EPSL-10691; No of Pages 12 Earth and Planetary Science Letters xxx (2011) xxx–xxx

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Earth and Planetary Science Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e p s l

A naturally constrained stress profile through the middle crust in an extensional terrane Whitney M. Behr ⁎, John P. Platt Department of Earth Sciences, University of Southern California, 3651 Trousdale Pkwy., Los Angeles, CA, 90089-0740, United States

a r t i c l e

i n f o

Article history: Received 29 April 2010 Received in revised form 29 November 2010 Accepted 30 November 2010 Available online xxxx Editor: Y. Ricard Keywords: crustal strength TitaniQ metamorphic core complex paleopiezometry brittle–ductile transition

a b s t r a c t We present a method in which paleopiezometry, Ti-in-quartz thermobarometry (TitaniQ), and 2-D thermal modeling are used to construct a naturally constrained stress profile through the middle crust in an area of exhumed mid-crustal rocks. As an example, we examine the footwall of the Whipple Mountains metamorphic core complex (WMCC). Rocks in the WMCC were initially deformed at ~ 20 km depth by distributed ductile shear, and were then progressively overprinted by localized ductile shear zones and eventually by discrete brittle fracture as the footwall was cooled and exhumed toward the brittle–ductile transition (BDT). Increasing strain localization and cooling during exhumation allowed earlier microstructures to be preserved, and rocks in the WMCC therefore represent several points in temperature–stress space (and by inference depth–stress space). We identify enough of these stress–depth points to construct a complete profile of the flow stress through the middle crust to a depth of ~ 20 km, from which we derive regional estimates of the ambient stresses in the brittle upper crust, and the peak strength at the brittle–ductile transition in this region during Miocene extension. Maximum differential stress reached ~ 136 MPa just below the brittle–ductile transition at a depth of ~ 9 km. Stress levels are consistent with Byerlee's law in the upper crust assuming a vertical maximum principal stress and near-hydrostatic pore fluid pressures, and suggest a coefficient of friction on the 25°-dipping Whipple fault of ~ 0.4. Differential stress decreases to 10–20 MPa at 20 km depths and ~ 500 °C. For strain rates typical of actively deforming regions (10− 12 to 10− 15/s), our stress profile is bracketed by the Hirth et al. (2001) flow law for wet quartzite, whereas the flow law of Rutter and Brodie (2004) overestimates the strength of this particular region. © 2010 Elsevier B.V. All rights reserved.

1. Introduction The magnitude and spatial distribution of deviatoric stresses in the earth's crust has remained a fundamental question in geodynamics for over four decades (Brune et al., 1969; Burov and Watts, 2006; Hanks, 1977; Hanks and Raleigh, 1980; Jackson, 2002a; Lachenbruch and Sass, 1992; McGarr and Gay, 1978; Scholz, 2000; Thatcher and Pollitz, 2008; Zoback and Healy, 1992). Much of our understanding of crustal strength is framed in the context of laboratory experiments, which predict that rocks in the upper crust follow a Coulomb frictional failure criterion in which the differential stress is linearly related to the effective normal stress via a coefficient of friction (Brace and Kohlstedt, 1980; Sibson, 1983). Rocks in the lower crust are predicted to deform plastically, so that the stress depends on strain rate, temperature and grainsize, as a function of deformation mechanism (i.e. dislocation or diffusion creep) (Brace and Kohlstedt, 1980). These laboratory constraints, extrapolated over several orders of magnitude

⁎ Corresponding author. E-mail address: [email protected] (W.M. Behr).

of strain-rate and temperature to natural conditions, predict that peak crustal strength resides at the brittle–ductile transition (BDT), such that rocks around the BDT may act as a ‘stress guide’ during continental deformation (Sibson, 1983). This high strength crustal beam is especially influential in continental deformation if its integrated strength exceeds the strength of the upper mantle (Jackson, 2002b). Direct observations of deviatoric stress levels are limited to the brittle upper crust, for which deep boreholes in several locations worldwide have confirmed that ambient stresses are consistent with cohesionless friction with a coefficient of friction on favorably oriented faults of 0.6 to 1.0 (i.e. Anderson–Byerlee mechanics) (Brudy et al., 1997; Byerlee, 1978; Fuchs et al., 1991; McGarr, 1980; Zoback and Harjes, 1997). Several observations, however, such as the absence of a heat flow anomaly along major transform faults (Brune et al., 1969; Lachenbruch and Sass, 1992), and the relatively low magnitude of earthquake stress drops, suggest that faults themselves may be significantly weaker, perhaps due to high pore fluid pressures, or the presence of low friction materials along the fault such as clay gouge (Boulton et al., 2009). This has led to several conflicting hypotheses: for example, all faults in the brittle upper crust are weak

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Please cite this article as: Behr, W.M., Platt, J.P., A naturally constrained stress profile through the middle crust in an extensional terrane, Earth Planet. Sci. Lett. (2011), doi:10.1016/j.epsl.2010.11.044

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(e.g. Hardebeck and Michael, 2004); only large-displacement faults are weak in an otherwise strong crust (e.g. Townend and Zoback, 2000), or all faults are strong and the heat flow argument is flawed (Scholz, 2000; Scholz and Hanks, 2004). For the ductile field, the applicability of laboratory-derived flow laws can only be assessed indirectly, using, for example, inferences from field observations of exhumed middle and lower crustal rocks (Handy and Zingg, 1991; Mehl and Hirth, 2008; Stipp et al., 2002a), modeling of GPS velocity fields in actively deforming regions (Fialko, 2004; Pollitz, 2003; Thatcher and Pollitz, 2008), measurements of elastic thickness (Burov et al., 1998; Jackson, 2002a), distribution of seismicity (Maggi et al., 2000), and thermomechanical modeling (Kusznir and Park, 1987). Geophysical estimates based on the time-dependent response of the lithosphere to tectonic loads are limited by the non-uniqueness of model rheology structures – Maxwell viscoelastic vs. nonlinear-viscous, for example – and by trade-offs between the viscosity of the upper mantle and the lower crust. Field observations from exhumed rocks place useful constraints on the dominant rheology when the deformation was occurring, but often represent deformation occurring at rates well outside the reach of geophysical measurements. Thus, large uncertainties contribute to a general lack of agreement as to how continental lithosphere responds to plate boundary and internal forces. It is clear, however, that crustal and lithospheric strength are likely to vary from region to region, and cannot be represented by a single universal strength profile. Methods of quantifying lithospheric strength in specific regions are thus extremely valuable. In this paper, we illustrate a new method in which recently developed microstructural and thermobarometric techniques can be combined to produce naturally constrained depth profiles of the stress associated with lithospheric deformation in specific regions. The technique we outline has the potential to be applied to both crustal and mantle rocks that have been exhumed to the surface from depth and that preserve various stages of their exhumation histories. As an example, we present results from the middle crust of the Basin and Range province of the North American Cordillera, by focusing on the well-described Whipple Mountains metamorphic core complex

(WMCC) in eastern California. Rocks in the WMCC were initially deformed at mid-crustal depths by distributed ductile shear, and were then progressively overprinted by localized ductile shear zones, and eventually by discrete brittle faulting as the footwall rocks were captured and exhumed toward the brittle–ductile transition (Davis, 1988; Davis et al., 1986). Increasing localization and cooling during exhumation allowed earlier microstructures produced by distributed deformation to be preserved, and we demonstrate that rocks in the WMCC footwall represent several points in stress–temperature space, and by inference, stress–depth space (Fig. 1). We estimate the magnitude of differential stress and the temperature at each point using recrystallized grainsize paleopiezometry and thermobarometry, respectively. We identify enough stress–depth points to construct a complete profile of the flow stress through the middle crust to a depth of ~ 20 km, from which we derive regional estimates of the ambient stresses in the brittle upper crust, the peak strength at the brittle– ductile transition (BDT), and the integrated strength of the continental crust in this region during Miocene extension. 2. Whipple Mountains Core Complex The WMCC is one of several Miocene metamorphic core complexes within the Colorado River extensional corridor of eastern California and Arizona. It forms a NE–SW-trending elongate dome with lower plate rocks exposed in the core beneath the Whipple detachment (Fig. 2) (Davis et al., 1986). The hanging wall rocks include Tertiary volcanic and sedimentary strata cut by moderately to steeply dipping normal faults that sole into the Whipple detachment (Davis, 1988; Davis et al., 1986; Yin and Dunn, 1992). Rocks in the lower plate consist of Proterozoic gneisses and Cretaceous granitoids intruded by several suites of Tertiary dikes (Anderson and Rowley, 1981; Anderson et al., 1988). In the eastern half of the WMCC, lower plate rocks are mylonitized, and early highangle gneissic fabrics are transposed into a gently SW-dipping mylonitic foliation with a top-NE sense of shear (Davis, 1988; Davis et al., 1986). Toward the west, however, the mylonitic foliation swings through the horizontal and then dips west beneath undeformed footwall granitoids

Fig. 1. Concept of constructing a crustal strength profile for the lower crust by examining rocks within a metamorphic core complex. Rocks initially deformed at mid-crustal depths via distributed ductile shear under low stress conditions are progressively overprinted by localized ductile shear zones under higher stress conditions and eventually by discrete brittle fracture as the footwall rocks are captured and exhumed toward the BDT. Each stage of deformation represents a point on a stress–depth profile as shown on the right-hand diagram. Abbreviations t, s, and n stand for thrust, strike-slip, and normal faulting regimes, respectively.

Please cite this article as: Behr, W.M., Platt, J.P., A naturally constrained stress profile through the middle crust in an extensional terrane, Earth Planet. Sci. Lett. (2011), doi:10.1016/j.epsl.2010.11.044

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Fig. 2. Geologic map and cross-section of the Whipple Mountains metamorphic core complex in eastern California after Anderson and Rowley (1981); Davis (1988) and unpublished mapping by G.A. Davis and J.L. Anderson.

and continues below the surface, where it can be traced for several kilometers toward the west in seismic reflection data (Davis, 1988; Wang et al., 1989).

The WMCC and adjacent core complexes are close to prominent zones of Mesozoic contraction (e.g. the Big Maria fold and thrust belt to the south), and some preserve both Late Cretaceous and Oligo–

Please cite this article as: Behr, W.M., Platt, J.P., A naturally constrained stress profile through the middle crust in an extensional terrane, Earth Planet. Sci. Lett. (2011), doi:10.1016/j.epsl.2010.11.044

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Miocene mylonites in their footwalls (e.g. the Chemehuevi mountains (John and Mukasa, 1990)). The rocks exposed in the WMCC, however, do not appear to have undergone Late Cretaceous mylonitization (Anderson et al., 1988; Davis, 1988; Spencer and Reynolds, 1990). PreTertiary sedimentary cover sequences are completely lacking, likely stripped off during early Tertiary erosional denudation, and K–Ar mica data from local gneisses give Proterozoic ages (Reynolds et al., 1986; Spencer and Reynolds, 1990). This is consistent with thermobarometric data from several igneous intrusive suites within the Whipple footwall, with ages of 89 ± 3 Ma, 73 ± 3 Ma and 26 ± 5 Ma, which indicate that the region underwent static decompression from 8.9 ± 0.6 kbar (~33 km) to 4.6 ± 0.9 kbar (~ 17 km) over that time period, yielding decompression rates of only 0.2–0.3 mm/yr (Anderson et al., 1988). The precise timing of the onset of mylonitization of the WMCC footwall rocks is unknown, but synkinematic tonalite dikes yield U/Pb ages of 26 ± 5 Ma (Wright et al., 1986) and 24 ± 0.5 Ma (Foster and John, 1999). Additionally, the oldest tilted volcanic and sedimentary strata in the region are 26 Ma, thus the Tertiary extension in the WMCC is thought to have started no earlier than late Oligocene time (Foster and John, 1999; Spencer and Reynolds, 1991). The cessation of mylonitization is constrained by the youngest and shallowest intrusive suite in the WMCC footwall (labeled Tgad in Fig. 2), which is undeformed and yields a U/Pb zircon age of 19 ± 2 Ma (Anderson et al., 1988). Rapid cooling from the period 21 to 14 Ma is recorded by both Ar/Ar ages on K-feldspar (Foster and John, 1999), and U–Th/He data on zircon and apatite (Stockli et al., 2006), and is attributed to capture of the footwall rocks by the Whipple detachment fault and their final exhumation to the surface. These studies imply slip rates on the Whipple detachment of 7.8 ± 4 mm/yr (Foster and John, 1999), 4.3 ± 2.7 mm/yr (on zircon) and 5.8 ± 3.2 mm/yr (on apatite) (Stockli et al., 2006), all of which overlap within error. The work of Anderson et al. (1988) provides an estimate of the peak pressure and temperature conditions in the deepest exposed structural levels of the WMCC, as well as a maximum pressure at which mylonitization ceased. Specifically, Anderson et al. (1988) used the muscovite–biotite–alkali feldspar–quartz barometer of Powell and Evans (1983) and the Si content in muscovite barometer of Massonne and Schreyer (1987) on structurally deep mylonitic granitoids in the WMCC (general location is marked with a white star on Fig. 2) to constrain the peak pressure of mylonitization to an average of 4.6 ± 0.9 kbar. Two-feldspar thermometry on the same rocks yielded temperatures of 535 ± 44 °C (Anderson et al., 1988), consistent with lower amphibolite facies conditions. Additionally, Anderson et al. (1988) used the Al-in-hornblende barometer of Hollister et al. (1987) on two post-kinematic granodioritic plutons, yielding maximum pressures of the final stages of mylonitization of 2.2 ± 0.8 kbar (corrected from 1.6 kbar after Anderson (1996)).

mylonitic foliation is gently dipping and pervasive, and is crosscut locally by more steeply dipping, ultramylonitic, ductile and ductile-tobrittle shear zones representative of later shear (Fig. 3). The localized

3. Constructing a crustal stress profile 3.1. Sampling and field relations The structural, thermobarometric, and geochronological relationships described above for the Whipple footwall led Davis (1988) and Davis et al. (1986) to propose the general tectonic scenario described in Fig. 1 for the WMCC, in which a mid-crustal mylonite zone formed during the early stages of extension is later captured by a kinematically linked, low-angle normal fault in the brittle upper crust. Observations from these studies and our own field observations indicate that deformational fabrics associated with these stages of exhumation are broadly distinguishable at the field scale. We collected samples along four transects around the perimeter of the range near the Whipple detachment fault, and along one transect in the core of the range where the exposed mylonites are farthest from the detachment (~300 m vertical distance beneath it) (Fig. 2). Within each transect, the main

Fig. 3. A. Small-scale ductile-to-brittle shear zone cross-cutting the mylonitic fabric in a deformed granitoid. The shear zone is defined by a discrete, brittle slip surface with pseudotachylite or ultra-fine-grained cataclasite along the shear zone core. Foliation within the surrounding granitoid forms a sigmoidal trajectory into the shear zone (visible just below the tip of the pencil in the photo) as shown schematically in the inset in lower left. Looking northwest. B. Outcrop-scale ductile-to-brittle shear zones crosscutting the main mylonitic foliation (horizontal) at an angle of ~ 30°. The main mylonitic foliation between the two cross-cutting shear zones is partially transposed and forms a sigmoidal foliation warping into and out of the shear zones. Sample PW77 was collected from outside the shear zone in the horizontally foliated mylonite, whereas sample PW80 was sampled from within the ductile part of the lower shear zone. Looking southeast.

Please cite this article as: Behr, W.M., Platt, J.P., A naturally constrained stress profile through the middle crust in an extensional terrane, Earth Planet. Sci. Lett. (2011), doi:10.1016/j.epsl.2010.11.044

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shear zones are identifiable from the cm to 1-m-scale and occur within ~100 m below the Whipple detachment. They typically cause a local reorientation of the dip of the main mylonitic foliation of up to 40° (Fig. 3). Within ~2–10 m of the Whipple detachment fault, all early fabrics are overprinted by late-stage cataclasis and chloritization, and locally by brittle fracture surfaces occupied by pseudotachylite. 3.2. Microstructural descriptions Previous microstructural work on the Whipple mylonites was carried out by Hacker et al. (1992), who used paleopiezometry on dynamically recrystallized quartz grains to infer flow stresses during mylonitization. Their flow stress estimates were coupled with the thermometry of Anderson et al. (1988) and used to calculate strain rates for several different quartzite flow laws. Their study focused on mylonites with intermediate grainsizes (or intermediate stress), which are most abundant in the WMCC, but they did not distinguish microstructures formed under different stress–temperature conditions. Most rocks in the WMCC show microstructures that we interpret as composite, however; that is, they reflect continued deformation under conditions of decreasing temperature and increasing stress during extensional exhumation and cooling. This complicates the identification and interpretation of early formed microstructures. Nevertheless, we can identify four microstructural types reflecting stages in this evolution, which we summarize below (see also Table 1). In our descriptions we have focused specifically on identifying the dominant recrystallization mechanisms in quartz in each type of microstructure, including bulge nucleation (BLG), subgrain rotation (SGR), and grain boundary migration (GBM) (as in Table 1). Whilst it is well documented that these mechanisms often occur in tandem (Hirth and Tullis, 1992; Stipp and Kunze, 2008; Stipp et al., 2002a), the relative contribution of each mechanism to the bulk microstructure has been demonstrated to vary with stress/temperature in laboratory experiments (Hirth and Tullis, 1992) and in observations of natural microstructures (Stipp et al., 2002a). Specifically, these studies have

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shown that BLG tends to dominate at low temperature/high stress conditions, SGR dominates at intermediate temperature and stress conditions, and GBM dominates under high temperature/low stress conditions (Hirth and Tullis, 1992; Stipp and Kunze, 2008). Based on these correlations, these workers have proposed different microstructural classifications for zones of recrystallization in quartz, and we attempt here to relate our microstructural descriptions to their classifications. In a recent compilation of natural quartz recrystallization mechanisms, Stipp et al. (2010) also suggested that the transitions between these mechanisms occur at characteristic grainsizes, but we have not been able to confirm this in the Whipple mylonites. 3.2.1. Type 1 Some deformed granitoids show lenticular quartz aggregates several mm in length, representing deformed primary quartz grains (e.g., PW77, PW25) (Fig. 4A,B). These are completely recrystallized to a granular aggregate of dynamically recrystallized grains, showing a strong crystallographic preferred orientation (CPO) characterized by a Y-axis maximum indicating dominant prism baN slip (Schmid and Casey, 1986; Stipp et al., 2002b). Grain-boundaries where unmodified by later deformation form large-amplitude (N20 μm) lobes and are highly irregular (Fig. 4A-B, Fig. A.3). This indicates the activity of large-scale grain-boundary migration and may correspond approximately to GBM I of Stipp et al. (2002a) or Regime 3 of Hirth and Tullis (1992). Primary feldspar grains are plastically deformed, with internal undulatory extinction and subgrains, and are cut by relatively broad zones of dynamic recrystallization. In some cases grains have been largely dismembered by this process, and grains commonly show extended tails of recrystallized feldspar. In some deformed dike rocks that have a fine-grained matrix, feldspar porphyroclasts are elongate and fish-shaped, indicating plastic deformation without accompanying dynamic recrystallization. Some rocks contain bands of finely recrystallized and homogeneously mixed quartz, feldspar, and biotite, which may indicate dominant grain-boundary sliding deformation in these polyphase mixtures (Fliervoet et al., 1997). Biotite in these rocks shows dynamic recrystallization without retrogression. We interpret

Table 1 Summary of grain size, Ti concentration and inferred temperature (T) and pressure (P) for the Whipple mylonites. Sample

Grain size

# of maps

Ng

σ

Ti (ppm)

# of regions

NT

T (°C)

P (kbar)

Type

Comments

PW77 PW4 PW5 PW25 PW101 PW104Q PW44 PW87 PW75b PW80b PW34b PW24b PW79b PW24a PW34a PW75a PW79a PW80a

135 ± 50 73 ± 11 53 ± 15 80 ± 21 75 ± 30 68 ± 30 43 ± 7 52 ± 20 33 ± 13 18 ± 5 24 ± 6 36 ± 8 16 ± 3 11 ± 2 7±1 8±2 6±1 5±1

n/aa 6 2 2 2 n/aa 4 n/aa 2 4 5 5 2 3 5 2 3 4

32 227 92 86 40 30 561 30 272 403 722 447 54 623 2961 305 2586 3225

10 (− 2/+4) 16 (− 2/+2) 21 (− 4/+6) 15 (− 3/+4) 16 (− 5/+10) 17 (− 4/+7) 24 (− 3/+4) 21 (− 5/+10) 31 (− 7/+15) 49 (− 9/+15) 39 (− 6/+10) 28 (− 4/+6) 54 (− 7/+10) 73 (− 9/+13) 104 (− 11/+14) 94 (− 15/+24) 119 (− 16/+24) 136 (− 17/+23)

23 ± 7.7 1.9 ± 0.3b 2.1 ± 0.6b 6.3 ± 1.6b 13.2 ± 7.6 12.8 ± 5.8 5.4 ± 1.7 6.3 ± 1.9 5.5 ± 1.4 5.5 ± 2.8 4.1 ± 1.0 3.5 ± 0.5 2.3 ± 0.4 2.6c 1.1c n/ad 1.7c n/ad

1 1 1 1 2 1 2 1 1 2 2 1 n/a 1 3 n/a 1 n/a

8 7 14 14 15 14 19 10 26 30 8 19 n/a 19 36 n/a 6 n/a

544 (+ 41/−51) 500 ± 50b 500 ± 50b 500 ± 50b 478 (+ 52/−70) 475 (+ 41/−51) 405 (+ 20/−26) 416 (+ 20/−25) 406 (+ 16/−20) 406 (+ 31/−47) 387 (+ 14/−18) 376 (+ 9/−9) 350 (+ 9/−11) 357 ± 40 308 ± 40 308 ± 40 331 ± 40 308 ± 40

5.6 4.8 4.8 4.8 4.3 4.3 3.4 3.6 3.4 3.4 3.2 3.1 2.8 2.9 2.4 2.4 2.6 2.4

I

Biotite stable, DRX in feldspar, GBM in quartz

II

Biotite stable, DRX in feldspar, SGR in quartz

III

Biotite breakdown, brittle feldspar, SGR in quartz

IV

Chlorite pervasive, brittle feldspar, SGR + BLG in quartz

-Abbreviations in column headings: Ng (number of grains), NT (number of Ti measurements included in average), Type (microstructural type from Section 3.2). -a and b after sample numbers refers to composite microstructures: a = late overprint; b = early host grains. -Q after sample number indicates that the sample is a quartz vein, whereas all others are deformed granitoids. -Uncertainties on temperature estimates are rounded to the nearest 10 °C and represent analytical precision except where otherwise noted. -Pressure estimates are rounded to the nearest 0.1 kilobars. a Grain size estimated optically. b Ti concentration is inconsistent with mineral assemblage and qualitative microstructural observations; reported T estimate is therefore based on the presence of recrystallization and recovery in feldspar. c Ti concentration is the minimum measured concentration taken to approximate the lowest temperature recrystallization in regions where Ti contents are not completely reset during overprinting deformation. d Temperature is inferred from Ti concentrations in similar high stress, low temperature microstructures nearby.

Please cite this article as: Behr, W.M., Platt, J.P., A naturally constrained stress profile through the middle crust in an extensional terrane, Earth Planet. Sci. Lett. (2011), doi:10.1016/j.epsl.2010.11.044

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Fig. 4. Photomicrographs of quartz microstructures showing a range of deformation conditions from low-σ/high-T to high-σ/low-T, corresponding to microstructure types I–IV described in Section 3.2. All thin sections were cut perpendicular to foliation and parallel to the stretching lineation. White bar in all photomicrographs is 100 μm. A. Type I microstructure in which grains are irregular in size and shape and grain boundaries form large-amplitude (N 20 μm) lobes. There is a lack of well-defined subgrains in each of these microstructures. B. Type I microstructure in which early dynamically recrystallized grains exhibit lobate grain boundaries and are highly irregular. Smaller wavelength sutures and smaller diameter newly recrystallized bulges superimposed on larger grain boundaries indicate that this may be a composite microstructure. C. Type II microstructure in which quartz exhibits evidence for SGR and a strong oblique new grain shape fabric with top-to-the-left (northeast) sense of shear. D. Composite microstructure in which early relict dynamically recrystallized grains of Type III exhibit an oblique new grain shape fabric associated with SGR. These relict grains are deformed and flattened and new, smaller, Type IV grains and local bulges are present along the old grain margins. This texture results in a broadly bimodal grainsize distribution E. Cross-cutting quartz vein from same sample shown in [D] exhibiting a late-stage phase of Type IV recrystallization. Recrystallized grainsize in this deformed quartz vein matches the size of the recrystallized grains in the composite microstructure shown in [D] F. Type IV microstructure in which relict recrystallized quartz grains are highly strained and contain newly recrystallized patches of much finer grained material along old grain margins, exhibiting a core-and-mantle structure.

these rocks to represent the earliest and highest temperature mylonites, possibly formed at temperatures of 500 °C and above, in view of the evidence for plastic deformation, recovery, and recrystallization in feldspar (Pryer, 1993; Simpson, 1986; Tullis and Yund, 1987), and they form a zone that may be several km thick beneath the core of the range. Most of them, however, show signs of extensive overprinting by later microstructures. 3.2.2. Type 2 In these mylonites the primary quartz grains may be flattened, with internal subgrains, and incomplete recrystallization (PW44) (Fig. B.2); or where completely recrystallized the new grains are elongate with a systematic orientation that is oblique to the main foliation and consistent with the sense of shear. Strong CPOs are

dominated by Y-axis maxima. We interpret this microstructure as reflecting recrystallization by subgrain rotation (SGR), and it may correspond to Regime 2 of Hirth and Tullis (1992) or the zone of SGR of (Stipp et al., 2002a). Feldspar in these rocks shows narrow zones of finely recrystallized new grains transecting the host grains, as well as recrystallized tails. There is little evidence for internal plastic deformation of feldspar or recovery to produce subgrains. Biotite is dynamically recrystallized without retrogression. These rocks occur as zones of high strain near the upper boundary of the main mylonite zone, close to the mylonitic front. 3.2.3. Type 3 In these mylonites primary quartz has internal subgrains and shows evidence for recrystallization by SGR, with a distinct oblique

Please cite this article as: Behr, W.M., Platt, J.P., A naturally constrained stress profile through the middle crust in an extensional terrane, Earth Planet. Sci. Lett. (2011), doi:10.1016/j.epsl.2010.11.044

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grain-shape fabric and dominant Y-axis maxima in the CPO (PW75) (Fig. 4C). As in microstructure Type 2, this may correspond to the zone of SGR of Stipp et al. (2002a) or Regime 2 of Hirth and Tullis (1992). In contrast to microstructure Type 2, however, feldspar in these rocks shows brittle fracture, and has been pulled apart with quartz filling the cracks (PW34b). In some samples, K-feldspar as well as quartz fills cracks and pressure-shadows around fractured plagioclase (PW75b). In the field, the fracturing of the feldspars creates grains that are elongate at a high angle to the stretching lineation, producing a distinctive cross-lineation. Biotite is dynamically recrystallized with some retrogression to chlorite. Late static retrogression is also common in these rocks, as they occur in zones a few tens of meters thick close to the Whipple Detachment. 3.2.4. Type 4 Several samples (e.g., PW34, PW79, PW80) contain highly localized, fine-grained (b10 μm), ductile-to-brittle shear zones that cut across a coarser-grained (N30 μm) recrystallized quartz microstructure (e.g. Fig. 5). CPOs in some samples show an evolution from Y-axis maxima in the more coarsely recrystallized regions to peripheral point maxima in the newly recrystallized regions, suggesting a transition in the dominant slip system from prism baN to rhomb baN and in some cases to basal baN glide (Fig. A.2). These composite microstructures can be correlated with field-scale brittleto-ductile features, occurring close to the Whipple detachment (e.g. Fig. 3). Deeper in the structure (N30 m below the detachment), however, many of the coarser-grained mylonites show a second generation microstructure, involving core-and-mantle structure or grain boundary bulging, with small (b10 μm) recrystallized grains developed along the larger grain margins (e.g. PW24, PW79, PW80) (Fig. 4D–F). This results in a broadly bimodal grainsize distribution.

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Recrystallization in these late microstructures appears to have involved nucleation by a combination of subgrain rotation and bulge migration mechanisms, and may correspond to the BLG II zone of Stipp et al. (2002a), or the lower part of Regime 2 of Hirth and Tullis (1992). Feldspar deformation under these conditions appears to have been brittle; biotite has been recrystallized to fine-grained chlorite, and there is some evidence for diffusive mass transport in quartz, which forms fibrous pressure shadows around rigid sulfide grains, for example. 3.3. Selected sample suite Out of a total of 100 samples exhibiting the range in microstructures described above, we chose 13 quartz-rich mylonites to represent the σ–T range for the Whipple Mountains. The sampled rock types include mylonitic quartz veins and felsic granitoids with N30% quartz. All samples in our selected suite contain quartz that is dynamically recrystallized with strong crystallographic preferred orientations (CPO) indicating that dislocation creep was the dominant deformation mechanism. Additionally, the microstructures in each sample suggest that quartz acted as an interconnected weak phase during deformation and can therefore be used to approximate the bulk rheology of the rock (Dell'Angelo and Tullis, 1996; Handy, 1990; Handy et al., 1999). 3.4. EBSD and paleopiezometry Following analysis by optical microscopy, we analyzed each sample by electron backscatter diffraction (EBSD) on an FEI Q400 FEG-SEM at the University of California, Santa Barbara. This allowed us to 1) measure the crystallographic preferred orientations in each

Fig. 5. A. Photomicrograph of a micro-scale ductile-to-brittle shear zone in sample PW34. Section was cut perpendicular to foliation and parallel to the stretching lineation. At [a] an oblique new grain shape fabric is defined by recrystallized quartz grains averaging 25 μm interpreted here to have formed early in the deformation history. At [b], the early quartz microstructure is cross-cut by a brittle shear zone, which transitions at [c] into a ductile shear zone with a well-defined sigmoidal foliation and newly recrystallized grains averaging 7 μm in size. Sphene (labeled sp) is abundant in these composite microstructures. Yellow rectangle is the position of the EBSD map shown in B. B. Electron backscatter diffraction (EBSD) image from the ductile portion of the shear zone near point [c] in the optical photomicrograph. C. CPO from the large quartz grains in the EBSD image (top) and the small, newly recrystallized grains at the shear zone core (bottom). CPOs were defined relative to the dominant foliation and stretching lineation in the rock, but the slight offsets of the CPOs from the x and z axes suggest that the local shear direction was oblique to the plane of the section. Strain may have been too low to completely reset the CPO within this micro-shear zone, but a general scatter of the CPO and an increase in cant toward the right within the new recrystallized grains is apparent.

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grainsize domain and track changes in the CPO with increasing strain and decreasing temperature; and 2) quantify recrystallized grainsizes with relative speed and accuracy, particularly for small grainsizes that are difficult to measure using optical methods. All samples used for EBSD were cut parallel to lineation and perpendicular to foliation. Grainsizes were measured using the grain reconstruction module within the HKL software by Oxford instruments, following the recommendations by Humphreys (2001) and the procedures we outline in Appendix A. Paleopiezometry is an empirically-based relationship between the dynamically recrystallized grainsize formed during dislocation creep and the applied stress. The theoretical basis for this relationship is not well understood, but experiments performed on a variety of materials, including quartz, olivine, calcite, and various metals indicate that the relationship holds. We used the empirical piezometer of Stipp and Tullis (2003), for which the experimentally-produced quartz microstructures are similar to those observed in the Whipple mylonites, suggesting that extrapolation to natural microstructures is reasonable. Holyoke-III and Kronenberg (2010) recently proposed a small systematic correction to the Stipp and Tullis (2003) piezometer based on calibration of a Grigg's deformation apparatus to a gas apparatus, which we incorporate here. The piezometer is most applicable to the grainsizes and recrystallization mechanisms for which it was calibrated (i.e. grainsizes b35 μm and BLG-dominated recrystallization). It may also apply to recrystallized grainsizes up to ~ 120 μm, corresponding to the transition from SGR-dominated to GBM-dominated recrystallization (Stipp et al., 2010), but stress estimates from larger grainsizes are minimum estimates only. All but one of our samples are within the range 5 - 120 μm. Within the uncertainties of the experimental data, the Stipp and Tullis (2003) piezometer exhibits no dependence on temperature, water content of the quartz, or the α–β transition (Stipp and Tullis, 2006). Grainsize measurements obtained in the Stipp and Tullis (2003) piezometer study did not include a stereological correction and we therefore neglect this in our grainsize measurements for consistency with the piezometer. Average recrystallized grainsizes in our samples range from ~ 135 μm to ~ 5 μm corresponding to differential stress ranging from ~10 to ~ 136 MPa (Table 1).

Several samples yielded tightly clustered Ti concentrations, whereas others yielded more variable results depending on whether we probed completely recrystallized regions, partially recrystallized regions, or relict host grains. For most samples, we used the average Ti concentration for the recrystallized grains, excluding what appeared to be relict host grains under CL or in optical imagery. In three samples, however, the Ti concentrations in late-stage cross-cutting shear zones appeared only partially reset in the recrystallized regions and a clear distinction between relict grains and newly recrystallized grains could not be made with confidence (e.g. Fig. B.3); for these, we used the minimum Ti concentration and inferences from the stable mineral assemblage, but we attribute higher uncertainties to these samples. In most samples, measured Ti concentrations and associated temperatures were consistent with qualitative temperature constraints based on mineral assemblage (e.g. retrogression of biotite to chlorite) and deformation microstructure (e.g. recrystallization vs. brittle deformation in feldspar). Three samples exhibiting Type 1 microstructures (PW4, PW5, and PW25), however, had anomalously low Ti concentrations, suggesting that the Ti concentration may have been reset during the late low temperature overprint or that our assumed Ti activity was not applicable. We therefore assigned a more uncertain temperature range consistent with the onset of recrystallization in feldspar at ~450 °C and discounted the Ti concentrations for these samples. There are two systematic sources of uncertainty associated with our temperature estimates: TiO2 activity and the effect of pressure. Reasonable outer bounds for TiO2 activities for sphene-bearing felsic granitoids are 0.6 to 1.0, which translates into a temperature uncertainty of b±20 °C for Ti concentrations under 25 ppm (decreasing for lower Ti concentrations) (Ghent and Stout, 1984; Kohn and Northrup, 2009; Wark and Watson, 2006; Wark et al., 2007). Outer bounds can also be placed on the pressure of mylonitic deformation in the Whipple Mountains based on thermobarometric data, which indicates that mylonitization occurred at confining pressure of between ~5.5 and 2 kbar (Anderson et al., 1988). These pressure bounds translate into temperature uncertainties of b±35 °C for Ti concentrations under 25 ppm (also decreasing for lower Ti concentrations). A summary of the grainsize and Ti concentration data for each sample is given in Table 1.

3.5. TitaniQ measurements 3.6. Refining T and P estimates using thermal modeling The titanium-in-quartz geothermobarometer (Titani-Q), calibrated by Thomas et al. (2010) and Wark and Watson (2006), is based on the P and T dependence of Ti substitution for Si in quartz tetrahedra. The Ti calibration was carried out at high T and P and for mineral assemblages containing rutile, but Kohn and Northrup (2009) and Spear and Wark (2009) showed that Ti concentrations in quartz can re-equilibrate during dynamic recrystallization at low temperatures, so that this technique can be applied to mylonites deformed at temperatures down to ~ 300 °C and for estimated TiO2 activities of less than 1. Applying the TitaniQ thermobarometer to the Whipple mylonites offered several advantages over multi-phase thermobarometers, particularly the ability to relate the measured Ti concentrations (and associated T and P) directly to individual grains within the quartz microstructure. All samples were first examined using cathodoluminescence (CL), which revealed significant complexity in the trace element concentrations in quartz, but indicated that recrystallized grains were generally darker (implied as less concentrated) than their host grains (Fig. B.2). Ti concentrations were then measured on a Cameca 6f secondary ion mass spectrometer (SIMS) at Arizona State University. Details of the analytical technique and results of the SIMS analyses are presented in Appendix B. In most samples, Ti measurements on the SIMS were collected from several different regions within a single thin section, including those for which EBSD data were also gathered (Table 1).

The TitaniQ thermobarometer is both temperature and slightly pressure dependent, but independent barometers for greenschist facies granitoids are scarce to non-existent. Therefore, in order to produce a more precise estimate of temperature and pressure for each sample we modeled the P–T path for the Whipple mylonites by solving the heat transfer equation in two dimensions for a rolling hinge fault geometry using standard material parameters (Table 2) (Fig. 6). We use a version of the Matlab-based, finite element code, Milamin (Dabrowski et al., 2008), modified to include 1) time-dependence using an implicit finite difference scheme, 2) heat advection using a

Table 2 Material parameters and initial conditions in thermal model. Density of upper crust Density of lower crust Conductivity of upper and lower crust Heat capacity of upper and lower crust Heat production of upper and lower crust Fault dip Fault slip rate Initial geothermal gradient Initial T of particle Initial P of particle Initial depth of particle

2700 kg/m3 2800 kg/m3 2.5 W/m·K 1000 J/kg/K 2.3e−6 W/m3 25° 5 mm/yr 25 °C/km 525 °C 5.7 kbar 21 km

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the TitaniQ thermobarometer at a TiO2 activity of 0.8. Temperature and pressure for each sample were estimated from Fig. 6B using the intersection between the Ti concentration measured in that sample and the modeled P–T path.

4. Crustal stress profile We plot differential stress vs. temperature and differential stress vs. depth below the surface in Fig. 7. The error bars on individual data points represent uncertainties in the measurements of grainsize and Ti concentrations only, and do not include potential errors related to

Fig. 6. A. Initial (top) and final (bottom) conditions for thermal model of metamorphic core complex evolution. White arrows in top diagram delineate imposed velocities. White circle represents the particle being tracked along the detachment fault. The particle is transported parallel to the fault until it reaches the surface. B. P–T path for the Whipple footwall based on the thermal model. Star indicates the starting condition for the particle shown in [A], which is constrained by the peak P–T estimate from Anderson et al. (1988). White circle indicates the pressure at which mylonitization ceased based on the barometry of post-kinematic plutons intruded at 19 Ma (Anderson et al., 1988). Ti concentrations at fixed TiO2 activity of 0.8 are also shown and refined P–T estimates are derived from the intersection between the measured Ti concentrations and the modeled P–T path.

Semi-Lagrangian solver, and 3) a Runge–Kutta ordinary differential equation (ODE) solver to track particles and predict the P–T paths for a specific initial condition and exhumation velocity. Previous thermobarometric, thermochronologic and structural data from the Whipple footwall allows us to place several constraints on our thermal model, including the following. 1) The work of Anderson et al. (1988) described in Section 2 provides upper bounds to the pressure and temperature conditions of mylonitization and lower bounds to the pressure, therefore pins the beginning and end points of the P-T path (Fig. 6). 2) We use a slip rate for the Whipple fault of 5.9 mm/yr, which is an average of the estimates from Foster and John (1999) and Stockli et al. (2006) described in Section 2. 3) We apply an initial geothermal gradient of 25 °C/km, consistent with the work of Foster and John (1999). 4) We prescribe a dip angle for the Whipple fault through the upper crust of 25° as indicated by the angle of discordance between the dip of Whipple detachment and mylonites at the mylonitic front (Davis, 1988). Shear heating is only likely to have been significant in the highest stress mylonites, and these give the lowest temperatures. We attribute the lack of evidence for shear heating to advective heat transport by fluid flow, which is likely to have been widespread in the Whipple mylonites (Axen and Selverstone, 1994; Morrison and Anderson, 1998). The resulting P–T path for footwall exhumation in the Whipple Mountains is shown in Fig. 6B, along with iso-concentration lines for

Fig. 7. A. Crustal stress profile in T–σ space. Note that the data shown are not expected to fit a single strain rate curve since deformation becomes increasingly localized through time during exhumation in metamorphic core complexes. For geologically reasonable strain rates for actively deforming regions of 10− 12 to 10− 15, however, the data are bracketed by the flow law of Hirth et al. (2001), whereas the flow law of Rutter and Brodie (2004) overpredicts the strength of this particular region. (See text for further discussion.) B. Crustal stress profile converted to depth–σ space based on the expected P–T path for the WMCC. Stresses of ~ 136 MPa approximates the peak ambient stress at the BDT. We also show the extrapolation of Byerlee's law to mid-crustal depths for pore fluid factor of 0.4 assuming a vertical maximum principal stress.

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assumed TiO2 activity, piezometer relationships, or thermal modeling parameters. Although we recognize that these uncertainties may be large, we neglect them in the following section merely to illustrate the type of information that can be gleaned from a stress profile constructed in this manner. It should be noted that the profile is plotted separately in depth–σ and temperature–σ space because we cannot assume a constant geothermal gradient. Attenuation of isotherms due to thinning and advection of lower crustal rocks toward the surface during extension is well-documented (England and Thompson, 1984; Ketcham, 1996; Marotta et al., 2009; Platt et al., 2003). We have attempted to account for this effect by modeling the P–T path for the Whipple Mountains, and in this case the geotherm evolves from a linear gradient of 25 °C/ km at the start of extension to a local, nonlinear gradient averaging 33 °C/km by the time the rocks cross the BDT and cease to deform ductilely. This implies that the resulting strength profile in depth– stress space is composite, representing an ‘average’ of the strength as the geothermal gradient evolves during extension. It is therefore best thought of as a stress–temperature or stress–depth path through time, rather than a snapshot of the strength of the middle crust at any particular time.

5. Discussion 5.1. Implications for quartzite flow laws Taken at face value, the profile can be used to extract information about applicable quartzite flow laws for this region, although the uncertainties in the individual flow laws are neglected in Fig. 7A. For example, on the temperature–σ diagram in Fig. 7 we also plot the most recently published quartzite flow laws assuming a P- and T-dependent water fugacity with lithostatic pore fluid pressures. For geologically reasonable strain rates associated with Basin and Range extension of 10− 12 to 10− 15 (Campbell-Stone and John, 2002; Gans and Bohrson, 1998) our data are bracketed by the Hirth et al. (2001) flow law for which the stress exponent, n, is equal to 4 and the activation energy, Q, is equal to 135 kJ/mol. The flow law of Rutter and Brodie (2004), on the other hand, significantly overestimates the strength of this particular region. Note that the stress-T data are not expected to ‘fit’ a single strain rate curve. It is well documented in metamorphic core complexes that as rock strength increases and temperature decreases near the BDT, strain becomes more localized leading to higher strain rates in narrower and narrower regions of the crust until culminating in brittle faulting (e.g. Davis et al., 1986; Gessner et al., 2007). This is also illustrated schematically by our stress profile data, which, rather than defining a single flow law curve, better define an envelope of data ranging from low stress at low strain rates and evolving to higher stress and higher strain rates over time. Independent constraints on the strain rate for the later stages of deformation in the Whipple Mountains can also be estimated from our field observations of the cumulative shear zone width and from published determinations of the slip rate on the Whipple fault during extension. The data from Stockli et al. (2006) discussed in Section 2 suggest a slip rate on the Whipple fault of ~5 km/Myr. The narrow, brittle to ductile shear zones we describe that produce the highest stress microstructures are localized within the upper 100 m beneath the Whipple detachment, but we estimate that their cumulative width is less than 10% by volume (10 m). This provides a maximum estimate of the shear zone width during the final stages of deformation and leads to a minimum strain rate of ~ 1.6 × 10− 11/s within these shear zones. This strain rate is somewhat higher than predicted by the Hirth et al. (2001) flow law for these stresses, but the high degrees of weakening that we demonstrate here are likely associated with a change in the flow law parameters.

5.2. Peak strength at the brittle–ductile transition The profile as plotted in stress–depth space allows us to make observations about the peak strength at the BDT and use it to infer the frictional strength in the brittle upper crust for this region. The three samples (PW34a, PW79a PW80a) with stresses ranging from 104 to 136 MPa at around 9 km depth can be interpreted as approximating the peak strength because all three exhibit clear evidence for brittleto-ductile behavior, although it is possible that these samples were affected by transient stresses generated during the seismic cycle. If we interpret 136 MPa as the steady state peak strength at the BDT, however, we can construct a Mohr's circle diagram by assuming that the maximum principal stress was vertical and by assigning a pore fluid pressure. Ample evidence suggests that fluids played an important role in both the brittle and ductile deformation within the Whipple footwall (Axen and Selverstone, 1994; Morrison and Anderson, 1998). Axen and Selverstone (1994) estimated a range of possible pore fluid factors (λ) for the deepest parts of the Whipple detachment fault of between λ = 0.37 (hydrostatic) and λ = 0.7. A Mohr circle diagram assuming λ = 0.37 and differential stress of 136 MPa is shown in Fig. 8. This value for the peak strength at the BDT is broadly consistent with Byerlee's law (coefficient of friction, ϕ = 0.85), whereas pore fluid factors greater than hydrostatic are inconsistent with the high ambient differential stresses we have measured in the ductile field. These data do not provide an explanation for how slip on the low-angle Whipple fault was initiated, since it is in a relatively unfavorable orientation for slip if the maximum principal stress was vertical. However, it suggests that the ~25°-dipping detachment would have had a coefficient of friction of ~ 0.4 for continued slip once initiated (Fig. 8). 5.3. Comparison to other paleopiezometric measurements of strength at the BDT A recent compilation of paleopiezometric estimates of lower crustal strength produced by Bürgmann and Dresen (2008) revealed a conspicuous gap in measurements from mid-crustal rocks near the brittle–ductile transition. This has likely been at least in part due to the difficulty in measuring recrystallized grainsizes from high stress domains using optical techniques—an issue which the application of EBSD largely circumvents. Some recent measurements have been produced, however, primarily within the last decade. Stipp et al. (2002b), for instance, measured recrystallized grainsizes ranging from 4.9 to 354 μm in natural mylonites deformed between 250 and 700 °C

σ1

σs 200

θ = 25

σ1 - σ3= 136 MPa σ1 = σn = pgh = 257 MPa Pf = σ1λ = 95 MPa

ο

nt

hme

etac

ple d

Whip

ο

25 dip

)

85

100

s

e’

le er

w La

(μ

. =0

Whipple detachment, μ = 0.4

By

λ = 0.37 100

ο

2θ = 50

200

σn-Pf

Fig. 8. Mohr construction for our estimated maximum steady-state stress measurement in the WMCC of ~ 130 MPa. Within the uncertainties, peak ambient stress at the BDT in the WMCC is consistent with Byerlee's law.

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in the Tonale mylonite zone. These mylonites were formed at constant confining pressure within a thermal aureole, so cannot be interpreted in terms of regional crustal strength, but the temperature and stress at the onset of brittle deformation can be compared to our measurements from the Whipple Mountains. The minimum grainsize in the Tonale mylonite zone of 4.9 μm at ~ 300 °C corresponds to a differential stress from the Stipp and Tullis (2003) piezometer (with the Holyoke-III and Kronenberg (2010) correction) of ~139 MPa, consistent with our peak BDT stress estimate of ~ 136 MPa. Work by Gueydan et al. (2005), on the other hand, suggested that differential stresses at the BDT (again using the Stipp and Tullis (2003) piezometer) in the Tinos Island extensional shear zone were only around 50 MPa at ~ 300 °C, although the precise depth of the BDT in that region was not constrained. Such low differential stresses could reflect a regional weakness (e.g. due to a high geothermal gradient, high pore fluid pressures, and/or low coefficient of friction) in the integrated crustal strength for that region during extension (Gueydan et al., 2005).

6. Conclusions We have presented a method in which detailed field and microstructural techniques applied to exhumed rocks that preserve a record of their stress evolution can be used to construct profiles of the strength of the lithosphere in specific regions. Results from the Whipple Mountains metamorphic core complex place basic constraints on applicable coefficients of friction and quartzite flow laws for the southeastern Basin and Range during Miocene extension. Peak stresses of 136 MPa at ~9 km depth are consistent with Byerlee's law for near-hydrostatic pore fluid pressures, and predict a coefficient of friction on the Whipple detachment of ~0.4. Of the most recently published flow laws for dislocation creep in quartzite, the Hirth et al. (2001) flow law brackets our data for geologically reasonable strain rates whereas the flow law of Rutter and Brodie (2004) over-predicts the strength of this region. Although uncertainties for this strength profile are currently large, we emphasize that the more complete the geochronological data and P–T arrays are for a specific region, the more well constrained the strength profile will be. Further work will go toward refining the P–T–time history in the Whipple Mountains, thereby improving the accuracy and precision of the crustal strength profile exhibited here. We also note that well documented P–T–time arrays exist for numerous crustal and mantle shear zones world-wide, and this method can be applied to assess the strength of these regions.

Acknowledgements This research was supported by NSF grant EAR-0809443 awarded to J.P. Platt. We are indebted to Greg Davis and Lawford Anderson for providing a wealth of images, geologic maps, and useful discussion on the WMCC. We are grateful to Gareth Seward and Brad Hacker for assistance during visits to the EBSD lab at UCSB, Rick Hervig and Lynda Williams at the SIMS facility at Arizona State University for assistance with the TitaniQ measurements and Jorge Vazquez for use of the CL detector at CSUN. Thorsten Becker and Boris Kaus are thanked for their help with the thermal modeling. Steve Kidder and Elena Miranda of the Pasadena Rheological Society are acknowledged for their helpful discussion of microstructural issues. Michael Stipp and two anonymous reviewers provided excellent reviews that greatly improved the quality of the manuscript.

Appendix A. Supplementary data Supplementary data to this article can be found online at doi:10.1016/j.epsl.2010.11.044.

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Please cite this article as: Behr, W.M., Platt, J.P., A naturally constrained stress profile through the middle crust in an extensional terrane, Earth Planet. Sci. Lett. (2011), doi:10.1016/j.epsl.2010.11.044