fabric attractor (lineation) in the WISZ samples is consistent with CPO patterns formed by activation of the prism [c] slip system during high-temperature (>650 °C) simple shear deformation. In contrast, when the quartz CPO data from the WISZ samples are viewed in a kinematic reference frame (i.e., normal to the bulk vorticity axis determined by CVA analysis), the quartz CPO pattern is effectively flipped ∼90° about the pole to foliation (Fig. 6). In this perspective, the pattern of quartz [c] and <a> axes closely match patterns produced by dominantly prism <a> slip during simple to subsimple shear deformation.

Our misorientation analysis results resolve this issue: the WISZ samples deformed by dominantly prism <a> slip. The interpretation of slip systems from misorientation axes patterns is conducted in the crystallographic reference frame and is thus independent of assumptions about the geometric relationship to bulk vorticity and lineation. Consequently, the vorticity-normal section appears as the better reference frame in which to interpret transpressional fabrics. Furthermore, the computational independence of CVA analysis relative to misorientation index and CPO data provides an objective manner with which to interpret quartz CPO patterns in a transpressional shear zone.

The critical aspect of our analysis is that we cannot expect to adequately interpret quartz CPO patterns if we presume simple shear–dominated kinematics and fabric geometry in lieu of independent determination. The results of intragranular misorientation analysis should broadly agree with any slip system inferences made by interpreting CPO patterns, and therefore represent a useful double-check for the relevance of a chosen reference frame. Moreover, when there is reason to suspect that deformation may deviate significantly from simple shear, an independent vorticity determination can be critically useful for identifying an appropriate kinematic reference frame. An advantage of using CVA analysis for independent vorticity determination is that it can be conducted using the same crystallographic data as those used for CPO and misorientation analyses. The agreement between CPO patterns viewed in a vorticity-normal perspective and the misorientation analyses supports the overall theme of this paper: the WISZ is a pure shear–dominated transpression zone in which vorticity and lineation are subparallel.

Regional Implications

Kinematic Vorticity Estimates

The magnitude of vorticity provides information about the relative contributions of coaxial versus noncoaxial deformation. For deformations such as transpression, the degree of coaxiality of deformation also provides information about the orientation of relative plate motion recorded by the shear zone (i.e., the angle of oblique convergence). The vertical stretching lineation and vertical foliation observed in the WISZ further south in the Owyhee segment provide further constraints (Benford et al., 2010). This segment of the WISZ is oriented at 020 as compared to 000 in the McCall segment. The presence of a vertical stretching lineation in the Owyhee segment indicates that local angle of oblique convergence in that section must also be >20°. Both the Owyhee and McCall segments of the WISZ are active at the same time (Giorgis et al., 2008; Benford et al., 2010), and therefore it is reasonable to assume that these two segments had different orientations during deformation. This inference is confirmed by the preservation of a primary bend in the shear zone in the Sage Hen area of West Mountain (Fig. 3; Braudy et al., 2016). Consequently, as assumed by Benford et al. (2010), the deformation may result from a regionally consistent plate motion. If that is the case, then the McCall segment must record an angle of oblique convergence of >40° for the Owyhee segment to have an angle >20° (Figs. 8 and 9) (Benford et al., 2010). Results from the PHD analysis support the conclusion that the WISZ is characterized by a strong contractional component of deformation (α = 60°–90°).

Although these results are consistent from a regional tectonics perspective, there are potential problems with using 2D data from the vorticity-normal section to characterize a 3D deformation such as transpression. Li and Jiang (2011) highlighted potential problems that could arise with this method by failing to take into account the 3D shape of the rigid clasts used in a vorticity analysis. Specifically, the apparent 2D cross section of an ellipsoid in the vorticity-normal section will change throughout a progressive deformation as that ellipsoid rotates in three dimensions. That is, the PHD method assumes that the ellipsoid rotates about an axis that is perpendicular to the plane of view. The 3D nature of ellipsoid rotation, however, can also affect the PHD method. This method relies on breaking porphyroclasts into clockwise versus counterclockwise cohorts. Li and Jiang (2011), however, found that triaxial clasts may rotate clockwise in the vorticity-normal section and then switch to counterclockwise during the same progressive deformation. It is unclear how quickly porphyroclasts tails will reset in this case, which calls into question the interpretation of rotation direction via strain shadows. This problem, however, only arises with triaxial ellipsoids, i.e., clasts that have three unequal axes. Spheroids, i.e., clasts with two axes of equal length, do not demonstrate this behavior (e.g., Passchier, 1987; Giorgis and Tikoff, 2004). On those few boulders and slabs where the full, 3D shape of the feldspar porphyroclasts in the Little Goose Creek Complex are visible, they are much closer to spheroidal rather than triaxial in shape, suggesting that the 3D shape effect noted by Li and Jiang (2011) should be minimal.

Variation in Vorticity Vector Along Strike

The northern extension of the WISZ shear zone continues directly into the Ahsahka shear zone (Schmidt et al., 2016), as the zone of deformation bends 90° westward at Orofino following the 87Sr/86Sr = 0.706 isopleth (Fig. 2; e.g., Armstrong et al., 1997; Fleck and Criss, 1985; Gaschnig et al., 2013). This bend was likely a primary feature of the western margin of North America prior to the initiation of deformation (e.g., Gaschnig et al., 2013). Schmidt et al. (2016), focusing on the Ahsahka shear zone, document timing constraints indicating that the two shear zones acted simultaneously ca. 100–90 Ma.

The vertical fabrics of the WISZ are continuous with the moderately to steeply dipping foliations and downdip lineations of the Ahsahka shear zone. Schmidt et al. (2016) report the identical types of analyses on quartzites (CVA, CPO, and misorientation analysis) within the Ahsahka shear zone that we present here for the WISZ. Thus, we can directly compare between different orientations within the same overall shear zone. CVA analyses from quartz-rich rocks in the Ahsahka shear zone indicate a subhorizontal vorticity axis that is oriented perpendicular to the field lineation. Misorientation analyses from the Ahsahka shear zone indicated that samples deformed by dominantly prism <a> slip, similar to the WISZ (Schmidt et al., 2016). Quartz CPO and misorientation axes patterns throughout all localities in the WISZ and Ahsahka shear zones indicate similar deformation temperature conditions (>500 °C).

The regional significance of the vorticity results presented herein is best understood when combined with the Schmidt et al. (2016) study. Specifically, we infer that pure shear–dominated dextral transpressional deformation along the north-south–striking segment of the WISZ resulted during oblique collision between the North American craton and outboard terranes during the Late Cretaceous (e.g., Giorgis et al., 2008). If we accept the interpretation that the location of the WISZ and Ahsahka shear zone was controlled by the cratonic margin of the North America (e.g., Tikoff et al., 2001; Gaschnig et al., 2013), then we can observe why the kinematics are so different in the two shear zones. In the McCall and Owyhee segments of the WISZ, the cratonic margin was at an ∼40°–60° angle to the collision and thus there was a significant transcurrent component of deformation. As a result, transpressional deformation is recorded, which shortened the margin and therefore enhanced the sharp isotopic boundary (Giorgis et al., 2005). If our vorticity analysis is correct, the angle of convergence is >60° for the McCall segment and >40° for the Owyhee segment. However, this same angle of convergence results in nearly orthogonal collision in the northwest-oriented Ahsahka shear zone (Fig. 9). That is, the lack of transcurrent deformation resulted in dominantly southwest-vergent kinematics, as North America overrode the accreted terranes of the Blue Mountains. There is significantly more structural complexity (e.g., Lund, 2004) and a longer tectonic history (e.g., McClelland et al., 2000) in the Ahsahka shear zone, relative to the WISZ; we attribute this to this orthogonal convergence. Regardless, the entire arc-craton margin can generally be considered in the context of a single collisional vector, constrained by the vorticity estimates of the different shear zone segments. The compatibility of kinematics and quartz deformation conditions between the different areas further supports the conclusion that deformation along both the McCall and Owyhee segments of the WISZ and Ahsahka shear zone was coeval with regional northeast-southwest–directed convergence (Fig. 9).


The WISZ is characterized by a vertical vorticity vector nearly parallel to the vertical field lineation, when the Miocene–present extension is restored, consistent with transpressional kinematics. Populations of rigidly rotating feldspars in the McCall region, when aggregated, require a subvertical vorticity vector. Rare feldspar porphyroclasts with strain shadows can be used to estimate vorticity using the PHD method, which suggests high (α > 60°) angles of oblique convergence. A vertical vorticity vector is also inferred from quartzites in a wall-rock screen in the West Mountain area, using CVA. The CPOs, when combined with misorientation plots indicating that prism <a> slip is active, are best interpreted in the context of the vorticity-normal reference frame. Field fabrics, including boudinaged and folded dikes, require a right-lateral wrench component of deformation.

Schmidt et al. (2016) provide evidence that the Ahsahka shear zone occurred simultaneously with the WISZ, and is part of the same geological structure. The quartzites of the Ahsahka shear zone also undergo dislocation creep with prism <a> slip, although they occur in a reverse shear sense with a horizontal vorticity vector. Together, the WISZ, Ahsahka, and the Owyhee segment of the WISZ to the south (Benford et al., 2010) present a coherent picture of northeast-southwest–directed convergence. Plate motion in this orientation acting on a curved plate boundary would have produced pure shear–dominated transpression in the Owyhee (α = 40°) and McCall (α = 60°) segments, while generating convergence (α = 90°) in the Ahsahka shear zone.

Discussions with Joshua Davis improved this manuscript. Editing and figure consultation by Maureen Kahn is greatly appreciated. Constructive reviews by Eric Ferré and an anonymous reviewer resulted in significant improvements. This work was supported by the Geneseo Foundation (Giorgis) and National Science Foundation grants EAR-0844260 and EAR-1251877 (Tikoff).