Documenting the magnitude of finite strain within ductile shear zones is critical for understanding lithospheric deformation. However, pervasive recrystallization within shear zones often destroys the deformed markers from which strain can be measured. Intensity parameters calculated from quartz crystallographic preferred orientation (CPO) distributions have been interpreted as proxies for the relative strain magnitude within shear zones, but thus far have not been calibrated to absolute strain magnitude. Here, we present equations that quantify the relationship between CPO intensity parameters (cylindricity and density norm) and finite strain magnitude, which we calculate by integrating quartz CPO analyses (
Quantifying the magnitude of strain accommodated during tectonism is fundamental for understanding the kinematic evolution of lithospheric deformation (e.g., Fossen & Cavalcante, 2017). This task, however, can be daunting within ductilely deformed rocks, in which penetrative strain is often heterogeneously partitioned between spatially localized, high-strain ductile shear zones and regions of distributed, lower-magnitude shearing (e.g., M. A. Evans & Dunne, 1991;Jessup et al., 2006;Long & Kohn, 2020;Ramsay, 1967Ramsay, , 1980;;Ramsay et al., 1983;Simpson & De Paor, 1993;Vitale & Mazzoli, 2009;A. Yonkee, 2005).
The quantitative analysis of crystallographic preferred orientations (CPO) collected from ductilely sheared rocks is a robust tool that has long been utilized to understand the kinematics and temperature conditions of ductile shearing within contractional mountain belts (e.g., Barth et al., 2010;Larson & Cottle, 2014;Law, 1986Law, , 2014;;Law et al., 2011Law et al., , 2013;;Lister, 1977;Lister & Williams, 1979;Schmid & Casey, 1986), extensional shear zones (e.g., Faghih & Soleimani, 2015; J. Lee et al., 1987), and exhumed upper mantle rocks (e.g., Bernard et al., 2019;Boneh et al., 2015). In recent studies, statistical intensity parameters calculated from quartz CPO distributions have been employed as a proxy for finite strain magnitude, which can allow delineation of zones of high strain within the ductile portions of orogenic belts (e.g., N. J. Hunter et al., 2018;Larson et al., 2017). A small number of field-based applications of this approach, which have utilized the intensity parameter cylindricity (a quantity calculated from eigenvector analysis of quartz c-axis distributions; Vollmer, 1990), have elucidated the spatial patterns of relative strain magnitude across major Himalayan shear zones (e.g., Larson, 2018;Long et al., 2019;Starnes et al., 2020). Thus far, these studies have only been performed in packages of rock that have been 10.1029/2023TC008166 BLACKFORD ET AL.
2 of 35 pervasively recrystallized during ductile shearing, and therefore lack the deformation markers necessary for the quantitative measurement of finite strain magnitude. In the absence of finite strain data, the intensity of quartz CPO development can only provide information on the patterns of relative strain magnitude across ductile shear zones, which relies on the implicit assumption that CPO intensity is dominantly a function of strain magnitude. Therefore, a study that quantitatively relates quartz CPO intensity to finite strain magnitude will provide an important new approach for illuminating the spatial patterns of absolute strain magnitude within shear zones that lack deformation markers.
The Northern Snake Range metamorphic core complex in eastern Nevada (Figure 1), which accommodated highmagnitude Eocene-Oligocene crustal extension (J. Lee et al., 2017), is ideal for investigating relationships between strain and CPO intensity. The exhumed footwall of the primary extensional structure in the core complex, the top-down-to-ESE Northern Snake Range décollement (NSRD), contains Neoproterozoic-Cambrian metasedimentary rock units that were pervasively ductilely sheared during extension (e.g., J. Lee et al., 1987;Miller et al., 1983). The Lower Cambrian Prospect Mountain Quartzite is semi-continuously exposed in the NSRD footwall across a ∼30 km transport-parallel (i.e., WNW-ESE) distance (Figure 1b). Previous studies in the NSRD footwall (Gébelin et al., 2011(Gébelin et al., , 2015; J. Lee et al., 1987) demonstrate that the Prospect Mountain Quartzite exhibits well-developed quartz CPO distributions that were generated during ESE-oriented, Eocene-Oligocene ductile extensional shearing. The Prospect Mountain Quartzite also preserves micro-scale (stretched detrital quartz clasts in thin sections) and macro-scale (structural thinning measured by comparing the attenuated thickness of the Prospect Mountain Quartzite to its undeformed regional thickness) strain markers, and exhibits an ESE-increasing gradient in strain and ductile thinning across the range (Hoiland et al., 2022;J. Lee et al., 1987;Long et al., 2022;Miller et al., 1983). The combination of well-developed quartz CPO distributions and preserved strain markers makes the Northern Snake Range an outstanding field locality to quantitatively relate quartz CPO intensity to finite strain magnitude.
In this study, we integrate quartz CPO intensity parameters from 87 quartzite samples (75 new analyses from this study and 12 published in Gèbelin et al., 2015) with 49 finite strain analyses (38 new analyses from this study and 11 published in J. Lee et al., 1987) and 7 macro-scale finite strain estimates from the ductilely attenuated Prospect Mountain Quartzite, which we collected on a 25 km-long transect across the NSRD footwall. Integration of these data sets yields equations that express average finite strain as a function of average quartz CPO intensity, which can be utilized to estimate the first-order finite strain magnitude within any package of ductilely sheared rocks that contains quartz-rich, LS tectonites but does not exhibit measurable finite strain markers. These equations provide a new tool that can be applied to elucidate the magnitude of finite strain within the exhumed ductile portions of a wide variety of structural systems, which is critical for understanding the structural processes that thicken, thin, or accommodate strike-slip displacement within the lithosphere during tectonic deformation.
From the late Neoproterozoic to the Devonian, eastern Nevada was situated on the western passive margin of Laurentia, where up to ∼10 km of shallow marine clastic and carbonate rocks were deposited (e.g., Poole et al., 1992;Stewart, 1980;Stewart & Poole, 1974). Between the Mississippian and the Triassic, semi-continuous deposition of shallow marine carbonates continued in eastern Nevada, contemporaneous with contractional deformation events along the continental margin in central and western Nevada (the Antler and Sonoma orogenies) (e.g., Dickinson, 2004Dickinson, , 2006;;Speed & Sleep, 1982). An Andean-style subduction zone developed along the western margin of North America during the Jurassic, which initiated construction of the Late Jurassic-Paleogene Cordilleran fold-and-thrust system across Nevada and western Utah (e.g., Allmendinger, 1992;Armstrong, 1968;Burchfiel et al., 1992;DeCelles, 2004;Dickinson, 2004;W. A. Yonkee & Weil, 2015). During Cordilleran shortening, eastern Nevada resided in a broad region that is often referred to as the Sevier hinterland, which is located to the west of the Sevier fold-thrust belt in western Utah (e.g., Armstrong, 1972).
By the late stages of Cordilleran shortening in the Late Cretaceous-early Paleogene, the Sevier hinterland in eastern Nevada and westernmost Utah was a high-elevation (∼2.5-3.5 km) plateau underlain by ∼50-60 km-thick crust (e.g., Allmendinger, 1992;Cassel et al., 2014;Chapman et al., 2015;Coney & Harms, 1984;DeCelles, 2004;Long, 2019Long, , 2023;;Snell et al., 2014). During the Paleocene and Eocene, deformation migrated eastward into Utah and Colorado, constructing the basement-cored uplifts of the Laramide province, most likely Long, 2019). Dark gray areas depict the locations of metamorphic core complexes (RAG, Raft River-Albion-Grouse Creek; REH, Ruby-East Humboldt; NSR, Northern Snake Range). (b) Generalized geologic map of the Northern Snake Range (modified from J. Lee et al., 2017) showing the line of section for cross section A-A′, the locations of our three sampling transects (shown in detail in Figures 345), and sample locations.
The Northern Snake Range metamorphic core complex (Figure 1) is a well-characterized domain of highmagnitude, Eocene-Oligocene extension in easternmost Nevada (e.g., Bartley & Wernicke, 1984;Cooper, Platt, Anczkiewicz, & Whitehouse, 2010;Cooper, Platt, Platzman, et al., 2010;Gans et al., 1985;Hoiland et al., 2022;J. Lee et al., 1987;Lewis et al., 1999;Long, 2019;Long et al., 2022Long et al., , 2023;;Miller et al., 1983;Wrobel et al., 2021), which accommodated at least ∼47 km of ESE-directed extension (Long et al., 2022). The primary extensional structure in the range, the NSRD (Figure 1b), is a top-down-to-ESE extensional detachment fault that separates a ductilely sheared footwall domain from a hanging wall domain that experienced polyphase normal faulting (e.g., J. Lee et al., 1987;Miller et al., 1983).
The stratigraphic package that was deformed by extension in the Northern Snake Range consisted of a ∼12 kmthick section of Neoproterozoic to Permian sedimentary rocks of the Laurentian passive margin basin, which is unconformably overlain by Eocene volcanic rocks (e.g., Drewes, 1967;Gans & Miller, 1983;Gans et al., 1999;Hose & Blake, 1976;J. Lee et al., 1999aJ. Lee et al., , 1999b;;Miller & Gans, 1999;Miller et al., 1983;Miller, Gans, et al., 1999;Stewart, 1980;Young, 1960). Neoproterozoic rocks in the Northern Snake Range consist of the McCoy Creek Group (from here on abbreviated "Zm") (Gans et al., 1985;Misch & Hazzard, 1962;Young, 1960), which is composed of amphibolite-facies quartzite and schist. The Zm is conformably overlain by greenschist-to amphibolite-facies quartzite and interlayered schist and phyllite of the Lower Cambrian Prospect Mountain Quartzite (from here on abbreviated "Cpm") and the overlying Pioche Shale. In the southern half of the Northern Snake Range, both the Cpm and Zm have been significantly ductilely thinned via extensional shearing in the NSRD footwall (e.g., J. Lee et al., 1987;Miller et al., 1983). Regionally, the Pioche Shale is conformably overlain by a thick section of Middle Cambrian to Triassic carbonates (e.g., Hose & Blake, 1976;Stewart, 1980). In the Northern Snake Range, Middle Cambrian to Permian carbonates are exposed within normal fault-bounded blocks preserved above the NSRD and are estimated to have had a cumulative pre-extensional thickness of ∼6-7 km (e.g., Gans et al., 1999;J. Lee et al., 1999aJ. Lee et al., , 1999b;;Miller et al., 1983). Eocene felsic tuffs and lavas locally overlie Pennsylvanian and Permian rocks in normal fault-bounded blocks above the NSRD (e.g., Gans et al., 1989;Johnston, 2000).
A regionally significant greenschist-to amphibolite-facies metamorphic event that affected the entire NSRD footwall took place during the Late Cretaceous (∼78-91 Ma; Cooper, Platt, Platzman, et al., 2010;D. E. Lee & Fischer, 1985;Lewis et al., 1999;Miller & Gans, 1989;Miller et al., 1988). NSRD footwall rocks on the northwestern flank of the range locally exhibit intersection and stretching lineations that trend NNW-SSE, which are interpreted to have been generated by low-strain, distributed ductile shearing during Late Cretaceous Cordilleran contractional deformation (J. Lee et al., 1999a;Miller et al., 1988).
During Eocene-Oligocene extensional tectonism, Middle Cambrian-Permian carbonates in the NSRD hanging wall were extended by two sets of top-down-to-ESE normal faults that sole or terminate downward into the NSRD (Figure 2) (Johnston, 2000;Miller et al., 1983). Neoproterozoic-Lower Cambrian clastic metasedimentary rocks in the NSRD footwall were penetratively stretched sub-horizontally and thinned sub-vertically during Eocene-Oligocene extension, and experienced greenschist-facies metamorphism. Extensional shearing was accommodated by the development of meso-scale, linear-planar ductile fabrics that are subparallel to the NSRD (J. Lee et al., 1987;Miller et al., 1983). Ductile extensional shearing of the NSRD footwall is interpreted to be temporally related to displacement along the NSRD (e.g., J. Lee, 1995;J. Lee et al., 1987;Miller et al., 1983). Mineral stretching lineations generated during Eocene-Oligocene extensional shearing record an average trend of 298°/ 118°, which is interpreted as the direction of maximum extension (J. Lee et al., 1987;Miller et al., 1983). WNW-ESE-trending mineral stretching lineations are ubiquitous in NSRD footwall rocks in the central and eastern 10.1029/2023TC008166 BLACKFORD ET AL. 6 of 35
portions of the Northern Snake Range, but die out at the northwestern flank of the range (Figure 1b) (e.g., Gans et al., 1999;Johnston, 2000;J. Lee et al., 1999aJ. Lee et al., , 1999bJ. Lee et al., , 2017;;J. Lee, Miller, et al., 1999;Miller & Gans, 1999;Miller, Gans, et al., 1995).
Ductile extensional shearing in the NSRD footwall is bracketed between ∼38 Ma and ∼22 Ma, based on U-Pb zircon dating of deformed and undeformed rhyolitic dikes that intrude the footwall (J. Lee et al., 2017). Thermochronometry ( 40 Ar/ 39 Ar of muscovite and K-feldspar, and zircon fission-track) from NSRD footwall rocks defines an overall eastward progression of cooling, which has been interpreted to represent the migration of extensional exhumation (Gébelin et al., 2011(Gébelin et al., , 2015;;J. Lee, 1995;J. Lee & Sutter, 1991;Miller, Dumitru, et al., 1999).
Previous studies have presented differing interpretations for the magnitude and style of extension in the Northern Snake Range (c.f., Bartley & Wernicke, 1984;Cooper, Platt, Platzman, et al., 2010;Hoiland et al., 2022;J. Lee, 1995;J. Lee et al., 1987J. Lee et al., , 2017;;Lewis et al., 1999;Long, 2019;Long et al., 2022;Miller et al., 1983;Wrobel et al., 2021), much of which stems from a long-standing debate over the pre-extensional burial depths of NSRD footwall rocks. At the latitude of our studied transect (Figures 1b), Miller et al. (1983) interpreted that the NSRD initiated as a subhorizontal, brittle-ductile transition at a depth of ∼7 km, and that rocks in the NSRD footwall were never buried beyond their original stratigraphic depths of ∼7-12 km. In contrast, Lewis et al. (1999) estimated peak conditions of ∼610°C and ∼8.1 kbar from NSRD footwall rocks in the southeastern part of the range. They interpreted that NSRD footwall rocks were buried to pre-extensional depths of ∼30 km by a westvergent Jurassic-Cretaceous thrust fault and were exhumed via ∼50 km of displacement on the NSRD. Cooper, Platt, Anczkiewicz, and Whitehouse (2010) estimated peak conditions of ∼500-650°C and ∼5.7-6.1 kbar from NSRD footwall rocks at the latitude of our studied transect, and interpreted that these rocks attained ∼21-22.5 km peak depths via Jurassic-Cretaceous fold-thrust thickening. In contrast, structural reconstructions of the Northern Snake Range core complex and surrounding ranges indicate maximum NSRD footwall burial depths of ∼15-20 km (Bartley & Wernicke, 1984;Wrobel et al., 2021) and NSRD displacement magnitudes on the order of ∼30-35 km (Long et al., 2022;Wrobel et al., 2021).
Significant NSRD-subparallel stretching and NSRD-subnormal thinning was accomplished by the development of Eocene-Oligocene, linear-planar ductile fabrics within the Zm and Cpm in the NSRD footwall. The 118° average trend of mineral stretching lineations is interpreted to demarcate the maximum stretching direction (X strain axis) (e.g., J. Lee et al., 1987;Miller et al., 1983). J. Lee et al. (1987) quantified 11 3D finite strain ellipsoids from thin section measurements of stretched detrital quartz ribbons and outcrop measurements of stretched quartzite pebbles within the Cpm and Zm (Figures 1b and 2). They obtained foliation-normal, lineation-parallel (XZ strain plane) tectonic strain ratios (Rs [X/Z] ) that increase from 5.8 in the Salt Creek (note: this is referred to as "Negro Creek" in previous studies, but here we will refer to it as "Salt Creek") window on the western side of the range to as high as ∼31 in the Hendry's Creek drainage on the eastern side, and estimated ∼250% total extension of the NSRD footwall. Their data show that the NSRD, transposed bedding, and tectonic foliation (XY strain plane) are everywhere subparallel in the NSRD footwall, and that 3D strain was plane strain to slightly constrictional (7% average lineation-normal [Y strain axis] shortening, with a total range between 0% and 17%). Long et al. (2022) incorporated the strain data of J. Lee et al. (1987) into a range-wide cross section and estimated 19 km (220%) of total extension of the NSRD footwall.
The finite strain data of J. Lee et al. (1987) have been corroborated by macro-scale structural thinning of NSRD footwall rocks, estimated by comparison of the ductilely attenuated thickness of the Cpm in the Northern Snake Range to its approximately consistent regional stratigraphic thickness of ∼1.2 km in the Schell Creek and Egan Ranges to the west, the Southern Snake Range to the south, and the Deep Creek Range to the north (Fritz, 1968;Gans & Miller, 1983;Hose & Blake, 1976;J. Lee et al., 1987;Long et al., 2022;Miller et al., 1983;Rodgers, 1987;Young, 1960). The Cpm has been thinned to ∼500-800 m (∼30%-55% thinning) in the southwestern part of the Northern Snake Range and has been thinned to ∼250-50 m on the eastern flank of the range (∼80%-95% thinning) (J. Lee et al., 1987;Miller et al., 1983). axis pole plots from both of these studies define symmetric crossed-girdles in the western part of the Salt Creek window, top-to-ESE asymmetric crossed-girdles and single girdles in the eastern part of the Salt Creek window, and top-to-ESE asymmetric single girdles in the Hendry's Creek drainage (Gébelin et al., 2015;J. Lee et al., 1987). These CPO data have been interpreted to record pure shear-dominant ductile shearing in the western part of the range, with an increasing component of top-to-ESE simple shear eastward (J. Lee et al., 1987).
The footwall of the NSRD provides an exceptional opportunity to quantify ductile strain within a major extensional detachment fault system as it preserves micro-and macro-scale deformation markers (e.g., J. Lee et al., 1987;Miller et al., 1983). Here, we present 3D finite strain measurements from samples that span the transport-parallel width of the NSRD footwall.
We collected 38 quartzite samples from the Zm and Cpm in three separate transects that collectively span the E-W width of the southern part of the range (Figures 1 and 2; Table 1). From west to east, these are the Fourmile Canyon (Figure 3; n = 8), Salt Creek (Figure 4; n = 14), and Hendry's Creek (Figure 5; n = 16) transects. We combined our new samples with the 11 finite strain ellipsoids of J. Lee et al. (1987), which include eight from the Salt Creek transect (Figure 4) and three from the Hendry's Creek transect (Figure 5). We projected the locations of these 49 combined finite strain samples onto their corresponding transport-parallel position and structural level on a cross section of the Northern Snake Range (Figure 2; line of section shown on Figure 1b). The cross section (modified from Long et al., 2022) is oriented at an azimuth of 118°, which is the average trend of mineral stretching lineations in the NSRD footwall (e.g., Miller et al., 1983).
The majority of our strain samples were collected to span the extension-parallel (i.e., WNW-ESE) width of the range. Most of these samples were collected near the top of the Cpm, with a transport-parallel spacing of ≤∼1 km within each transect. We collected a smaller number of samples that span the vertical thickness of rocks exposed beneath the NSRD (e.g., samples 35-52 in the Hendry's Creek transect). The NSRD is located at a similar structural level across the full width of the cross section, either at the top of the Cpm or above a ∼10-20 m structural thickness of the overlying Pioche Shale (e.g., Johnston, 2000) (Figure 2). Therefore, we express the structural (i.e., foliation-normal) depths for our strain samples relative to the NSRD.
Thin sections of our finite strain samples exhibit a partial area percentage of non-recrystallized quartz ribbons (Figure 6). These ribbons grains may represent grains that had their c-axes oriented subparallel or at a low angle to the intermediate direction (i.e., the Y strain axis) of Eocene-Oligocene ductile shearing, as grains with this crystallographic orientation are often preferentially stretched into (and preserved as) ribbon grains, while quartz grains with other initial c-axis orientations are preferentially recrystallized, particularly at higher strain magnitudes (Ceccato et al., 2017;Muto et al., 2011;Pennacchioni et al., 2010). We assume that these quartz ribbons are the result of ductile deformation of detrital quartz clasts and that the strength contrast between these ribbons and the surrounding recrystallized quartz-rich matrix was negligible during ductile shearing. Studies of the initial preferred orientation of strain markers in conglomerates suggest that if measured objects contain an initial ellipticity they should be more easily deformed compared to their matrix, and therefore likely overestimate bulk strain (e.g., De Paor, 1980). However, for objects with an initial Ri < 2.0, the difference in strain recorded in the matrix versus the objects is predicted to be insignificant (Treagus & Treagus, 2001). Finite strain from Cretaceous ductile shearing in the Cpm in the Schell Creek Range, which lies to the west of the Northern Snake Range, defines average Rs (XZ) and Rs (YZ) values of 1.6 and 1.5, respectively (Stevens et al., 2022). If the ribbons grains measured in our study had a similar initial ellipticity prior to Eocene-Oligocene ductile shearing, then their strength contrast with the matrix would be insignificant under the results of Treagus and Treagus (2001). Strength contrasts can also arise when measured objects have a different mineralogical composition from the matrix (e.g., Gay, 1968;Odonne, 1994;Treagus & Treagus, 2002). However, the Cpm contains minimal other phases besides quartz (e.g., see our calculations of mica area percentage below). Therefore, because our measured strain markers are the same composition as the rock matrix (i.e., quartz), we assume that the rheology contrast between the two is Table 1 Continued WNW-to-ESE Lineation-Lineation-Foliation-Quartz Structural NSRD-parallel Octahedral parallel (X) normal (Y) normal (Z) CPO Density Mica Rock depth a distance b Rs (X/Z) φ (X/Z) Rs (Y/Z) φ (Y/Z) shear strain extension extension shortening analytical Cylindricity norm area Strain Sample Sampling transect Unit (m) (km) (±1 SE) (±1 SE) (±1 SE) (±1 SE) (ε) (%) c (%) c (%) c Method (B) (Jpf) % Domain JL1-155 Salt Creek (J. Lee et al., 1987) Cpm -60 8.7 --------EBSD 0.84 2.25 -JL1-156 Salt Creek (J. Lee et al., 1987) Cpm -80 8.7 --------EBSD 0.74 1.94 -26 Salt Creek Cpm -80 8.8 --------OFA 0.80 2.80 1.4 27 Salt Creek Cpm -100 9.0 --------OFA 0.89 2.97 1.8 JL1-139 Salt Creek (J. Lee et al., 1987) Cpm -60 9.3 --------EBSD 0.88 2.64 -28 Hendrys Creek Cpm -10 13.3 --------OFA 0.82 2.78 4.1 29 Hendrys Creek Cpm -20 13.8 6.9 ± 0.5 9 ± 1 4.0 ± 0.2 -4 ± 1 1.41 128 ± 7 32 ± 1 67 ± 1 OFA 0.87 2.91 0.8 30 Hendrys Creek Cpm -10 14.5 8.2 ± 0.5 9 ± 1 4.1 ± 0.2 -3 ± 1 1.52 154 ± 6 27 ± 2 69 ± 1 OFA 0.85 2.93 1.5 SP 4 Hendrys Creek (J. Lee et al., 1987) Zm unit 2 -500 15.4 12.7 -3.4 -1.80 262 -3 71 ----JL2-32 Hendrys Creek (J. Lee et al., 1987) Zm unit 1 -300 15.4 13.8 -3.6 -1.86 275 -2 73 ----JL1-197 Hendrys Creek (J. Lee et al., 1987) Zm -400 15.5 --------EBSD 0.91 4.34 -JL1-202 Hendrys Creek (J. Lee et al., 1987) Zm unit 1 -260 15.5 15.9 ± 0.7 -1 ± 0 4.5 ± 0.2 d -1.96 299 + 22/ 13 ± 6 d 75 ± 2 EBSD 0.95 4.85 --10 JL1-204 Hendrys Creek (J. Lee et al., 1987) Cpm -200 15.6 18.0 ± 1.1 4 ± 1 4.8 ± 0.2 d -2.05 324 + 29/-6 13 ± 6 d 76 ± 2 EBSD 0.86 3.38 -JL1-205 Hendrys Creek (J. Lee et al., 1987) Cpm -80 15.6 19.4 ± 1.0 3 ± 0 5.0 ± 0.2 d -2.10 340 + 27/-9 13 ± 6 d 77 ± 2 EBSD 0.83 2.66 -JL1-201 Hendrys Creek (J. Lee et al., 1987) Zm -600 15.6 --------EBSD 0.79 3.44 -31 Hendrys Creek Cpm -60 18.0 --------OFA 0.91 3.46 3.8 32 Hendrys Creek Cpm -80 18.3 17.6 ± 0.9 3 ± 0 4.3 ± 0.5 1 ± 1 2.03 316 + 0/-1 2 ± 6 76 ± 1 ----33 Hendrys Creek Cpm -100 18.8 22.8 ± 1.1 2 ± 0 5.4 ± 0.2 d -2.21 377 + 28/ 13 ± 6 d 79 ± 2 OFA 0.86 3.01 10.2 -10 34 Hendrys Creek Cpm -90 19.3 17.2 ± 0.6 1 ± 0 9.0 ± 0.4 3 ± 1 2.11 220 ± 3 68 ± 3 81 + 1/-0 ----35 Hendrys Creek Cpm -90 19.9 --------OFA 0.97 3.00 3.0 36 Hendrys Creek Cpm -100 20.0 --------EBSD 0.87 3.22 3.4 37 Hendrys Creek Cpm -150 20.0 --------EBSD 0.77 2.69 5.8 38 Hendrys Creek Zm unit 1 -300 20.0 13.9 ± 0.6 3 ± 0 4.2 ± 0.2 d -1.86 273 + 21/-9 13 ± 6 d 73 ± 2 EBSD 0.86 3.58 5.5 39 Hendrys Creek Zm -320 20.1 --------EBSD 0.74 2.69 8.9 40 Hendrys Creek Zm unit 2 -350 20.1 14.1 ± 0.7 6 ± 1 4.2 ± 0.2 d -1.87 275 + 23/-8 13 ± 6 d 73 ± 2 ----41 Hendrys Creek Zm -380 20.1 --------EBSD 0.89 3.56 4.4 42 Hendrys Creek Cpm -90 20.2 26.8 ± 1.4 -1 ± 0 6.0 ± 0.5 -8 ± 1 2.33 393 + 3/-4 10 ± 4 82 ± 1 OFA 0.89 2.80 1.9 43 Hendrys Creek Zm -480 20.2 --------EBSD 0.90 3.59 3.8 44 Hendrys Creek Cpm -90 20.3 14.0 ± 0.9 4 ± 1 4.5 ± 2.2 -4 ± 1 1.87 252 ± 5 13 ± 4 75 ± 1 ----45 Hendrys Creek Zm -420 20.3 --------OFA 0.93 3.16 1.4 46 Hendrys Creek Zm unit 3 -460 20.3 13.5 ± 0.6 4 ± 0 4.2 ± 0.2 d -1.84 267 + 21/-9 13 ± 6 d 73 ± 2 EBSD 0.47 1.65 2.0 47 Hendrys Creek Zm -520 20.3 --------OFA 0.93 2.62 4.4 48 Hendrys Creek Zm -360 20.4 --------OFA 0.90 3.33 4.0 49 Hendrys Creek Cpm -10 20.4 24.9 ± 2.1 2 ± 0 5.2 ± 0.4 3 ± 1 2.27 392 + 16/ 3 ± 2 80 ± 1 OFA 0.90 2.35 1.0 -15 50 Hendrys Creek Zm unit 4 -470 20.4 9.7 ± 0.7 6 ± 1 3.6 ± 0.3 9 ± 1 1.61 197 ± 6 10 + 4/-3 69 + 2/-1 OFA 0.87 2.77 2.1 51 Hendrys Creek Cpm -160 20.5 27.5 ± 2.3 2 ± 0 6.6 ± 0.5 3 ± 1 2.35 386 + 15/ 17 ± 3 82 ± 1 OFA 0.86 2.32 0.0 -14 52 Hendrys Creek Zm -550 20.5 --------EBSD 0.90 4.44 7.2 Table 1 Continued WNW-to-ESE Lineation-Lineation-Foliation-Quartz Structural NSRD-parallel Octahedral parallel (X) normal (Y) normal (Z) CPO Density Mica Rock depth a distance b Rs (X/Z) φ (X/Z) Rs (Y/Z) φ (Y/Z) shear strain extension extension shortening analytical Cylindricity norm area Strain Sample Sampling transect Unit (m) (km) (±1 SE) (±1 SE) (±1 SE) (±1 SE) (ε) (%) c (%) c (%) c Method (B) (Jpf) % Domain 53 Hendrys Creek Cpm -140 20.8 --------OFA 0.89 2.47 8.0 5 JL2-91 Hendrys Creek (J. Lee et al., 1987) Cpm -150 21.2 31.1 -4.2 -2.44 513 -17 80 ----5 54 Hendrys Creek Cpm -250 21.3 --------OFA 0.92 2.63 6.4 5 55 Hendrys Creek Zm -640 21.5 --------OFA 0.88 2.69 4.1 5 56 Hendrys Creek Zm -250 21.8 --------OFA 0.96 2.77 3.8 5 57 Hendrys Creek Zm -250 22.4 --------OFA 0.94 2.52 3.9 5 SR08-20 Hendrys Creek (Gébelin et al., 2015) Zm -300 22.7 --------EBSD 0.97 --5 58 Hendrys Creek Cpm -150 22.8 --------OFA 0.94 2.63 3.0 5
Hendrys Creek (Gébelin et al., 2015) Zm
Hendrys Creek (Gébelin et al., 2015) Zm
Hendrys Creek (Gébelin et al., 2015) Zm
Hendrys Creek (Gébelin et al., 2015) Zm
59 Hendrys Creek Cpm -100 23.3 --------OFA 0.96 2.63 0.8 5 60 Hendrys Creek Cpm -60 24.0 --------OFA 0.94 2.52 2.3 5 SR08-6A Hendrys Creek (Gébelin et al., 2015) Cpm -60 24.4 --------EBSD 0.91 --5 SR08-3 Hendrys Creek (Gébelin et al., 2015) Cpm -40 24.4 --------EBSD 0.95 --5 SR08-11B Hendrys Creek (Gébelin et al., 2015) Zm -100 24.5 --------EBSD 0.96 --5 61 Hendrys Creek Cpm -40 24.7 --------EBSD 0.92 2.71 1.1 5 62 Hendrys Creek Cpm -70 24.7 --------EBSD 0.91 3.01 1.9 5 63 Hendrys Creek Zm -140 24.7 --------EBSD 0.92 3.16 2.7 5 64 Hendrys Creek Cpm -100 24.7 --------EBSD 0.85 2.96 -5 65 Hendrys Creek Cpm -90 24.7 --------EBSD 0.92 3.02 2.3 5 66 Hendrys Creek Cpm -50 24.7 --------EBSD 0.68 1.81 1.3 5 67 Hendrys Creek Cpm -40 24.8 --------OFA 0.91 2.92 2.0 5
Note. Definitions: Rs, tectonic elongation (long axis to short axis ratio); φ, angle between long axis and trace of tectonic foliation (equivalent to θ' of Ramsay & Huber, 1983; see text for discussion of sign convention); CPO, crystallographic preferred orientation; SE, standard error; EBSD, electron backscatter diffraction; OFA, optical fabric analyzer. a Structural depths were measured from the projected positions of samples onto Figure 2b and were measured normal to the trace of the NSRD. b WNW-to-ESE NSRD-parallel distance was measured on Figure 2b (starting with the position of sample 01 at 0.0 km) and was measured by projecting samples structurally upward to the NSRD. c Calculated by restoring the 3D strain ellipsoid of each sample to a sphere of the same volume, and then comparing lengths before and after strain. Error ranges are calculated from the ±1 standard error values reported for Rs values for each 2D strain ellipse. d To determine approximate 3D ellipsoids for these seven samples, the 13 ± 6% average lineation-normal (Y) extension value from 3D strain ellipsoids from the Hendry's Creek transect was used in order Toback-calculate an Rs (YZ) value. Error is ±1 standard error. negligible and therefore that the measured quartz ribbons can be utilized as deformed markers from which 3D finite strain can be measured (e.g., Dunnet, 1969;Ramsay, 1967;Ramsay & Huber, 1983).
To quantify 3D finite strain, we performed the Rf-φ method (e.g., Dunnet, 1969;Ramsay, 1967) on minimally recrystallized, visually distinct quartz ribbons from thin sections cut from 38 total samples from the Fourmile Canyon, Salt Creek, and Hendry's Creek transects. Quartz ribbons were outlined based on domains of similar extinction when compared to the surrounding variable extinction domains of <0.05-0.10 mm recrystallized subgrains (Figure 6). A detailed description of our methods, as well as graphs and tables of supporting data, are available in Supporting Information S1.
We cut two foliation-normal thin sections from each sample: one parallel (thin sections ending with "A") and one normal (thin sections ending with "B") to mineral stretching lineation (Table 1). We interpret that the "A" and "B" thin sections contain the XZ and YZ strain planes, respectively. We took photomicrographs of each thin section with the apparent dip of foliation oriented horizontal, structural-up toward the top, and ESE (for "A" thin sections) or NNE (for "B" thin sections) toward the right (Figure 6). We outlined quartz ribbons using Adobe Illustrator, and we used ImageJ (Schneider et al., 2012) to calculate best-fit ellipses for each ribbon.
We measured Rs (the ratio of long axis length to short axis length) for at least 30 quartz ribbons in each thin section, and corresponding φ values were measured between the long axis of each quartz ribbon and the apparent dip of foliation. The harmonic mean of all Rs values measured for each thin section (±1 standard error) is reported as the overall Rs value, after Lisle (1977aLisle ( , 1977bLisle ( , 1979)). The use of harmonic mean to calculate Rs has been demonstrated to yield comparable results to other strain calculation methods (including eigenvector-based methods), particularly for higher-strain samples (Rs values > ∼2.5) (e.g., Babaie, 1986;Parui & Bhattacharyya, 2024;Paterson, 1983). We used a sign convention for φ where the apparent dip of foliation is defined as 0°, positive values are counterclockwise relative to foliation and negative values are clockwise relative to foliation. The mean φ angle of all quartz ribbons measured for each thin section (±1 standard error) is reported as the overall φ value. Mean φ values in lineation-parallel ("A") thin sections can be used to interpret shear-sense (e.g., Passchier & Trouw, 2005;Ramsay, 1967). Under our sign convention, a positive mean φ value corresponds to a top-to-ESE shear-sense and a negative mean φ value corresponds to a top-to-WNW shear-sense. XZ and XY 2D strain ellipses for each sample are plotted on Figures 2345, respectively. 3D strain ellipsoids for each sample were determined by directly comparing the Rs values in "A" thin sections (Rs (X/Z) ) to those in "B" thin sections (Rs (Y/ Z) ), and assumption of constant-volume deformation.
We also calculated octahedral shear strain (ε) (Nadai, 1963) using the scaled X, Y, and Z values measured from our Rf-φ analyses, where scaled X, Y, and Z represent the stretch values along the principal strain axes (please see Supporting Information S1 for further discussion of methods). Octahedral shear strain is a parameter that estimates of the amount of work done to homogeneously deform an object during coaxial deformation, accounts for total 3D deformation, and is a useful tool for determining total strain as it is independent of strain geometry.
To quantify trends in finite strain with transport-parallel distance and structural depth, we also calculated percent extension in the lineation-parallel (X) and lineation-normal (Y) directions, and percent shortening normal to foliation (Z) by comparing the relative lengths of the 3D finite strain ellipsoid for each sample to the diameter of a sphere with the same volume (e.g., Ramsay, 1967) (Table 1; additional details in Supporting Information S1). We projected our strain samples to their respective locations on the cross section in Figure 2b, which allowed us to measure the projected WNW-to-ESE distance of each sample along the NSRD. NSRD-parallel distances for each sample were measured relative to the position of sample 01 in the Fourmile Canyon transect (Table 1).
Here, we discuss the results of our 38 new finite strain samples, which we combine with 11 finite strain analyses from J. Lee et al. (1987), from west to east.
Fourmile Canyon transect: Eight Cpm samples from the Fourmile Canyon transect (Figure 3) yielded Rs (XZ) and Rs (YZ) values that increase eastward from 3.0 to 6.5 (average 4.4) and from 1.9 to 4.2 (average 2.7), respectively (Figures 7d-7f). ε increases eastward from 0.79 to 1.38 (average 1.04). Two samples plot near the plane strain line and the rest plot in the flattening field (Figures 8a and 8b). φ(XZ) values between 3 and 10° are consistent with a top-to-ESE shear-sense for all eight samples (Figure 8e). X extension, Y extension, and Z shortening all increase eastward, from 65% to 116% (average 91%), 3%-39% (average 17%), and 45%-67% (average 54%), respectively (Figures 7g-7i). These data define the beginning of an eastward-increasing finite strain gradient (Figures 2, 7d-7i). Salt Creek transect: Twenty-two Cpm samples from the Salt Creek transect (Figure 4) yielded Rs (XZ) values that generally increase eastward from 5.5 to 17.9 (average 9.7), Rs (YZ) values between 2.0 and 4.5 (average 3.2), and ε values that generally increase eastward from 1.22 to as high as 2.04 (average 1.58) (Figures 7c-7f). Ten samples overlap the plane strain line, six lie in the flattening field, and six lie in the constrictional field (Figures 8a and 8b).
Sixteen samples exhibit positive φ(XZ) values that define a top-to-ESE shear sense (Figure 8e). X extension and Z shortening increase eastward from 116% to 321% (average 207%) and 56%-76% (average 67%), respectively, and Y extension varies between -18% and 20% (average 2%) (Figures 7g-7i). These data define a continuation of the eastward-increasing finite strain gradient observed in the Fourmile Canyon transect (Figures 2 and 7).
Hendry's Creek transect: Of the 19 strain analyses from the Hendry's Creek transect (Figure 5), 12 were collected from Cpm quartzites and 7 were collected from Zm quartzites. We only had XZ thin sections available for seven samples (JL1-202, JL1-204, 33,38,40,and 46). Given that 3D strain geometry does not change with depth below the NSRD (Figures 8c and 8d), in order to estimate an approximate 3D finite strain ellipsoid for these seven samples, we used the 13 ± 6% (±1 standard error) average percent Y extension of the 12 remaining Apparent constr ction Apparent fiatteni 5 10 lineation foliation -5 lineation --------0 Tectonics 10.1029/2023TC008166
Hendry's Creek samples to back-calculate 3D ellipsoids assuming constant volume deformation (Table 1). Additionally, due to pervasive dynamic recrystallization in Hendry's Creek samples (e.g., Figure 6c), which has likely limited the final preserved length of the quartz ribbons that we measured, we interpret the following results to likely represent minimum values for finite strain. The Hendry's Creek ellipsoids yielded Rs (XZ) values between 6.9 and 31.1 (average 17.3), Rs (YZ) values between 3.4 and 9.0 (average 4.8), and ε values between 1.41 and 2.44 (average 1.97) (Figures 7a, 7c-7f). Fourteen samples lie in the flattening field, four overlap the plane strain line, and one lies in the constrictional field (Figures 8a and 8b). Seventeen samples yielded positive φ(XZ) values that define a top-to-ESE shear-sense (Figure 8e). X extension ranges from 128% to 513% (average 297%), Z shortening ranges from 67% to 82% (average 75%), and Y extension has an average of 13% (Figures 7g-7i). The Hendry's Creek samples exhibit an apparent decrease in Rs (XZ) with structural depth, from typical values of ∼16-28 between 0 and 150 m below the NSRD to values of ∼10-13 at 450-500 m below (Figure 7a). The decrease in ε with structural depth below the NSRD is less apparent, with typical values of ∼1.8-2.2 between 0 and 150 m below the NSRD to values of ∼1.8-2.0 at 450-500 m below. Rs (XZ) , ε, X extension, and Z shortening in Hendry's Creek all exhibit a general eastward increase in their maximum values (Figures 7c, 7d, 7g, and 7i), which defines a continuation of the eastward-increasing finite strain gradient observed in the Fourmile Canyon and Salt Creek transects. However, there is significant variability recorded in Rs (XZ) ε, and X extension in Hendry's Creek (Figures 7c, 7d, and 7g), which we interpret as the consequence of a significant increase in the area percentage of quartz recrystallization (e.g., compare Figures 6a-6c).
Quantifying macro-scale ductile thinning of the Cpm provides an additional means to estimate strain in the NSRD footwall. We calculated % ductile thinning by comparing the structural thickness of the Cpm in the Northern Snake Range to its undeformed stratigraphic thickness in surrounding ranges. These ductile thinning measurements are important for estimating finite strain in the Hendry's Creek transect, where pervasive dynamic recrystallization has likely minimized the magnitude of finite strain recorded in quartz ribbons (e.g., Figure 6c).
We measured the structural thickness of the Cpm at 34 locations (Figure 9). We measured thicknesses from published cross sections through the Schell Creek (Long et al., 2022), Deep Creek (Rodgers, 1987), Southern Snake (Whitebread, 1969) and Northern Snake ranges (Gans et al., 1985;J. Lee et al., 1999a), and we utilized published geologic maps (Gans et al., 1999;Johnston, 2000;J. Lee et al., 1999b;Miller & The Stanford Geological Survey, 2007;Miller, Grier, & Brown, 1995;Miller et al., 1994) to draft 21 new cross sections through portions of the Northern and Southern Snake ranges (cross sections, supporting data, and additional details on methods are in Supporting Information S1). We used our measured thicknesses to construct a contour map of the structural thickness of the Cpm (Figure 9).
The thickness of the Cpm in the Schell Creek, Deep Creek, and Southern Snake Ranges varies between 1,100 and 1,390 m (n = 8; excluding one outlier of 1,530 m) and has an average of 1,220 ± 30 m (±1 standard error) (Figure 9). The Cpm has been thinned to a typical range between ∼50 and 250-m-thick in the southeastern part of the Northern Snake Range, corresponding to ∼80%-95% ductile thinning.
Seven structural thickness measurements of the Cpm from the Hendry's Creek transect were collected proximal to the A-A′ cross section line (Figure 9). We calculated % foliation-normal (Z) shortening for each of these measurements by comparing the structural thickness of the Cpm to its 1,220 ± 30 m average regional thickness. We combined this % Z shortening with the 13 ± 6% average Y extension from finite strain ellipsoids from the Hendry's Creek transect in order to back-calculate % X extension as well as the Rs ratios and ε of the 3D strain ellipsoids for each of these thickness measurements (Table 2). These results demonstrate an increase from 80% to 95% Z shortening and 338% to 1,702% X extension eastward across the Hendry's Creek transect. A positive mean φ value is compatible with a top-to-the-ESE shear-sense and a negative mean φ value is compatible with a top-to-the-WNW shear-sense. Note that samples where only one thin section was available for finite strain analysis are not included in the graphs.
Tectonics 10.1029/2023TC008166
Here, we integrate our micro-scale finite strain and macro-scale ductile thinning data sets to develop a geometric model for ductile strain in the NSRD footwall (Figure 10). Using trends in the averages of Rs (XZ) and % X extension values from our micro-scale finite strain analyses, we divided the NSRD footwall into five strain domains (abbreviated SD1, SD2, SD3, SD4, and SD5) (Figures 1b, 2b, and 10). Strain domain divisions were typically made where Rs (XZ) increased by ∼3-5 (or more) from the average of adjacent values and/or where % X extension increased by ∼50% (or more) from the average of adjacent values. We favored a minimal number of strain domain divisions so that each is supported by a larger number of analyses and thus yield more robust average Rs (XZ) , % X extension, and % Z shortening values.
SD1 is defined by eight strain analyses from the Fourmile Canyon transect and the five westernmost strain analyses from the Salt Creek transect, which define an average Rs (XZ) of 5.4 ± 1.4, ε of 1.14 ± 0.20, 119 ± 32% X extension, and 59 ± 7% Z shortening. SD1 has a modern width of 4.7 km and restores to a pre-Eocene-Oligocene width of 2.1 km (Figures 10b and 10c) (the five strain domains were restored to their pre-extensional geometry by restoring the average 3D strain ellipsoid of each strain domain to a sphere with the same volume). SD2 is supported by 15 strain analyses from the central portion of the Salt Creek transect, which define an average Rs (XZ) of 10.2 ± 1.9, ε of 1.63 ± 0.12, 220 ± 32% X extension, and 68 ± 3% Z shortening. SD2 has a modern width of 2.7 km and a pre-Eocene-Oligocene width of 0.8 km (Figures 10b and 10c).
SD3-SD5 lie in the easternmost portion of the Salt Creek transect and across the width of the Hendry's Creek transect (Figure 10). Within these rocks, the high area percentage of dynamically recrystallized quartz (e.g., Figures 6b and 6c) likely indicates that the quartz ribbons that we measured underestimate finite strain. Therefore, for SD3-SD5 we present a range of strain magnitudes obtained from our micro-scale finite strain data and our macroscale ductile thinning measurements of the Cpm (Figures 10b and 10c). SD3 is supported by two finite strain analyses from the easternmost portion of the Salt Creek transect and eight finite strain analyses from the western two- (Rodgers, 1987), Southern Snake Range (Miller & The Stanford Geological Survey, 2007;Whitebread, 1969), Northern Snake Range (J. Lee et al., 1999b), and Spring Valley (Gans et al., 1985), as well as our 21 new cross sections from published mapping in the Southern Snake Range (Miller & The Stanford Geological Survey, 2007;Miller, Gans, et al., 1995;Miller, Grier, & Brown, 1995;Miller et al., 1994) and Northern Snake Range (Gans et al., 1999;Johnston, 2000;J. Lee et al., 1999aJ. Lee et al., , 1999b) ) thirds of the Hendry's Creek transect, which define an average Rs (XZ) of 13.4 ± 4.4, ε of 1.84 ± 0.23, 263 ± 75% X extension, and 73 ± 4% Z shortening. SD3 has a modern width of 11.4 km and a pre-Eocene-Oligocene width of 3.1 km (Figures 10b and 10c). Three Cpm thickness measurements within SD3 (247, 230, 234 m; Table 2) define 80 ± 1% average Z shortening, which corresponds to 351 ± 51% X extension, Rs (XZ) of 23.5 ± 4.0, ε of 2.22 ± 0.11, and yields a pre-Eocene-Oligocene width of 2.5 km. SD4 is supported by nine finite strain analyses from the eastern part of the Hendry's Creek transect, which define an average Rs (XZ) of 16.4 ± 5.9, ε of 2.00 ± 0.23, 294 ± 75% X extension, and 76 ± 4% Z shortening, and has a modern width of 1.8 km and a pre-Eocene-Oligocene width of 0.5 km. Two Cpm thickness measurements within SD4 (174, 140 m; Table 2) define 87 ± 2% average Z shortening, which corresponds to 588 ± 131% X extension, Rs (XZ) of 57.2 ± 17.8, ε of 2.83 ± 0.22, and yields a restored width of 0.3 km. SD5 is supported by two finite strain analyses from the easternmost part of the Hendry's Creek transect, which define an average Rs (XZ) of 29.3 ± 2.5, ε of 2.40 ± 0.05, 449 ± 90% X extension, 81 ± 1% Z shortening, and has a modern width of 6.7 km and a pre-Eocene-Oligocene width of 1.2 km. Two Cpm thickness measurements within SD5 (85, 60 m; Table 2) define 94 ± 1% average Z shortening, which corresponds to 1,387 ± 387% X extension, Rs (XZ) of 282 ± 122, ε of 3.94 ± 0.32, and yields a pre-Eocene-Oligocene width of 0.5 km. Cpm structural thickness (m) Strain domain Octahedral shear strain (ε) Rs (X/Z) (±1 SE) b Rs (Y/Z) (±1 SE) b Rs (X/Y) (±1 SE) b Lineationparallel (X) extension (%) b
Foliationnormal (Z) shortening (%) d Johnston (2000) 7 (This study) 247 3 2.18 21.7 ± 0.8 5.6 ± 0.2 3.9 ± 0.2 338 ± 24 13 ± 6 80 ± 1 Long F-F′ 230 3 2.28 25.0 ± 1.0 6.0 ± 0.2 4.2 ± 0.2 370 ± 26 13 ± 6 81 ± 1 et al. (2022) Johnston (2000) 8 (This study) 234 3 2.26 24.1 ± 0.9 5.9 ± 0.2 4.1 ± 0.2 362 ± 25 13 ± 6 81 ± 1 Johnston (2000) 9 (This study) 174 4 2.67 43.6 ± 1.7 7.9 ± 0.3 5.5 ± 0.3 521 ± 31 13 ± 6 86 ± 1 Long F-F′ 140 4 2.98 67.4 ± 2.6 9.9 ± 0.4 6.8 ± 0.4 672 ± 37 13 ± 6 89 ± 1 et al. (2022) Long F-F′ 85 5 3.69 182.9 ± 7.1 16.2 ± 0.6 11.3 ± 0.6 1,172 ± 58 13 ± 6 93 ± 1 et al. ( 2022) Johnston (2000) 10 (This study) 60 5 4.18 367.1 ± 14.3 23.0 ± 0.9 15.9 ± 0.9 1,702 ± 79 13 ± 6 95 ± 1 a See Supporting Information S1 for cross sections used for structural thickness calculations. b Calculated using the 13 ± 6% average Y extension (1 standard error) from Hendry's Creek 3D finite strain ellipsoids and the % Z shortening from Cpm macro-scale structural thinning estimates to back-calculate a 3D ellipsoid. c Calculated by taking the average % Y elongation (±1 standard error) from 3D Hendry's Creek finite strain ellipsoids. d Calculated by comparing the measured Cpm structural thickness with the average regional Cpm thickness of 1,220 ± 30 m.
For SD3-SD5, our strain estimates from macro-scale ductile thinning are higher than those attained from microscale finite strain measurements, and the disparity between the two techniques increases eastward. We attribute this to an eastward increase in the area percentage of dynamic recrystallization of quartz as a consequence of greater strain magnitudes (e.g., Figure 6). Accordingly, we interpret that our micro-scale strain analyses underestimate finite strain in SD3-SD5, and therefore that our macro-scale ductile thinning estimates from the Cpm are more representative of the magnitude of finite strain in this part of the range.
In summary, finite strain in the NSRD footwall increases significantly eastward, from ∼119% X extension and ∼59% Z shortening in SD1 on the western flank of the range to as high as ∼1,387% X extension and ∼94% Z shortening in SD5 on the eastern flank (Figure 10b). Assuming that the upper contact of the Cpm was subhorizontal prior to Eocene-Oligocene extension, we can compare present-day and restored lengths to measure the cumulative ductile extension of the NSRD footwall (Figures 10b and 10c). Restoration using only micro-scale finite strain analyses for SD1-SD5 yields 19.6 km of cumulative ductile extension (255%) (Figure 10c), which we interpret as an underestimate. Restoration of micro-scale analyses for SD1-SD2 combined with restoration of macro-scale ductile thinning measurements for SD3-SD5 yields 21.1 km of cumulative ductile extension (340%) (Figure 10c), which is our preferred estimate. Our estimates are similar to published estimates of ductile extension of the NSRD footwall in the southern part of the range, which vary from 19.1 to 21.9 km (220%-250%) (J. Lee et al., 1987;Long et al., 2022). Three-dimensional strain is variable, with 21 samples that lie entirely in the flattening field, 13 samples with error ranges that overlap the plane strain line, and 8 samples that lie entirely in the constrictional field (Figure 7a). The overall average k value (the "deformation path" of Flinn, 1962) is 0.9, defining minor stretching in the Y direction on average. Thirty-eight of the 49 total strain samples exhibit asymmetrically stretched quartz ribbons that are consistent with a top-to-ESE shear sense (Figure 7b), which is consistent with the top-down-to-ESE displacement direction of the NSRD (e.g., J. Lee et al., 2017).
In order to quantitatively compare quartz CPO intensity to finite strain magnitude in the NSRD footwall, we analyzed foliation-normal, lineation-parallel thin sections from 75 total Cpm and Zm quartzite samples (Table 1), consisting of four from the Fourmile Canyon transect (Figure 3), 30 from the Salt Creek transect (Figure 4), and 41 from the Hendry's Creek transect (Figure 5) (quartz CPO distributions from 11 of our samples from the Salt Creek transect and 5 of our samples from the Hendry's Creek transect were originally measured using a universal stage, with results published in J. Lee et al. (1987). In this study, we re-collected quartz CPO data from these same samples using electron-backscatter diffraction [EBSD], and we report the results below). To define quartz CPO intensity patterns in the ESE-oriented extension direction, we collected samples from approximately the same structural level within the upper part of the Cpm, with an east-west spacing typically ≤∼0.5 km. To delineate quartz CPO intensity patterns with structural depth below the NSRD, we also analyzed samples in one vertical transect through the Cpm in the Salt Creek transect (Figure 4) and three vertical transects through the Cpm and Zm in the Hendry's Creek transect (Figure 5). We combined our 75 CPO analyses with 12 published CPO analyses of Gébelin et al. (2015) (samples listed with an "SR08" or "SR09" prefix), which include four from the Salt Creek transect and eight from the Hendry's Creek transect (Figures 4 and 5). We projected these 87 total quartz CPO samples onto the A-A′ cross section (Figure 11) and measured their NSRD-parallel distance relative to sample 01 (Table 1). All thin sections analyzed in this study exhibit subgrain rotation recrystallization, which is characterized by equigranular, polygonal, ∼20-50 μm subgrains (e.g., Figure 6) (e.g., Stipp et al., 2002).
We analyzed 45 samples using a Russell-Head Instruments G60+ optical fabric analyzer. This instrument determines the trend and plunge of the c-axis for each pixel in a composite image of the entire thin section, which is used to build a spatially referenced quartz CPO distribution using a variety of plane-and cross-polarized images to verify minerology (additional details in Supporting Information S1). The CPO distributions measured using this method produce equivalent results to those measured using EBSD, x-ray goniometry, and neutron diffraction, with the exception that it only measures quartz c-axis orientations (e.g., N. J. R. Hunter et al., 2017;Peternell et al., 2010;Wilson et al., 2007). For each sample, we used Crystal Imaging Systems fabric analyzer software to manually select all recrystallized grains in the field of view until at least 1,000 representative grains had been selected, while avoiding non-recrystallized ribbon quartz grains and non-quartz grains. These selected grains were then used to build quartz c-axis pole figures. We also utilized EBSD to measure crystallographic orientations of quartz cand a-axes for 30 samples (Table 1), using methods outlined in Langille et al. ( 2010) (additional details in Supporting Information S1). Approximately one orientation was measured per grain, and as many as 1,000 grains were selected at random to support pole figures (Figure 11).
Following grain selection, the 75 samples were processed using the custom R scripts of Larson (2023) to calculate the intensity (i.e., non-randomness) of quartz CPO development (Table 1). Two CPO intensity parameters were calculated for each sample: cylindricity (B) of Vollmer (1990) and the density norm (Jpf) of Mainprice et al. (2015). B was measured by calculating the point (P), girdle (G), and random (R) end-member CPO types (Vollmer, 1990), which are determined by matrix summation of eigenvalues assigned to each end-member, where P + G + R = 1. B is the sum of the non-random components (B = P + G) and varies between a value of 0 for a completely random CPO distribution and a value of 1 for a completely non-random CPO distribution. Jpf was calculated as the L2 norm of the spherical density distribution (e.g., Kilian & Heilbronner, 2017;Larson et al., 2023), and ranges between a value of 1 for a completely random distribution and infinity for a completely non-random distribution (Mainprice et al., 2015). Additionally, Gébelin et al. (2015) presented P, G, R, and B values for their 12 quartz CPO samples (which were also calculated using the methods of Vollmer, 1990), but Jpf values are unavailable for these samples (Table 1).
Eigenvalue-based methods of calculated CPO intensity, such as B, can be impacted by CPO distribution geometry (e.g., crossed-girdle vs. single-girdle) and opening angles of crossed-girdle patterns, where the intensity of B tends to decrease with increased opening angle in crossed-girdle patterns (Larson et al., 2023). While we acknowledge the uncertainty introduced by comparing B calculated from both crossed-girdle and single-girdle patterns, the use of B as a measure of quartz CPO intensity is still widely used. Therefore, in addition to using B as an intensity parameter, we also calculated Jpf values for our samples (Mainprice et al., 2015), as this intensity parameter is less impacted by quartz CPO distribution geometry and opening angle (Larson et al., 2023). Readers are referred to Larson et al. (2023) for a detailed comparison of B (and other eigenvalue-based methods) and Jpf.
Here, we summarize the pole plots and B and Jpf values obtained from our 75 CPO distribution analyses, as well as the 12 analyses of Gébelin et al. (2015). Representative pole plots are shown on Figure 11 (pole plots for all samples are available in Supporting Information S1). We discuss these results below for each sampling transect from west to east.
The four samples from the Fourmile Canyon transect (Figure 3) yielded asymmetrical single-girdle patterns that are consistent with a top-to-the-ESE shear-sense (e.g., sample 06 on Figure 11). B for these samples ranges from 0.60 to 0.69 (average 0.65), and Jpf ranges from 1.79 to 2.27 (average 2.04) (Figures 12a and 12b; Table 1).
The 27 samples that span the western two-thirds of the Salt Creek transect (samples between 09 and 23 on Figures 4 and 11) dominantly yielded symmetrical type-I crossed-girdle patterns (e.g., samples 16 and 21 on Figure 11). Farther to the east in the Salt Creek transect, asymmetrical, top-down-to-ESE single-girdle patterns (e.g., sample 26 on Figure 11) are observed in eight samples that are distributed across the eastern third of the transect (samples between 24 and JL1-139B on Figures 4 and 11). This eastward increase in CPO distribution asymmetry across the Salt Creek transect was originally documented by J. Lee et al. (1987), who interpreted this to indicate an eastward-increasing component of simple shear. B varies between 0.26 and 0.69 (average 0.52) in the western two-thirds of the Salt Creek transect and increases to 0.74-0.89 (average 0.84) in the eastern third. Jpf varies between 1.27 and 2.33 (average 1.67) in the western two-thirds of the transect and increases to 1.94-2.79 (average 2.65) in the eastern third (Figures 12a and 12b; Table 1). A five-sample transect over a vertical distance of 100 m through the Cpm in the middle of the Salt Creek transect (samples JL1-148 to JL1-152 on Figures 4 and 10) did not yield any trends in B (Figure 12g) or Jpf (Figure 12h) with structural depth below the NSRD.
Hendry's Creek transect: The 49 total CPO distribution analyses from the Hendry's Creek transect all yielded asymmetric, top-down-to-ESE single-girdle patterns (e.g., samples 31 and 59 on Figure 11). B ranges between 0.75 and 0.96 (excluding two outliers: 0.47 for sample 30 and 0.68 for sample 66), with an average of 0.90, and the highest values generally occurring in the eastern part of the transect (Figure 12a). Jpf ranges between 2.32 and 4.85 (excluding two outliers: 1.65 for sample 40 and 1.81 for sample 51) (Figure 12b), with an average of 3.04. Three vertical transects through the Cpm and Zm (Figures 5 and 11 Tullis , 2006;Means, 1981). We tentatively interpret that such a steady state may have been achieved in the Hendry's Creek transect (which encompasses the eastern half of SD3 and the full widths of SD4 and SD5), where individual B values approach ∼0.90-0.95 and Jpf values approach ∼2.50-3.00 (Table 1), which correspond to Rs > ∼57 and ε > ∼2.83 (Table 3). Achievement of a steady state CPO fabric would explain why strain increases eastward in the Hendry's Creek transect (Figures 5, 8, and 10; Table 1) while CPO intensity remains approximately the same (Figures 11 and 12; Table 1).
The presence of mica in quartz-rich rocks has been shown to affect the development of quartz CPO distributions (e.g., Little et al., 2015;Starkey & Cutforth, 1978) and may play a role in controlling the grain size of dynamically recrystallized quartz (e.g., Herwegh et al., 2011;Song & Ree, 2007). Additionally, a higher degree of interconnectivity between mica grains can decrease the strength of quartz-bearing rocks, even when the mica is not in direct contact with quartz (N. J. Hunter et al., 2016). To determine if mica content affected the B and Jpf values that we calculated from our samples, we utilized methods outlined in Starnes et al. (2020) to measure the area percentage of mica within thin sections of 57 of our quartz CPO samples (Table 1) (additional details in Supporting Information S1). or ε value from ductile thinning measurements of the Cpm. Shown with the total error calculated from Cpm ductile thinning measurements and regional undeformed thickness measurements.
Mica area percentage exhibits a total variation between 0.0% and 10.2%, with an average of 2.9 ± 2.2% (1σ).
There is no apparent trend in mica area percentage with WNW-to-ESE distance (Figure 12c). Instead, each transect exhibits a range of mica area percentage values, with overall variability generally increasing as a function of the number of measured samples (e.g., the four samples from the Fourmile Canyon transect vary between 0.7% and 2.8%, the 19 samples from the Salt Creek transect vary between 0.3% and 6.4%, and the 34 samples from the Hendry's Creek transect vary between 0.0% and 10.2%). There is also no trend in mica area percentage with structural depth below the NSRD (Figure 12d). Mica area percentage does not exhibit any correlation with B (Figure 12e) or Jpf (Figure 12f), with both exhibiting significant scatter. These data indicate that mica did not play a significant role in strain partitioning within our samples (e.g., N. J. Hunter et al., 2016Hunter et al., , 2018;;Little et al., 2015).
To compare quartz CPO intensity to finite strain magnitude in the NSRD footwall, we calculated the average (±1σ) B and Jpf values for all quartz CPO samples that fell within each of the five strain domains that we defined across the width of the Northern Snake Range (Table 3; Figure 13). These values are: B = 0.52 ± 0.14 and Jpf = 1.68 ± 0.38 for strain domain 1, B = 0.52 ± 0.09 and Jpf = 1.68 ± 0.31 for strain domain 2, B = 0.83 ± 0.08 and Jpf = 2.97 ± 0.74 for strain domain 3, B = 0.87 ± 0.13 and Jpf = 3.01 ± 0.54 for strain domain 4, and B = 0.92 ± 0.06 and Jpf = 2.80 ± 0.52 for strain domain 5. We graphed these average CPO intensity values against the average Rs (XZ) and octahedral shear strain (ε) obtained from each of our five strain domains (Figure 13).
We chose to compare the average Rs (XZ) and ε values for each strain domain to the average quartz CPO intensity values from samples within these strain domains (as opposed to directly comparing individual Rs (XZ) and ε values to individual CPO intensity values) primarily because: (a) the eastward increase in the area percentage of quartz recrystallization across the range produces significant scatter, particularly in Hendry's Creek samples; and (b) many samples do not have both finite strain and CPO fabric intensity data, particularly in domains 4 and 5 (Figures 13c,13d,13g,and 13h). This resulted in Rs (XZ) and ε values from individual, thin section-scale finite strain analyses from strain domains 3-5 likely significantly underestimating the true finite strain magnitude within these domains. Instead, we interpret that finite strain in strain domains 3-5 is more accurately represented by the average Rs (XZ) and ε values determined from macro-scale measurements of ductile thinning of the Cpm (Figures 10 and 11). Additionally, comparison of average Rs (XZ) and ε to average quartz CPO intensity reduces the effect of individual sample-to-sample variability (which is a common feature of large finite strain and CPO intensity data sets, e.g., N. J. Hunter et al., 2018;Long et al., 2011;Starnes et al., 2020;A. Yonkee, 2005;W. A. Yonkee et al., 2013), and allows for the comparison of data sets with robust averages.
For strain domains 1-2, we utilized the average (±1σ) of all Rs (XZ) and ε values from the micro-scale finite strain analyses within each strain domain, which are Rs (XZ) = 5.4 ± 1.4 and 10.2 ± 1.9, and ε = 1.14 ± 0.20 and 1.63 ± 0.12, respectively (Figures 10 and 11; Table 3). Within strain domains 3-5, we used the average Rs (XZ) and ε values obtained from macro-scale ductile thinning measurements of the Cpm (Figures 10 and 11; Table 2). These values, which are reported with the total error associated with the measured range of ductilely thinned and regional undeformed thicknesses of the Cpm, are Rs (XZ) = 23.5 ± 4.0 and ε = 2.22 ± 0.11 for strain domain 3, ei-0------------------- u C ---Z ., 5 , .1so A -5D5_.. --Error envelor for s 1 3-SD -Rs[XZ EquaJon 1 I ]-((B ±-,14J ottalt(o.020-± o.@09) we; r ruJx" Error e Tectonics 3).
Graphing B versus Rs (XZ) yielded an overall positive correlation for data from strain domains 1-3, with an increase from B values of 0.52 ± 0.14 to 0.83 ± 0.08 as Rs (XZ) increases from 5.4 ± 1.4 to 23.5 ± 4.0 (Figure 13a). Strain domains 1 and 2 yielded similar mean B and Jpf values while domain 2 exhibits higher mean Rs and ε values (Figure 13). This relationship suggests that CPO intensity and finite strain may not scale perfectly at low strain (e.g., Rs ≤ ∼5-10 or ε ≤ ∼1.14-1.63). Data from strain domains 3-5 yielded a greatly diminished increase in B from 0.83 ± 0.08 to 0.92 ± 0.06 as Rs (XZ) increases from 23.5 ± 4.0 to 282 ± 122 (Figure 13a). The diminished increase in B at Rs (XZ) values greater than 23.5 ± 4.0 results in very large errors for Rs (XZ) , rendering any equation derived from the relationship between strain domains 3-5 ineffective for constraining Rs (XZ) . Additionally, the likelihood of attainment of steady state fabrics at B = ∼0.90 results in in a breakdown of the finite strain-CPO intensity relationship, where strain would continue to accumulate while CPO intensity remained the same. Therefore, we present a best-fit linear equation that is derived only from the relationship between strain domains 1-3:
Rs(XZ) = ((B ± 0.14) -0.35)/(0.020 ± 0.009) for B values between 0.52 ± 0.14 and 0.83 ± 0.08 (1) (R 2 = 0.93).
Graphing Jpf versus Rs [XZ] yielded a positive correlation for data from strain domains 1-3, with an increase from Jpf values of 1.68 ± 0.38 to 2.97 ± 0.74 as Rs (XZ) increases from 5.4 ± 1.4 to 23.5 ± 4.0. However, data for strain domains 3-5 do not show an overall increase, with Jpf values largely overlapping within error as Rs (XZ) increases from 23.5 ± 4.0 to 282 ± 122, most likely due to the achievement of a steady state fabric (Figure 13b). Therefore, we present a best-fit linear equation that is derived only from the relationship between strain domains 1-3: Rs(XZ) = ((Jpf ± 0.52) -1.14)/(0.069 ± 0.048) for Jpf values between 1.68 ± 0.38 and 2.97 ± 0.74
(2) (R 2 = 0.93).
Graphing B versus ε yielded a positive correlation for data from strain domains 1-3, with an increase from B values of 0.52 ± 0.14 to 0.83 ± 0.08 as ε increases from 1.14 ± 0.20 to 2.22 ± 0.11. Data from strain domains 3-5 yielded a greatly diminished increase in B from 0.83 ± 0.08 to 0.92 ± 0.06 as ε increases from 2.22 ± 0.11 to 3.94 ± 0.32 (Figure 13a), most likely as a result of steady state fabric, which (similar to above) renders any equation derived from the relationship between strain domains 3-5 ineffective. Therefore, we present a best-fit linear equation that is derived only from the relationship between strain domains 1-3: ε = ((B ± 0.57) -0.01)/(0.370 ± 0.310) for B values between 0.52 ± 0.14 and 0.83 ± 0.08 (R 2 = 0.78). (3) Graphing Jpf versus ε yielded a positive correlation for data from strain domains 1-3, with an increase from Jpf values of 1.68 ± 0.38 to 2.97 ± 0.74 as ε increases from 1.14 ± 0.20 to 2.22 ± 0.11. Data for strain domains 3-5 do not show an overall increase, with Jpf values largely overlapping within error as ε increases from 2.22 ± 0.11 to 3.94 ± 0.32 (Figure 13b), most likely due to development of a steady state fabric. Therefore, we present a best-fit linear equation that is derived only from the relationship between strain domains 1-3: ε = ((Jpf ± 2.46) -0.33)/(0.980 ± 1.570) for Jpf values between 1.68 ± 0.38 and 2.97 ± 0.74 (4) (R 2 = 0.79).
Figure 13. Graphs of (a) average cylindricity and (b) average density norm versus average Rs (XZ) for strain domains (abbreviated "SD") 1-5, along with best-fit lines for data from SD1-3 and their corresponding equations, 1σ error envelopes, and R 2 values. Graphs of (c) cylindricity and (d) density norm versus Rs (XZ) (±1σ) for individual samples where finite strain and fabric intensity were measured, along with best-fit lines and R 2 values. For SD3-5, cyclindricity and density norm were plotted versus the average Rs (XZ) calculated from Cpm structural thinning measurements. Graphs of (e) average cylindricity and (f) average density norm versus average octahedral shear strain (ε) for SD1-5, along with best-fit lines for data from SD 1-3 and their corresponding equations, 1σ error envelopes, and R 2 values. Graphs of (g) cylindricity and (h) density norm versus ε for individual samples where finite strain and fabric intensity were measured, along with best-fit lines and R 2 values. For SD3-5, cyclindricity and density norm were plotted versus the average ε calculated from Cpm structural thinning measurements. Errors shown for cylindricity and density norm (a, b, e, and f) are 1σ. Errors shown for Rs (XZ) and ε for strain domains 1-2 are at a 1σ-level, but errors shown for Rs [XZ] and ε for strain domains 3-5 represent the total error from Cpm structural thickness measurements (a, b, e, and f) (see Table 3 footnote The principal utility of Equations 1-4 is for estimation of the first-order, average finite strain magnitude within packages of ductilely sheared, quartz-rich LS tectonics from which B and/or Jpf values are available but no finite strain data can be collected. This is a scenario that commonly arises as a consequence of complete recrystallization within the high-strain portions of ductile shear zones, which has obliterated any deformed markers from which finite strain can be measured. Here, we discuss the practical limitations of these equations.
Our data were collected from quartz-rich (≥∼90% quartz) LS tectonites that experienced plane strain to gentle flattening strain (average k = 0.9). Therefore, the equations derived here likely apply best to rocks with a similar lithology and 3D strain geometry. Additionally, quartzites in the Northern Snake Range likely achieved a steady state fabric in the eastern portion of the Hendry's Creek transect, corresponding to B ≥ ∼0.90 and Jpf ≥ ∼2.50. As such, caution must be taken when applying Equations 1-4 to B values ≥ ∼0.90 and Jpf ≥ ∼2.50, and researchers are encouraged to evaluate the possibility (or lack thereof) of steady state CPO fabrics within their own data sets.
Error magnitudes (1σ) for average B and Jpf values from strain domains 1-5 range between ±0.06-0.14 and ±0.31-0.74, respectively, and do not exhibit a trend with increasing strain magnitude (Figure 13; Table 3). Due to the variability of individual CPO intensity values in our data set, which is typical of other large CPO intensity data sets (e.g., N. J. Hunter et al., 2018;Larson et al., 2023;Starnes et al., 2020), Equations 1-4 are best applied to CPO intensity data sets that are large enough to yield robust averages. CPO intensity data sets that are numerous enough to be divided into domains that can be expressed as averages will result in a more representative range of Rs (XZ) and ε estimates compared to individual CPO intensity datapoints. Additionally, error magnitudes for average Rs (XZ) values in our data set increase significantly with increasing strain magnitude, which is common for large finite strain data sets (e.g., Long et al., 2011Long et al., , 2017;;Vitale & Mazzoli, 2009;A. Yonkee, 2005;W. A. Yonkee et al., 2013), and will result in a greater predicted range of Rs (XZ) values with higher CPO intensity when applying Equations 1 and 2. Because mica content within quartz-rich rocks can affect the development of CPO distributions (e.g., N. J. Hunter et al., 2016;Larson et al., 2017;Little et al., 2015;Starkey & Cutforth, 1978), measuring mica area percentage from quartz CPO samples is important to evaluate whether or not mica content is correlated with CPO intensity before applying Equations 1-4.
The lowest average B and Jpf values that we obtained from any of the strain domains in the Northern Snake Range are 0.52 ± 0.14 and 1.68 ± 0.38, respectively (Table 3), and therefore Equations 1 and 2 are not calibrated to lower B and Jpf values. Based on our data set, B and Jpf values that fall below these lower cutoff values are interpreted to correspond to average Rs (XZ) values <5.4 ± 1.4 and ε < 1.14 ± 0.20. Equations 1 and 3 allow estimating a first-order range of average Rs (XZ) and ε values for average B values between 0.52 and 0.83, and Equations 2 and 4 allow estimating a first-order range of average Rs (XZ) and ε values for Jpf values between 1.68 and 2.97. For B and Jpf values that are higher than these upper cutoff values, our data from strain domains 3-5 demonstrate that Rs (XZ) and ε either can only be constrained with exceptionally high errors (for the case of B; Figures 13a and 13e) or cannot be constrained (for the case of Jpf; Figures 13b and 13f). Below, we test the applicability of Equations 1 and 3 by applying them to transects across the Pioneer metamorphic core complex (Idaho) and the Himalayan Main Central thrust (MCT) and South Tibetan detachment system (STDS) in which both B and finite strain data have been collected. We also apply Equations 1 and 3 to portions of these shear zones in which B data were collected but finite strain data are lacking, in order to make a first-order estimate for average finite strain magnitude.
The Pioneer metamorphic core complex is a migmatite-cored core complex in central Idaho, USA (e.g., Silverberg, 1990). The Wildhorse Detachment system is a major extensional structure that borders the southern, western, and northern extent of the footwall of the Pioneer core complex. McFadden et al. (2024) collected 13 samples from mylonitic rocks at structural depths ranging from 10 to 210 m below the Wildhorse Detachment system for CPO intensity and finite strain data collection. Samples from McFadden et al. (2024) are predominantly quartz-rich, with eight samples containing over 95% quartz and the remaining five containing 35%-59% quartz. Cylindricity varies between 0.24 and 0.88 (average 0.66 ± 0.18; n = 13) and finite strain is between Rs (XZ) = 3.8-16.6 (average 10.0 ± 3.6; n = 9) (Figure 14a) and was assumed to have approximately plane strain geometry.
Using Equation 1, samples where B was available and larger than our minimum B = 0.52 ± 0.14 threshold yield Rs (XZ) values between 3.5 and 26.5 (n = 12; excluding one sample with B = 0.24) (Figure 14a), which overlaps within error but is generally higher than the 3.8-16.6 Rs (XZ) range measured on these samples by McFadden et al. (2024) (Figure 14a). Rs (XZ) calculated from the average cylindricity of all samples (B = 0.66 ± 0.18; n = 13) yielded an average Rs (XZ) of 15.7 with a total error range of Rs (XZ) values between 6.0 and 41.3 (or: Rs (XZ) = 15.7 + 25.6/-9.7) (Figure 14a). Our calculated average Rs (XZ) of 15.7 is slightly higher than the average of Rs 2024), particularly within the lower part of the error range (i.e., Rs (XZ) = 6.0-15.7) (Figure 14a). 2024) did not present octahedral shear strain estimates, but when Equation 3 is applied to their individual B data where B is greater than our minimum threshold, it yields ε values ranging from 1.16 to 2.41 (n = 12; Figure 14a). Application of Equation 3 to the average B of all samples (B = 0.66 ± 0.18; n = 13) yields an average ε of 1.82 and a total error range between 0.15 and 20.74 (or: ε = 1.82 + 18.92/-1.67) (Figure 14a).
The MCT is a top-to-the-south, Miocene ductile shear zone that is likely the largest-displacement structure in the Cenozoic Himalayan orogen (e.g., Gansser, 1964;LeFort, 1975;Martin, 2016;Searle et al., 2008). In the eastern portion of the Himalaya in Bhutan, Starnes et al. (2020) collected B values from quartzites on a transect across the MCT. They obtained B values of 0.32, 0.47, and 0.38 between 2.2 and 1.3 km below the mapped reference position of the MCT, B values of 0.39-0.93 (n = 16; average = 0.73) between 0.7 km below and 2.4 km above the reference position, and B values of 0.52 and 0.37 at 7.6 and 11.7 km above the reference position, respectively (Figure 14b). Long et al. (2016) collected thin section-scale finite strain data (Rf-φ method) from stretched detrital quartz clasts within quartzite, phyllite, and schist along this same transect, and measured an average Rs (XZ) value of 3.3 from three finite strain analyses distributed between 2.3 and 1.0 km below the reference position of the MCT. These Rs (XZ) values record predominantly flattening strain and fall below the 5.4 minimum Rs (XZ) cutoff value of Equation 1, thus implying predicted B values of 0.52 or lower, which is in agreement with the 0.32-0.47 range of B values obtained from this interval by Starnes et al. (2020) (Figure 14b). Between 30 and 50 km along-strike to the east and 50-70 km along-strike to the north of the B transect of Starnes et al. (2020), Long et al. (2011Long et al. ( , 2017) ) measured an average Rs (XZ) value of 3.8 from 22 finite strain analyses distributed between 2.5 and 5.4 km above the mapped reference position of the MCT, and an average Rs (XZ) value of 2.3 from 31 finite strain analyses distributed between 5.4 and 10.7 km above this reference position. These average Rs (XZ) values fall below the 5.4 minimum Rs (XZ) cutoff value of Equation 1, implying predicted B values of 0.52 or lower, which is in agreement with the B values of 0.52 and 0.37 obtained by Starnes et al. (2020) for samples at 7.6 and 11.7 km above the MCT reference position (Figure 14b). Between 0.7 km below and 2.4 km above the mapped reference position of the MCT, which is an interval for which there are no finite strain data available due to complete recrystallization, Starnes et al. (2020) obtained an average B value of 0.73. Using Equation 1 (including 1σ uncertainty), this corresponds to an average predicted Rs (XZ) value of 18.8, with a total error range of Rs (XZ) values between 8.1 and 46.9 (or: Rs (XZ) = 18.8 + 28.1/-10.7) (Figure 14b). Using Equation 1 on individual samples between 0.7 km below and 2.4 km above the mapped reference position of the MCT, with B values between 0.55 and 0.93 (n = 15), yields Rs (XZ) between 8.5 and 29.0, which fall within error of the Rs (XZ) range calculated from the average B value (Figure 14b). Applying Equation 3 to these same individual B data yields ε between 1.43 and 2.54, and applying Equation 3 to the average B value of 0.73 yields an average ε of 1.99 with an error range between 0.24 and 21.77 (or: ε = 1.99 + 19.78/-1.75) (Figure 13e).
The STDS is a top-down-to-north, normal-sense, Miocene ductile shear zone in the Himalayan orogen (e.g., Burchfiel et al., 1992;Kellett et al., 2018). Long et al. (2019) collected B data from quartzites on a transect across the STDS in northwestern Bhutan. They obtained a B value of 0.21 at 1,550 m below the mapped reference position of the detachment, B values of 0.48-0.87 (n = 5; 0.64 average) between 1,325 and 0 m below the reference position, and a B value of 0.10 at 150 m above the reference position (Figure 14c). Long et al. (2019) used the Rf-φ method on thin section-scale, stretched detrital quartz clasts, and measured an average Rs (XZ) value of 2.6 (n = 5) between 175 and 775 m above the reference position of the detachment.
Using Equation 1, these data imply Rs (XZ) values <5.4 at 1,550 m below and 150 m above the reference position of the detachment, which is in agreement with the 2.6 average Rs (XZ) value obtained from finite strain analyses between 175 and 775 m above the reference position. For the 0.64 average B value between 1,325 and 0 m below the reference position of the detachment, Equation 1 predicts an average Rs (XZ) value of 14.5, with a total Rs (XZ) error range between 5.2 and 39.1 (or: Rs (XZ) = 14.5 + 24.6/-9.3) (Figure 14c). Though no finite strain data are available for this interval, it was interpreted by Long et al. (2019) as the highest-strain portion of the detachment system. Applying Equation 1 to individual B data within this high strain zone yields Rs (XZ) between 6.5 and 26.0, which falls within error of the value calculated from average B (Figure 14c). Applying Equation 3to individual B values between 1,325 and 0 m below the reference position of the detachment (B = 0.48-0.87; n = 5) yields ε values between 1.32 and 2.37. When applied to the average B value of 0.64 for this same reference position, it yields an average ε of 1.76, with a total range between 0.12 and 20.33 (or: 1.76 + 18.57/-1.64).
1. In the southern part of the Northern Snake Range, the NSRD footwall exhibits a dramatic finite strain gradient, with average Rs (XZ) increasing from 5.4 ± 1.4 to 282 ± 122, ε increasing from 1.14 ± 0.20 to 3.94 ± 0.32, lineation-parallel extension increasing from 119 ± 32% to 1,387 ± 387%, and foliation-normal shortening increasing from 59 ± 7% to 94 ± 1% between the western and eastern flanks of the range. The NSRD footwall accommodated 21.1 km (340%) of total Eocene-Oligocene ductile extension. 2. Average B increases from 0.52 to 0.83 as average Rs (XZ) increases from 5.4 to 23.5 and ε increases from 1.14 to 2.22. Average B increases more gradually from 0.83 to 0.92 as average Rs (XZ) increases from 23.5 to 282 and ε increases from 2.22 to 3.94. Rs (XZ) is related to B through Equation 1: Rs (XZ) = ((B ± 0.14) -0.35)/ (0.020 ± 0.009) for B values between 0.52 and 0.83 and Rs (XZ) values between 5.4 and 23.5. Equations comparing B and ε produce large errors, demonstrating that further analysis is required to determine the relationship between B and ε. 3. Average Jpf increases rapidly from 1.68 to 2.97 as average Rs (XZ) increases from 5.4 to 23.5 and ε increases from 1.14 to 2.22. Average Jpf remains approximately constant above average Rs (XZ) values of 23.5 and ε values above 2.22. Rs (XZ) is related to Jpf through Equation 2: Rs (XZ) = ((Jpf ± 0.52) -1.14)/(0.069 ± 0.048) for Jpf values between 1.68 and 2.97 and Rs (XZ) values between 5.4 and 23.5. Equations comparing Jpf and ε produce large errors; further analysis is required to determine the relationship between Jpf and ε. 4. Equations 1 and 2 allow calculating first-order estimates of average Rs (XZ) as a function of B and Jpf, and are best applied to quartz CPO intensity data sets that are large enough to calculate robust averages, were collected from quartz-rich LS tectonites, and have experienced approximate plane strain conditions. 5. Equation 1 yields compatible ranges for intervals above and below the highest-strain portions of the Himalayan MCT and STDS, and within the footwall of the Wildhorse Detachment system. Equation 1 yields an average Rs (XZ) value of ∼16 in the footwall of the Wildhorse Detachment system, and average Rs (XZ) values of ∼16-19 and ∼14.5 for the highest-strain portions of the MCT and STDS, respectively.
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