PUBLICATIONS. Geochemistry, Geophysics, Geosystems

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1 PUBLICATIONS Geochemistry, Geophysics, Geosystems RESEARCH ARTICLE Key Points: Quartz [c]-axis girdles are 908 to shear bands and <a> maxima parallel to C slip In transpression, [c]-axis girdles are not 908 to shear zone boundary Geometry of quartz LPOs and C bands may be controlled by maximum shear strain rate not SZB Supporting Information: Supporting Information S1 Correspondence to: T. A. Little, timothy.little@vuw.ac.nz Citation: Little, T. A., D. J. Prior, and V. G. Toy (2016), Are quartz LPOs predictably oriented with respect to the shear zone boundary?: A test from the Alpine Fault mylonites, New Zealand, Geochem. Geophys. Geosyst., 17, , doi:. Received 23 NOV 2015 Accepted 18 FEB 2016 Accepted article online 23 FEB 2016 Published online 18 MAR 2016 VC American Geophysical Union. All Rights Reserved. Are quartz LPOs predictably oriented with respect to the shear zone boundary?: A test from the Alpine Fault mylonites, New Zealand Timothy A. Little 1, David J. Prior 2, and Virginia G. Toy 2 1 School of Geography, Environment and Earth Sciences, Victoria University of Wellington, Wellington, New Zealand, 2 Department of Geology, University of Otago, Dunedin, New Zealand Abstract The Alpine fault self-exhumes its own ductile shear zone roots and has a known slip kinematics. Within 1 km of the fault, the mylonitic foliation is subparallel to the boundary of the amphibolite-facies ductile shear zone in which it formed. Using EBSD, we analyzed quartz Lattice Preferred Orientations [LPOs) of mylonites along a central part of the Alpine Fault. All LPOs feature a strongest girdle of [c]-axes that is forward-inclined away from the pole to the fault. A maximum of <a> axes is inclined at the same angle relative the fault. The [c]-axis girdle is perpendicular to extensional (C ) shear bands and the <a> maximum is parallel to their slip direction. [c]-axis girdles do not form perpendicular to the SZB. Schmid factor analysis suggests that r 1 was arranged at to the Alpine Fault. These observations indicate ductile transpression in the shear zone. The inclined arrangement of [c]-axis girdles, <a> axes, and C planes relative to the fault can be explained by their alignment relative to planes of maximum shear-strain-rate in a general shear zone, a significant new insight regarding shear zones and how LPO fabrics may generally develop within them. For the Alpine mylonite zone, our data imply a kinematic vorticity number (Wk) of 0.7 to Inversions of seismic focal mechanisms in the brittle crust of the Southern Alps indicate that r 1 is oriented 608 to the Alpine Fault; that shear bands form at 308 to this direction, and that r 2 and r 3 flip positions between the brittle and ductile parts of the crust. 1. Introduction Ductile shear zones accommodate plate motion in the mid to lower crust of the continents [e.g., Hanmer, 1988]. Large strains develop as a result of prolonged aseismic creep in these zones and these deformations typically imprint a strong lattice preferred orientation (LPO) on minerals deforming as a result of dislocation creep. Where shear zones are exhumed, their LPOs may record the kinematics of flow and plate motion, and the temperature and deformation mechanisms that prevailed active at deep levels of ancient plate boundary zones [Behrman and Platt, 1982; Law, 1990, 2014; Schmid and Casey, 1986]. EBSD can be used to acquire rapidly large data sets of full crystallographic data [Prior et al., 1999]. In naturally deformed quartzose rocks, a key unresolved issue that hinders our ability to interpret quartz LPOs is uncertainty regarding their disposition to the kinematic reference frame, defined by the bounding shear zones and slip direction (Figure 1). Disagreement persists about how much quartz LPOs rotate relative to the shear plane as a function of the finite shear strain, and what their final stable orientation is. Some field, experimental, and modeling studies suggest that quartz [c]-axis girdles rotate with increasing finite strain eventually to stabilize at high strain at right angles to the shear zone boundary [e.g., Lister and Williams, 1979; Carreras and Garcia-Celma, 1982; Law, 1990; Morales et al., 2011, 2014] (Figure 1a). In such cases, the LPOs may rotate only slightly with respect to the foliation if both are rotating with respect to the SZB at similar rates. A second model infers that girdles of quartz [c]-axes are fixed at right angles to the shear plane whilst the foliation and XY plane of finite strain progressively rotate toward parallelism with the SZB as the deformation (leading to it rotating against the sense of shear in a foliation reference frame, as shear strain increases) (Figure 1b). This model is supported by theoretical modeling [e.g., Lister and Hobbs, 1980], experimental deformation [Bouchez and Duvall, 1982; Dell Angelo and Tullis, 1989], and field studies of naturally deformed rocks [Burg and Laurent, 1978; Schmid and Casey, 1986; Takeshita et al., 1999; Pennacchioni et al., 2010]. This LITTLE ET AL. QUARTZ LPOS RELATIVE TO SHEAR ZONE 981

2 Figure 1. Cartoon showing models for quartz LPO development as a function of increasing finite shear strain in a ductile shear zone. (a) Model in which the central segment of the [c]-axis girdles rotate with respect to the shear zone boundary (SZB) to become perpendicular to the SZB at very high strains [e.g., Carreras and Garcia-Celma, 1982; Carreras, 2001]; (b) model in which the central segment of the [c]-axis girdles form perpendicular to the SZB at low strains after which they remain in that stable orientation [e.g., Lister and Hobbs, 1980]; (c) model in which the [c]-axis girdles rotate with respect to the SZB as a function of strain and dynamic recrystallization, and eventually achieving a stable, forward-rotated inclination relative to that boundary with increasing shear strain and degree of dynamic recrystallization; and (d) experimental results of Heilbronner and Tullis [2006]. relationship (fixed [c]-axis girdle aligned 908 to the SZB) is typically attributed to the dominance of easyslip on the basal-<a> and r-<a> slip systems, a situation which causes these easy slip planes (and the slip direction <a>) to align with SZB and its shearing vector [Etchecopar and Vasseur, 1987; Keller and Stipp, 2011; Schmid and Casey, 1986]. Based on this assumption, the angle between the [c]-axis single girdle and the foliation is commonly used to calculate the kinematic vorticity number, W m, or the magnitude of finite strain [e.g., Platt and Behrman, 1986; Xypolias, 2010]. A third model predicts that with increasing shear strain and dynamic recrystallization, [c]-axis fabric skeletons rotate past perpendicularity with the shear zone boundary to stabilize at some forward-inclined angle (Figure 1c). Experiments by Heilbronner and Tullis [2006] produced quartz single-girdle LPOs that forwardrotated relative to the SZB to reach a final stable orientation forward-inclined by 268 relative to SZB at finite shear strains >8 (Figure 1d). Recent field-based studies have inferred that the final, stable position of a single-girdle quartz LPO may be forward-inclined to the SZB by [Keller and Stipp, 2011; Kilian et al., 2011], and such a process has been modeled using self-consistent viscoplastic (VPSC) theory in cases where multiple slip systems are simultaneously active [Keller and Stipp, 2011; Nie and Shan, 2014]. Numerical modeling studies of LPOs have so far been limited largely to simple and pure shear end members, and can achieve only low values of finite shear strain (typically < 2.0). They also cannot model realistically the progressive effects of dynamic recrystallization on LPO development. Experimental studies are hindered by difficulties in upscaling of microstructural processes to geological strain rates. In this paper, we evaluate these models for quartz LPOs using data from naturally deformed, moderate to high-strain rocks observed in the context of an active, and self-exhuming shear zone of known attitude and kinematics the Alpine Fault mylonite zone in a central part of the Southern Alps. LITTLE ET AL. QUARTZ LPOS RELATIVE TO SHEAR ZONE 982

3 A takeaway point based on our study of the Alpine fault natural laboratory is that the geometry of LPO fabrics, and also of extensional shear bands, reflects the kinematics of flow in the shear zone (which may not be simple shear), rather than simply recording the attitude of the shear zone boundary and its sense of shear. Understanding the arrangement of quartz LPOs in well-constrained, active ductile shear zones is important, because such analysis informs the much more widespread practise of using such fabrics to infer the kinematics of long inactive, ancient shear zones, as used, for example, in plate reconstructions; and also for modeling of seismic anisotropy in deformed middle crustal sections, a task that is often based on LPO fabrics. 2. The Alpine Mylonite Zone The Alpine Fault accommodates 70% [Norris and Toy, 2014] of the mm/yr of obliquely convergent motion that is currently accommodated between the Pacific and Australian Plates across South Island, New Zealand (Figure 2a) [DeMets et al., 2010]. In central Southern Alps, vertical-slip occurs at 6 8 mm/yr, which is equivalent to erosional denudation rates [Norris and Cooper, 2007; Little et al., 2005] a balance that causes the fault to self-exhume its hanging wall rapidly to the surface. Exhumed fault rocks include a km thick zone of Alpine mylonites on the SE side of the fault. These formed by ductile creep in a shear zone inferred to be the downdip continuation of the Alpine Fault [Norris and Cooper, 2007; Sibson et al., 1981]. The lowermost 150 m of the zone is dominated by ultramylonite, whereas the upper m consists of less deformed protomylonites preserving abundant inherited Mesozoic fabric elements [Little et al., 2002; Norris and Cooper, 2007; Toy et al., 2012, 2013]. Extensional (C ) shear bands are abundant throughout [Gillam et al., 2013]. Finite shear strains increase from 12 to 22 in the protomylonites, to 120 in the central mylonites, to >150 in the ultramylonites [Norris and Cooper, 2003; Toy et al., 2013]. Most workers infer that the mylonite zone has experienced ductile thinning by a factor of >3 [Norris and Cooper, 2003; Toy et al., 2013; Gillam et al., 2013]. Integrated over 5 Myrs, the finite shear strains imply an average shear strain rate of to s 21. Late Cenozoic ductile shearing in the Alpine mylonite zone took place at depths of up to 35 km [Grapes, 1995; Little et al., 2005; Stern et al., 2007], and presumably ceased after the rocks crossed the brittle-ductile transition. In the exhumed mylonites, the quartz LPOs, GBM-dominated recrystallization microstructures, and high Ti contents in dynamically recrystallized quartz grains mostly record deformation temperatures 5008C, suggesting that amphibolite-facies conditions prevailed immediately prior to the rocks passing through the brittle-ductile transition [Cross et al., 2015; Little et al., 2015; Toy et al., 2008]. Based on the base of shallow seismicity, the brittle-ductile transition is inferred to reside at 8 10 km depth [Boese et al., 2012]. The mean plane of the Alpine fault dips SE at depths of up to 15 km, before shallowing downward into a lower crustal detachment at 35 km depth. This inference is based on (1) fault outcrop data [e.g., Sibson et al., 1981; Norris and Cooper, 2007]; (2) shallow drill hole intersections of the fault [Sutherland et al., 2012]; and (3) seismic reflection data [Stern et al., 2007]. Mylonitic object and mica-streak lineations, quartz CPO-determined X directions, and S/C intersections indicate a ductile shearing direction of 0908 [Toy et al., 2012; Gillam et al., 2013]. Inversion of local seismic focal mechanism data indicate a near-horizontal maximum principal direction at and an intermediate principal stress direction (r 2 ) that is near vertical (Figures 2a and 2e) [Boese et al., 2012]. 3. Field Context of the Samples and Microstructures Nine of fourteen LPOs that we present were collected in Stony Creek, which exposes the full width of the Alpine mylonite zone (Figures 2a and 2b). In the near surface, the fault is here an oblique thrust-segment. The mylonite zone crops out in a typical fault rock sequence that consists (from structurally lower to higher) of chlorite-carbonate cemented cataclasites (1.5 m thick), ultramylonite, mylonite, protomylonite, and nonmylonitic Alpine Schist wall rock (Figures 2b and 2c). These rocks consist chiefly of garnet-micabearing mylonitic schists of quartzofeldspathic to pelitic composition, together with minor mafic amphibolite and siliceous schist (metachert). Most of the rocks are L-S tectonites containing foliation-parallel layers that are <1 mm thick. Except where deformed by late-stage kinks, the mylonitic foliation in Stony Creek LITTLE ET AL. QUARTZ LPOS RELATIVE TO SHEAR ZONE 983

4 Figure 2. (a) Tectonic index map of New Zealand, with an enlarged inset map in the lower right of South Island plotting metamorphic zones in the Alpine Schist, and showing field localities along the Alpine Fault mentioned in this paper. Local velocity of Pacific Plate relative to Australian (40 mm/yr) from DeMets et al. [2010]. (b) Simplified geological map of Stony Creek, central Southern Alps, showing distribution of mylonitic zones, attitudes of foliations and lineation, and selected sample locations (red dots). Maximum principal horizontal stress direction from Boese et al. [2012]. Grid marks are in meters (NZ Map Grid, eastings and northings). (c) Cross-section A-A through the Alpine mylonite zone in Stony Creek, showing location of the selected samples, trace of Alpine Fault, and trace of extensional shear bands (esbs, or C ). (d) Lower hemisphere, equal-area stereogram of measured foliations, lineations measured in lower Stony Creek. dips uniformly at 358 SE across the width of the mylonitic to nonmylonitic section (Figure 2d) presumably because the Alpine Fault has a dip of 358 in the near surface (Figure 2c). The azimuth of the dominant lineation changes significantly between the nonmylonitic wall rock and the main part of the mylonite zone: LITTLE ET AL. QUARTZ LPOS RELATIVE TO SHEAR ZONE 984

5 plunging to the SW in the wall rock, where it is an inherited (Mesozoic) intersection lineation, but trending 083, on average, in the mylonite zone, where it is a Neogene mylonitic stretching direction [Little et al., 2002a; Toy et al., 2012]. In nearby Tatare Stream (Figure 2a), Gillam et al. [2013] measured hundreds of extensional (C ) shear bands and found them to intersect the mylonitic foliation (S) at a mean dihedral angle of (2r), a geometry that the C shear bands in Stony Creek also exhibit (Figures 2c, 2d, and 3d). They used this intersection geometry to infer a late-stage ductile shearing direction of 090. At other locations in the central Southern Alps, including in Gaunt and Hare Mare Creeks (see below), a mean E-trending direction for the mylonitic shearing vector has been inferred using several other techniques [Toy et al., 2012, 2013]. In Stony Creek, samples for LPO analysis in were collected at two locations (red dots in Figures 2b and 2c). The first of these is in the mylonite zone at 280 m structurally above the Alpine fault in a sequence of metachert layers (e.g., sample SCZ-02, Figure 3a) that occur intercalated with pelitic to quartzofeldspathic schist (parts of samples SC-05a, SCZ-05b, SCZ-06, ST-11a, and ST-11c). The second location was in the protomylonite zone at 523 m above the Alpine fault in garnet-bearing micaceous schists (sample ST-12c, see Figure 3f). For details about the lithology and microstructure of the Stony Creek samples, see Little et al. [2015]. Two other samples were collected in Hare Mare Creek, located 12 km to the south of Stony Creek (samples HM1 and HM9); and three from Gaunt Creek, located 10 km to the north (samples GC4, GC12, GC16) (see Figure 2a). Of these last-mentioned five samples, two are from the ultramylonite zone at locations 125 and 135 m structurally above the fault (samples HM 1 and GC 4); two from the main part of the mylonite zone 209 and 330 m above the fault (samples GC12, GC 16); and one from the outer fringes of the protomylonite zone, at 639 m above the fault (sample HM9). For details about the lithology and microstructure of the rocks from Gaunt and Hare Mare creeks, see Toy et al., [2008]. Foliation-parallel layers in these samples are alternately quartz-rich and biotite1garnet1plagioclase-rich, and wrap around garnet porphyroclasts inherited from the wall rock Alpine Schist (Figures 3a, 3e, and 3f). Most quartz grains have curved and indented, interlobate boundaries (Figures 3b, 3d). Strongly deformed quartz veins, up to 2 cm thick, occur as rodded sheets subparallel to the foliation. These deformed veins and primary metachert bands up to several centimeter thick are entirely recrystallized, commonly showing an oblique grain-shape fabric, and contain coarse (>1 mm) ribbon-like quartz grains that are have aspect ratios of >5 and that are inferred to have grown dynamically by GBM (Figures 3b, 3c, and 3d) [Little et al., 2015]. A lineation is defined by deformed quartzose aggregates, streaking of muscovite fish, and strain shadows abutting garnet. The mylonitic foliation is cut and offset by abundant extensional (C ) shear bands (Figures 3e and 3f). 4. Analytical Methods Thin-sections were cut from oriented samples perpendicular to foliation and parallel to lineation. These were polished using SYTON fluid [Lloyd, 1987] and carbon coated to prevent charging. The EBSD patterns were collected using a 20 kv acceleration voltage and a beam current of 30 na. For the Stony Creek samples, crystallographic orientation data were obtained from automatically indexed EBSD patterns collected in a Zeiss Sigma VP SEM fitted with a field emission gun. The EBSD mapping runs covered a rectangular area on the thin section of 3 4 mm x 2 mm and used a grid spacing of 1 5 lm. Further details about the analytical settings are given in Little et al. [2015]. Whole thin sections of the five samples from Hare Mare and Gaunt Creek were mapped as a series of 10 mm 3 10 mm tiles (for details, see Toy et al. [2008]). All the EBSD data were cleaned and processed using the MTEX (v.4.0), in which quartz grains were mapped on the basis of a Voronoi decomposition in order to produce an orientation data set based on one point per grain [Bachmann et al., 2011]. Grain boundaries were defined at misorientation angles of 108. Prior to grain definition for LPO analysis, adjoining Dauphine twin domains were merged together by undertaking a 608 rotation about [0001]. For each sample, MTEX plotted a pole diagram for the [c], <a>, {m}, {r}, and {z} crystallographic directions in quartz. 5. Quartz LPOs and Their Relationship to Quartz Content Quartz LPOs from the mylonite zone show little geometrical variation as a function of composition (Figure 4). Figure 5b depicts the mean angles measured between the key elements of the LPOs and the fabric axes in 36 LITTLE ET AL. QUARTZ LPOS RELATIVE TO SHEAR ZONE 985

6 Figure 3. Microstructures in Alpine Fault mylonites. (a) EBSD phase map for metachert sample SCZ_02 from Stony Creek based on EBSD indexing, showing garnet-micaceous versus quartz-rich layers. (b) Inverse Pole Figure (IPF) map for part of a quartz-rich layer in the same rock. IPF legend indicates that fabric X (lineation) directions concentrate subparallel to {m} plane poles in quartz. Derived grain boundary map on right shows interlobate quartz-quartz boundary morphologies, large grains ( ribbons ) consisting of similarly oriented grains and subgrains, and oblique grain-shape fabrics. (c) Optical photomicrograph (crossed polars) of part of the same sample showing elongate ribbon-like quartz grains, and finer-recrystallized grains. (d) Optical photomicrograph (crossed polars) of sample ST 11C showing elongate ribbon-like quartz grain, and lobate to bulged shape of recrystallized quartz grains. (e) Enlarged photomicrograph (plain light) of micaceous layer in sample SCZ_02 showing extensional (C ) shear bands. (f) Optical scan (plain light) of protomylonitic micaeous schist in Stony Creek (Sample ST_12c) showing abundant extensional (C ) shear bands and location of EBSD scans in a quartz layer inside and outside of one of these shear bands (LPO data shown in Figures 6f and 6g, respectively). LITTLE ET AL. QUARTZ LPOS RELATIVE TO SHEAR ZONE 986

7 Figure 4. Representative quartz LPOs in rocks of differing quartz content taken from the larger data set of Little et al. [2015]. Crystallographic data are plotted on lower hemisphere, equal area pole diagrams that employ a conventional fabric reference frame and a geographical perspective that is looking westward. Foliation is plotted as EW vertical plane and the lineation as E-W horizontal line. The pole diagrams were contoured using a Gaussian half-width angle (GHW) of 8.58 and their densities were color-coded and contoured in Multiples of a Uniform Distribution (M.U.D.) using a consistent scheme. Although all the data are fully contoured, regions having a pole density of >4.0 M.U.D. are shown in dark red. Samples were derived from six compositional layers in four samples of mylonitic metachert or psammitic schist in Stony Creek in the main part of the Alpine mylonite zone (280 m structurally above the Alpine Fault) [Little et al., 2015]. Quartz contents are specified on the left-hand side and increase down the page. Note the increase in LPO strength as a function of increasing modal quartz, especially strengthening of the asymmetric [c]-axis single girdle, but without a significant change in the inclination of that girdle or the strongest <a>-axis mode relative to the foliation (XY fabric plane). Lower hemisphere, equal-area pole figures for (left to right) quartz crystallographic directions [0001] 5 c axes, {11 20} 5 a poles, {1 100} 5 m poles, {10 1-1} 5 r poles, and {01 11} 5 z poles. The pole diagrams for each crystallographic direction are contoured and shaded in multiples of a uniform distribution (M.U.D.) using a density shading scheme that is uniform for all the samples, and which is defined with a scale bar on the right of each row. LITTLE ET AL. QUARTZ LPOS RELATIVE TO SHEAR ZONE 987

8 Figure 5. (a) Pole figures depicting the quartz LPO of a representative mylonitic metachert in Stony Creek (sample SCZ_02). Same symbols and plotting schemes as in Figures 4 and 5. (b) [c]-axis skeletal diagram for the same sample (far left), and characteristic LPO angles for 36 quartz LPOs in Stony Creek that were analyzed in detail by Little et al. [2015]. Mean values for these angles are presented together with the standard deviation of each angle. Where n < 36, the LPO angle was not measurable or defined in one or more of the samples. Mean dihedral angle of C extensional shear bands relative to the foliation ( ) is from Gillam et al. [2013]. (c) Inverse pole diagram plotting fabric X direction. (d) Inverse pole diagrams plotting C slip direction. samples of diverse composition from a central part of the mylonite zone at Stony Creek, 280 m from the Alpine Fault. All of these fabrics feature an asymmetrical single girdle of [c] axes. Two maxima of <a>-axes occur on the perimeter on either side of X to define a conjugate pattern (Figure 5a). Neither of these maxima, which are of unequal strength, coincide with the X direction, a relationship that is also clear from the IPF diagram of Figure 5c. The strongest <a>-axis maximum lies anticlockwise from X at a angle (angle, b, Figure 5b). This coincides with the pole to the [c]-axis single girdle and the slip direction of the extensional (C ) shear bands in the surrounding mylonites (Figure 5d). We also observe a concentration of {m}-poles on the perimeter that is rotated anticlockwise from X (angle /, Figure5b).This crystallographic arrangement of {m} poles near X is expressed by a dominance of blue and green colors on the Inverse Pole Figure (IPF) map of Figure 3b and by the IPF diagram of Figure 5c. Morales et al [2014] simulated such fabrics using self-consistent viscoplastic (VPSC) theory in simple shear where basal-<a> and rhomb-<a> slip were made soft relative to prism-<a> slip. The symmetry and shape of the quartz LPOs are similar regardless of quartz content. For all compositions, the [c]-axes define a girdle that passes through Y and that is rotated anticlockwise from Z (angle a, Figure 5b). As a rule, the strength of definition and narrowness of the girdle increases with increasing modal quartz content. Most of the single girdles of [c] axes include a point maximum concentration of [c] axes in the lower half of the YZ plane, at from Y, whereas a secondary [c]-axis point maximum lies at a small angle to Y on the opposite side of the foliation from the maximum. The {r} and {z} poles may be dispersed into a pair of partial small circles opening at a wide angle to X that are joined near Y (e.g., Figures 4c, 4e, 5a). In most samples, the rhomb poles define double concentrations on the perimeter of the pole diagram (Figure 5a). One of the conjugate modes (angles h and q) is arranged anticlockwise from Z (e.g., Figures 4f and 5b); whereas the other (angles g and x) is arranged at clockwise from Z (e.g., Figures 4d and 5b). In most samples, the {r} and {z} LPOs are different. At lower quartz contents (<80%), the [c]-axis LPOs are diffuse and may include two crossed girdles, one of which is stronger than the other (Figure 4). As the quartz content increases, the synthetic girdle becomes LITTLE ET AL. QUARTZ LPOS RELATIVE TO SHEAR ZONE 988

9 Table 1. Characteristic Quartz LPO Angles a (Degrees) Angle, a, From Z (Degrees) Angle, b, From X Data Strongest C-Axis Girdle Strongest a-axis Mode Location Mean Stony Creek 1 r 4 4 This paper n Little et al. [2015] Mean Gaunt Ck 1 r 6 2 Toy et al. [2008] n 25 3 This study b Mean Hare Mare Ck 1 r 3 2 Toy et al. [2008] n 7 2 This study b a For definition of angles a, b, see Figure 5b. b Toy et al. [2008] did not present <a> axis pole diagrams. predominant and vestiges of the antithetic girdle disappear. At high quartz contents (97 100%), the remaining single girdle decomposes into a scatter of point concentrations. The LPOs for these nearly pure quartz mylonites are commonly single-crystal like: featuring one or two hexagonally arranged concentrations of <a> axes and {m} poles that lie in the planes perpendicular to one or two strongest [c]-axis concentrations (Figure 4). Little et al. [2015] attributed the removal of vestiges of the antithetic crossed girdle to selective consumption of less well-oriented quartz grains by strain-energy-driven GBM recrystallization, a process that is able to operate most efficiently in nearly pure quartz rocks because grain boundaries in such rocks are rarely impeded by second-phase pinning. From these LPOs, and from the orientation of crystallographic misorientation axes in deformed quartz grains, the authors inferred that shearing of the Alpine mylonite zone in this part of Stony Creek was accommodated by dislocation creep involving chiefly the [c] <a>, {z} <a>, and {r} <a> slip systems. Angles a and b measure the obliquity of the [c]-axis single girdle and the maximum <a>-axis concentration relative to foliation (Figure 5b). Both are anticlockwise angles that average (Table 1). In addition, we note that the mean angles, h and x, of the anticlockwise concentrations of in {r} and {z} poles at are indistinguishable from a and b. The {r} and {z} planes that occupy these maxima are disposed parallel to C shear bands, whereas the maximum concentration of <a> axes is parallel to the slip direction of those shear bands (Figure 5b). 6. Relationship of Quartz LPOs to Position and Finite Strain in Mylonite Zone Figure 6 presents quartz LPOs from samples that span different parts of the Alpine mylonite zone: from <140 m from the fault (highest strain ultramylonites) to 640 m from the fault (lowest strain protomylonites). As previously noted by Toy et al. [2008], asymmetric crossed-girdle patterns in protomylonitic parts of the zone, >300 m from the fault transition to single-girdle patterns in mylonitic and ultramylonitic parts of the zone at <300 m from the fault. An exception are 2 3 samples from Gaunt Creek that Toy et al. [2008] describe as exhibiting Y-maximum [c]-axis fabrics. The single girdles are inclined relative to Z in a forward sense relative to the shearing. The crossed girdle [c]-axis patterns are asymmetrical, featuring a stronger girdle that is forward inclined relative to Z in the same sense, and at a similar angle, as the more proximally located (higher strain) single girdles. Despite this transition in [c]-axis skeletal pattern, we note that the inclination relative to the foliation pole (angle a in Figure 5b) of the single or strongest of the two cross-girdles (whichever is present) does not change with position in the mylonite zone (Figure 7a). This indicates an invariance of [c]-axis girdle geometries to the magnitude of finite shear strain, which varies between 12 and >150 for the sample set [Norris and Cooper, 2003; Toy et al., 2013]. In all samples, the <a> axis maximum is inclined away from the foliation plane (angle b in Figure 5b) at the same angle as the [c]-axis girdle is inclined away from Z (angle, a). For the above-cited range of finite shear strain magnitudes, foliation is expected to lie <58 to <18 from the shear zone boundary (SZB) for a case of simple shear. However, the transpressive Alpine shear zone has ductilely thinned by a factor >3 [Norris and Cooper, 2003; Toy et al., 2013; Gillam et al., 2013]; in which case the foliation and the SZB are predicted to differ by <18 even at a finite shear strain as low as 12. We analyzed a deformed quartz layer in protomylonitic schist (1) inside of an extensional shear band (Map 4, Figure 3f); and (2) outside it (Map 1, Figure 3f). The corresponding LPOs are presented in Figures 6f and 6g. The wall-rock to the shear band, which is less affected by Neogene deformation, contains crossed-girdles of [c] axes, one of which is inclined forward at 308 (a). The adjacent shear band contains a single girdle with this orientation, and its overall LPO resembles that found in all the more highly strained mylonitic and LITTLE ET AL. QUARTZ LPOS RELATIVE TO SHEAR ZONE 989

10 Figure 6. Quartz LPOs as a function of proximity to Alpine Fault. Crystallographic data plotted on lower hemisphere, equal area pole figures employing conventional fabric reference frame and geographical perspective looking westward. Foliation is plotted as EW vertical plane and the lineation as E-W horizontal line. The pole diagrams were contoured using a Gaussian half-width angle (GHW) of 8.58 and their densities were color-coded and contoured in Multiples of a Uniform Distribution (M.U.D.) using a consistent scheme. Representative quartoze mylonite samples from Stony Creek, Hare Mare Creek and Gaunt Creek (for locations see Figure 1a) are presented for the ultramylonite, main mylonite, and protomylonite zones. For each, structural distance above Alpine Fault (perpendicular to foliation) is specified on the left and decreases down the page. [c]-axis LPO data for Hare Mare and Gaunt Creeks were first presented in Toy et al. [2008]. All plotting schemes and symbols same as Figure 4. Note persistent, nearly uniform obliquity of these to foliation plane, which we infer to closely parallel the Alpine Fault and its shear zone boundaries at depth. LITTLE ET AL. QUARTZ LPOS RELATIVE TO SHEAR ZONE 990

11 ultramylonitic rocks closer to the fault (e.g., Figures 6a 6d). Figure 7b plots the angles a and b in the Stony Creek samples as a function of LPO strength, as measured using the M Index of Skemer et al. [2005]. It shows that mylonites embracing a wide range of LPO strength share a common [c]-axis fabric skeleton geometry. Rocks with weaker LPOs show more variation in these angles because the angles in the fabric skeleton are more difficult to measure precisely where the girdle is diffuse. Figure 7. (a) Graph of the LPO girdle angle a, versus structural distance above Alpine Fault in the Alpine mylonite zone. Data are from Stony Creek (this study) Little et al., 2015] and from Gaunt Creek and Hare Mare Stream [Toy et al., 2008]. Estimated magnitudes of finite shear strain for different parts of the Alpine mylonite zone are from Norris and Cooper [2003]. (b) Graph of LPO strength (M-Index value for a random subsample of 500 grains, from Little et al. [2015]) versus the [c]-axis girdle angle from Z (angle a, Figure 4b; also versus the inclination of the strongest <a>-axis mode from X (angle b, Figure 4b). 7. Schmid Factor Analysis At the high finite strains inferred for the transpressive Alpine mylonite zone, the foliation is expected to lie within one degree of the SZB. In easyslip models of LPO development, progressive simple shear is expected to yield a concentration of easy-slip planes parallel to the shear zone boundary (SZB) and crystallographic slip directions parallel to the shearing vector [e.g., Bouchez and Duvall, 1982]. This model does not work for the Alpine mylonites, because for the several dominant slip systems in quartz no such alignment exists parallel to the SZB and its shearing vector. For an Inverse Pole Figure (IPF) that depicts crystallographic directions parallel to the slip direction of the C shear bands, a strong alignment of <a> is apparent in that reference frame (Figure 5d). In other words, the most relevant kinematic reference frame may be that of the C shear bands rather than the bulk shear zone boundary (SZB). We explore these relationships by calculating Schmid factors for quartz in two metacherts from Stony Creek (samples SCZ_02 and ST_11a). We defined loading schemes with the intermediate principal stress, r 2, taken to be parallel to the intersection of foliation and shear bands. We chose a uniaxial stress system (r 2 5 r 3 5 0), because that is approximately what exists in the Southern Alps (see below), and it is what one would generally infer to exist in zones of transpression. The maximum principal stress, r 1, was rotated in 58 increments from parallel (u50) to perpendicular (u590) to the foliation (Figure 8a). Maximum shear stress was resolved onto the plane of the foliation (5 SZB) at u545, and onto that of the shear bands at u573. For each loading angle, we calculated Schmid factors for the (c) <a>, {z} <a>, {r} <a>, and {m} <a> slip systems. This was done for each pixel in the EBSD data set, and the Schmid factor data are thus weighted by area rather than point-per-grain. Figure 8b shows the percentage of pixels with high Schmid factors (>0.4) as a function of loading angle u. Only two slip systems (c) <a> and {z} <a> yield their highest Schmid factors at u angles that resolve shear stresses on the shear bands in a sense that matches the observed offsets (i.e., at u > 28). For the {m}<a> systems, highest Schmid factors are obtained for u < 20. This range of loading angle resolves shear stress on the shear bands opposite to the offsets a relationship LITTLE ET AL. QUARTZ LPOS RELATIVE TO SHEAR ZONE 991

12 Figure 8. Schmid factor analysis of two quartz rich (>98% quartz) mylonites that have representative single-girdle LPOs (samples SCZ_02 and ST_11a). (a) Diagram defining the Schmid loading schemes. The angle, u, between r 1 and the foliation (5 SZB) was varied in 58 increments between 0 and 90. r 2 is parallel to the intersection of the shear bands and the foliation. A u angle of 45 maximizes shear stress on the foliation/bulk shear zone boundary, whereas one of 73 maximizes shear stress on the inclined C planes. For each u angle tested, HKL Channel calculated Schmid factors for the (c) <a>, {z} <a>, {r} <a>, and {m} <a> slip systems for each quartz pixel in the EBSD data set. (b) Graph of percentage of high Schmid factors (>0.4, plotted on vertical axis) versus loading angle, u, broken down by slip system (data from sample SCZ_02, the other sample yielded nearly identical results and is not shown). (c) Plot of percentage of high Schmid factors (>0.4) for combined (c) <a 1 {z} <a> 1 {r} <a> slip systems for each of the analyzed samples. that supports an interpretation from the LPO data that {m} <a> slip was not significant in these rocks [Little et al., 2015]. Thus, for simplicity, we do not plot Schmid factors for {m} <a> slip in Figure 8. For the (c) <a> and {z} <a> systems, highest Schmid factors are calculated for h angles of and 708, respectively. Both of these loading arrangements resolve the correct sense of shear on the C bands. This supports the interpretation [Little et al., 2015 that basal ((c) <a>) and rhomb ({z} <a> 1 {r} <a>) slip were both active in these rocks. If one combines the basal ((c) <a>) and the two rhomb systems ({z} <a> 1 {r} <a>), weighting slip system equally, then highest Schmid factors for the combined systems are achieved at a loading angle, u, of 708, which is 428 forward-inclined relative to the C planes (Figure 8b). Varying the relative weighting (basal-<a>/rhomb-<a>) between the slip systems (range 1:2 to 5:1), causes the angle at which maximum Schmid factors are obtained to shift between u560 and u580 with higher h angles corresponding to increasing dominance of basal <a> slip. In none of the loading schemes did a u value close to 458 the orientation expected for simple shear yield a peak in calculated Schmid factors. Instead, highest Schmid factors occur on the inferred dominant slip systems (basal and rhomb <a> slip) where u is placed at This loading scheme implies transpression, and imparts a high shear stress of the correct sense on the inclined C bands. 8. Discussion 8.1. Shear Zone Reference Frame for the LPOs The active Alpine Fault plane bounds a very high-strain [Norris and Cooper, 2003] mylonite zone that is observed (Supporting Information S1) to have a foliation essentially parallel to the SZB (i.e., the extensional eigenvector of the flow). Subsequent to ductile shearing, brittle slip on a segmented Alpine fault at shallow depths caused the foliation, in parallelism with the nearby fault, to be variably tilted in the near surface. The classical fabric reference frame (foliation plotted vertically EW on pole diagrams, X on the periphery) can be considered to be equivalent to a SZB reference frame (shear plane plotted vertically EW on pole diagrams, shear direction on the periphery). Thus, the girdles of [c] axes are inclined at 288 relative to not only to the pole of the mylonitic foliation but also to that of the bulk SZB. The LPO angles a and b are indistinguishable (at ) from the dihedral angle between the C shear bands and the foliation ( ) Gillam et al. [2013], see also Figures 3d, 4f and 5b. In other words, the LPOs are more obviously aligned with respect to the C bands than to the SZB. LITTLE ET AL. QUARTZ LPOS RELATIVE TO SHEAR ZONE 992

13 8.2. Geometry of Quartz LPOs in Transpressive Amphibolite-Facies Shear Zones We have shown that in the central part of the Southern Alps, single or strongest girdles of quartz [c]-axes are persistently inclined at 288 from the pole to the SZB in protomylonites, mylonites, and ultramylonites that have experienced finite shear strains of 12 to >150 [Norris and Cooper, 2003; Toy et al., 2013]. The [c]-axis girdles are nowhere arranged perpendicular to the Alpine Fault (5 mylonitic foliation 5 SZB). Instead, they are everywhere perpendicular to the C extensional shear bands that pervade the Alpine mylonite zone (Figures 5a and 5b). Quartz <a> axes define a strong maximum concentration on the perimeter of the pole diagram parallel to the slip direction of the C shear bands. A robust conclusion of our study, therefore, is that single (or dominant) girdles of quartz [c] axes in transpressive shear zones are not necessarily arranged orthogonal to the SZB at high finite strain. Our data from the Alpine mylonites suggest a transition between quartz [c]-axis skeletal patterns featuring asymmetrical cross girdles to ones featuring single girdles at finite shear strains between 12 and 120. In the crossed-girdle fabrics, the conjoined central segment (near Y) of the skeletal pattern is arranged approximately orthogonal to the foliation and SZB, and the individual girdles nearer to the perimeter of the pole figure (XZ plane) are unequally developed, with one forward inclined being more strongly developed. With increasing strain, this girdle is strengthened without changing its mean 288 angle relative to the pole to the SZB while the weaker, backward-inclined [c]-axis girdle is removed, presumably as a result of dynamic recrystallization [Little et al., 2015]. A strongly defined, asymmetrical single girdle [c]-axis fabric is the stable end result at high strains. Of the three models depicted in Figure 1, our data support that depicted in Figure 1c, and resembles the experimental results of Heilbronner and Tullis [2006] (Figure 1d) Models for Extensional Shear Bands Boudinage of SZB-parallel layers and the pattern of deformational reorientation of pre-neogene lineations indicate that the Alpine mylonite zone has thinned by a factor >3, though the direction of shear zone stretching is debated [Gillam et al., 2013; Toy et al., 2013]. One model for extensional (C ) shear bands infers that they form parallel to planes of maximum shear-strain rate in a deforming rock [Platt and Vissers, 1980; Simpson and De Paor, 1993], and to back rotate toward the SZB with increasing finite strain [e.g., Platt and Vissers, 1980]. In a thinning general shear zone, the contractional instantaneous stretching axis (ISA) is predicted to be >458 from the SZB. The particular angle depends on kinematic vorticity number (W k ), and increases with increasing pure shear (smaller W k ). Gillam et al. [2013] inferred that SZB stretching in the Alpine mylonite zone was parallel to the shearing vector (monoclinic flow symmetry). Interpreting conjugate shear bands in the mylonites as planes of maximum shear strain rate [e.g., Xypolias, 2010], they calculated a Wk of <0.8 for the Alpine mylonite zone at Tatare Stream (Figure 1a). They observed both synthetic and antithetic-sense shear bands with the antithetic ones are sparse compared to synthetic ones. The geometrical correspondence between the extensional (C ) shear bands and quartz LPOs in the mylonites suggests their origins are linked. The above model for C shear bands assumes homogeneous deformation of an isotropic material. If it is used as a context for interpreting quartz LPO data, then one might infer that single (or strongest) girdles of quartz [c] axes stabilize in orientation perpendicular to planes of high instantaneous shear strain-rate. However, unless the observed shear bands are a late-stage imprint, the model does not explain how the shear bands remained subparallel to a plane of high instantaneous shear strain rate across varying magnitudes of finite shear strain, without rotating away from that direction (especially in the highest strain rocks). Figure 9a shows how a Mohr circle construction can be used to depict finite deformation (stretch and rotation, in polar coordinates) of material lines in a general shear zone [Simpson and DePaor, 1993]. If area is conserved in the vorticity-normal plane (i.e., thinning orthogonal to the SZB is balanced by stretching in the shear direction, Gillam et al., 2013], the center of the Mohr circle plots at a radial stretch value of 1.0. Based on this, Figure 9b is a Mohr circle for flow where W k For an instantaneous flow approximation, the stretch and rotation of lines can be plotted vertically and horizontally on a Cartesian Mohr diagram [Simpson and DePaor, 1993]. For any isochorous flow, plans maximum instantaneous shear strain rate are expected to lie at 458 either side of the contractional ISA. Figure 9b predicts that synthetic shearing planes will be inclined at 288 to the SZB, a direction that is parallel to the C shear bands observed in the field. The construction also predicts that the contractional ISA (e 3 ) will be inclined at 738 to the SZB. LITTLE ET AL. QUARTZ LPOS RELATIVE TO SHEAR ZONE 993

14 Figure 9. Mohr Circles for deformation or flow in a general shear zone [after Simpson and De Paor, 1993]. (a; top) Diagram illustrating the geographical reference frame for the Mohr diagram. Lines are represented as points on the perimeter of the Mohr circle. These are referenced to the undeformed state, and are radially plotted at double angles relative to one another. (middle) The Mohr diagram plots the stretch (e) and rotation (a) of each line in polar coordinates. The shear zone pole (red arrow) is the only line that is simultaneously depicted in Mohr space and deformed geographical space, with the SZB being the baseline of the parallelogram representing the deformed shear zone. The undeformed and deformed orientations of a line (e.g., line p) can be constructed from their position on the Mohr diagram by pivoting through the anchor point (red square) representing the shear zone pole (not shown, see Simpson and De Paor [1993]). e 1 and e 3 are the stretches of the eigenvectors of the flow in the vorticity-normal plane. They plot on the vertical axis of the Mohr diagram, with e 1 representing the SZB. (bottom) The kinematic vorticity number (W k ) is the cosine of the angle (m) between the two eigenvectors. (b) Mohr circle for instantaneous flow for Wk Following Gillam et al. [2013], flow is inferred to conserve area in the vorticity normal plane and to involve a stretching parallel to the shear zone boundary (SZB) balanced by thinning perpendicular to it. The plane of maximum shear strain rate (c max ) is inclined at 288 to the SZB. The direction e 3, is the minimum instantaneous stretching rate axis (ISA) and is inclined at 738 to the SZB. (c) Mohr circle for deformation for Wk Original SZB normal has been deflected 368 clockwise at this arbitrary stage of the deformation. c max refers to planes of maximum finite shear strain and e 1 and e 3 to directions of maximum and minimum finite strain. (d) Mohr circle for flow with same boundary conditions as in part (b) but for Wk This predicts that e 3 is inclined at 608 to the SZB, whereas the contractional eigenvector of the flow (e3) is parallel to C bands in the Alpine mylonite zone which are at to the SZB. LITTLE ET AL. QUARTZ LPOS RELATIVE TO SHEAR ZONE 994

15 Figure 9c is a Mohr diagram for finite deformation on a finite deformation path that has proceeded steadily at W k It depicts that arbitrary point in the deformation at which the shear zone normal had been deflected through an angle of 368. The figure shows that the plane of maximum finite shear strain is predicted to have back rotated by 178 relative to the plane of maximum shear strain rate depicted in Figure 5b. Gillam et al. [2013] saw no evidence for shear bands inclined at low (<158) angles to the SZB and concluded that the observed shear bands did not form parallel to planes of maximum finite shear strain, and that they did not rotate much during the deformation. They inferred that the shear bands formed at a late stage in the exhumation history somewhere near the planes of maximum shear-strain rate. Other models for C shears argue predict they form at 308 to the contractional ISA similar to Coulomb fractures [Blenkinsop and Treloar, 1995]; or that they align subparallel to the inclined eigenvector of the (nonsimple shear) flow [Bobyarchick, 1986], another reason why an angle of <458 might be expected. This eigenvector (e 3 in Figure 9a) is a metastable direction of low rotation rate. Figure 9d shows that if the Alpine mylonite had deformed with a W k of 0.85, then the orientation of its C shear bands relative to the SZB could be explained by either of the last-cited two concepts. All the models that can explain our observations imply the Alpine shear zone must be thinning in order to explain the inclined disposition of C shears relative to the SZB. Such shear zone thinning has important implications for the structure of mountain belts, including the role of stretching faults in accommodating displacements, and the origin of collapsed metamorphic isograds. Much debate is still focused on the kinematics of major plate boundary shear zones, and whether ductile flow in them may deviate significantly from simple shear; for example, near the Main Central Thrust in the Himalayas, [e.g., Law et al., 2007; Thigpen et al., 2010]; and near the Alpine Fault in New Zealand (e.g., Norris and Cooper, 2003; Toy et al., 2013; Gillam et al., 2013]. In transpression, the contractional ISA is predicted to be >458 from the SZB. In an isotropic material, this ISA will parallel the greatest principal stress, r 1. Our Schmid Factor analysis showed that loading schemes in which r 1 was arranged at to the SZB ( to the inclined C planes) yield the largest proportion of high Schmid factors (>0.4) for LPOs in the Alpine mylonite zone. Perhaps real C shears bands form in transpressive zones at a compromise position between the inclined maximum shear stress and eigenvector orientations: near enough to the planes of maximum shear strain rate to acquire a shear offset and to strain soften, but close enough to the inclined eigenvector to acquire a large finite offset without rotating very much. The above discussion does not consider the effect of fabric anisotropy on nucleation of shear instabilities, nor of any associated predicted rotation of r 1 to >45 to the SZB, something that might occur even in a simple shear zone [e.g., Carreras et al., 2013; Kilian et al., 2011; Platt and Vissers, 1980; Ramsay and Lisle, 2000]. However in the Alpine mylonites, Little et al. [2015] did not find evidence for flow partitioning between foliation-parallel micaceous and quartose layers, as might be expected in models invoking the effects of foliation anisotropy Relationship of Quartz LPOs and C Shear Bands to Principal Stress Directions Contemporary stress directions have been inferred for the upper crust (<12 km) of the central Southern Alps near Franz Josef Glacier from inverted focal mechanisms of local earthquakes [Boese et al., 2012]. These directions are plotted in Figure 10a (solid red dots). An obvious feature is the subhorizontal disposition of r 1, and its high angle relative to the dipping Alpine Fault at depth. Estimating this angle is hindered by uncertainty in the mean dip of the fault at seismogenic depths. For an inferred fault dip of 458, r 1 intersects at 488 to the plane; for a dip of 608, at578. The best-fit stress inversion [Boese et al., 2012] yields a stress ratio: /5ðr 2 2r 3 Þ=ðr 1 2r 3 Þ50:25 6 0:27 (1) Based on this inversion and assuming a fault dip of 458, the direction of maximum resolved shear stress on the Alpine Fault plane (black square, Figure 10a) is calculated to be nearly parallel to the observed 090 mean trend of ductile shear vectors and maximum finite extension directions in the mylonite zone (red square) in the central Southern Alps [Gillam et al., 2013; Toy et al., 2012]. Assuming a steeper fault dip would result in the calculation of a more gently NE-pitching shear stress direction (Figure 10a, blue square). To estimate stress orientations in the ductile part of crust, one might relate them to the exhumed orientations of the C shear bands. Figure 10b depicts possible principal stress directions as viewed in the fabric LITTLE ET AL. QUARTZ LPOS RELATIVE TO SHEAR ZONE 995