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1 Department of Geology and Geophysics, University of Wisconsin—Madison, 1215 West Dayton Street, Madison, Wisconsin 53706, USA
2 Department of Geosciences, University of Wisconsin—Milwaukee, 3209 North Maryland Avenue, Milwaukee, Wisconsin 53211, USA
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONGEOLOGY OF THE EAST-CENTRAL...CENTIMETER-SCALE ANALYSISMETER-SCALE ANALYSISKILOMETER-SCALE ANALYSISCONCLUSIONSAPPENDIX 1. BOOTSTRAP RESAMPLINGAPPENDIX 2. INCLINED...REFERENCES CITED |
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10 between layers. Bulk composition controls variations in deformation of the different layers. At the kilometer scale, variation in finite-strain magnitude and orientation in similar rock types both within and outside the shear zone demonstrates that deformation inside the zone was relatively intense. Comparing these results to numerical models of heterogeneous regional deformation, we estimate that the angle of oblique convergence inside the zone was 15 ± 10°, while outside it was greater than 60°. These kilometer-scale results imply regional deformation was moderately strike-slip partitioned during the Late Cretaceous and suggest regional effective viscosity varied by a factor between 6 and 17. At each scale of observation, the apparent range of effective viscosity varies by an order of magnitude or less. Consequently, we infer that relatively modest strength variations produced the structures observed at hand sample to tectonic scales.
Key Words: Rheology • strain • structural analysis • Sierra Nevada • viscosity
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONGEOLOGY OF THE EAST-CENTRAL...CENTIMETER-SCALE ANALYSISMETER-SCALE ANALYSISKILOMETER-SCALE ANALYSISCONCLUSIONSAPPENDIX 1. BOOTSTRAP RESAMPLINGAPPENDIX 2. INCLINED...REFERENCES CITED |
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Rheology, the relationship between stress and strain rate, is traditionally studied in the laboratory. Numerous studies have used results of experimental deformation to infer the rheology of naturally deformed heterogeneous rocks (e.g., Tullis et al., 1991; Gilotti, 1992; Handy, 1994; Abalos et al., 1996; Handy et al., 1999). This approach is very informative but is limited to microstructure-scale analysis and requires considerable extrapolation due to technical limitations on experimental strain rates (Paterson, 1987, 2001).
In this study, we take a different approach to the study of natural rock rheology. We quantify deformation in naturally deformed rocks at several scales and compare observations among various constituent rock types in light of numerical models. This approach provides an estimate of the range of rock viscosity present at each scale studied. The Late Cretaceous Sierra Nevada is an ideal region for our study because (1) the rocks are compositionally and mechanically heterogeneous at several scales, (2) strain is quantifiable because deformation and metamorphism have not completely obscured primary features such as bedding, and (3) the regional tectonic history is relatively well understood. Thus, from hand sample to tectonic scales, our results provide constraints on rock rheology as well as insight into how rheological heterogeneity produces structures and localization of deformation.
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GEOLOGY OF THE EAST-CENTRAL SIERRA NEVADA |
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TOPABSTRACTINTRODUCTIONGEOLOGY OF THE EAST-CENTRAL...CENTIMETER-SCALE ANALYSISMETER-SCALE ANALYSISKILOMETER-SCALE ANALYSISCONCLUSIONSAPPENDIX 1. BOOTSTRAP RESAMPLINGAPPENDIX 2. INCLINED...REFERENCES CITED |
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5 km thick and consists of moderately to steeply dipping Late Triassic to Early Jurassic lapilli tuffs, tuff breccias, and volcaniclastic sedimentary rocks, along with occasional lava flows and hypabyssal intrusions (Kistler, 1966a, 1966b; Brook et al., 1974; Greene, 1995; Greene and Schweickert, 1995). The upper Koip sequence is an 3.5-km–thick section of Middle Jurassic to mid-Cretaceous metavolcanic rocks exposed in the western portions of the Ritter Range pendant (Fiske and Tobisch, 1978; Tobisch et al., 2000). The section consists of shallowly to moderately dipping volcanic breccias, ash-flow tuffs and assorted other volcanic rocks (Fiske and Tobisch, 1978, 1994). Previous workers have investigated the regional deformation history of the Koip sequence metavolcanic rocks using a combination of detailed field mapping, structural analysis, and radiometric dating (Tobisch et al., 1977, 1986, 1995, 2000; Tobisch and Fiske, 1982; Tobisch, 1984; Schweickert and Lahren, 1987; Schweickert et al., 1994; McNulty, 1995; Sharp et al., 2000). These workers suggest that the lower Koip sequence was tectonically shortened 35%–50% through a combination of heterogeneous but penetrative strain, reverse faulting, and local downward flow of wall rock associated with pluton emplacement. Both shortening estimates and bedding dips are lower in the upper Koip sequence rocks in the less deformed western Ritter Range pendant (Tobisch et al., 1995).
Late Cretaceous Deformation and Tectonic History
Relative motion between the North American and Farallon plates rotated progressively clockwise throughout the Late Cretaceous (Engebretson et al., 1985; Kelley, 1993; Kelley and Engebretson, 1994). Regional deformation occurred in the east-central Sierra Nevada in response to these tectonic boundary conditions, but particularly intense deformation localized in a series of NW-striking shear zones (Fig. 2) that stepped NE over time (Tobisch et al., 1995; Sharp et al., 2000). We describe deformation within the youngest of these structures, the Gem Lake shear zone. Previous authors describe deformation in the older structures (Tong, 1994; McNulty, 1995; Tobisch et al., 1995; Sharp et al., 2000).
The Gem Lake shear zone (Fig. 1) is part of the hypothesized Sierra Crest shear-zone system, a zone of Late Cretaceous dextral transpression that continues for 200 km near the eastern margin of the Sierra Nevada batholith (Tikoff and Greene, 1997). South of the Gem Lake shear zone, the shear-zone system continues as the Rosy Finch and proto-Kern Canyon shear zones (Greene and Schweickert, 1995; Tikoff and Greene, 1997; Tikoff and Saint Blanquat, 1997), and to the north it may continue as the Cascade Lake shear zone (Tikoff et al., 2004).
Gem Lake Shear Zone
The Gem Lake shear zone is an 1-km–wide zone of mylonitic fabric that accommodated at least 20 km of dextral offset (Greene and Schweickert, 1995). Similar to other Late Cretaceous shear zones of the east-central Sierra Nevada, the Gem Lake shear zone strikes NNW and dips moderately to steeply SW. Exposures of the shear zone throughout the Northern Ritter Range pendant are excellent, but exceptional three-dimensional exposures are present in the vicinity of Gem Lake (Fig. 2).
Cleavage, defined primarily by phyllosilicate alignment, is prominently developed in the region and has similar, NW-striking, steeply SW-dipping orientations inside and outside the shear zone (Figs. 3A and 3B). In detail, cleavage dips 15° more steeply inside the shear zone than outside. Lineation, defined by stretched mineral grains and grain aggregates, varies from steeply SE-pitching outside to moderately NW-pitching inside the shear zone (Figs. 3C and 3D).
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100 m. For example, 1 km east of the study area, Rush Creek metasedimentary rocks are folded and faulted (Greene, 1995; Greene and Schweickert, 1995). With decreasing distance from the shear zone, these folds, bedding, and cleavage in the Rush Creek sequence rocks become parallel to shear-zone fabric. Centimeter- to decimeter-scale kink folds exist in portions of the Ritter Range pendant (Tobisch and Fiske, 1976) but are especially well developed in the Gem Lake shear zone (Fig. 3E). The folds deform the regional cleavage and record the last stage of regional deformation. Although conjugate sets of kink folds exist locally throughout the region, a single set of kinks with steeply dipping, NW-striking axial planes is predominant and is the only orientation observed in the shear zone. These folds sometimes affect metamorphic veins, which are relatively abundant inside the shear zone are rare outside.
Deformation within the shear zone took place at greenschist to sub-greenschist facies conditions (Greene and Schweickert, 1995). These relatively low-grade metamorphic conditions are distinct from the regional lower amphibolite facies metamorphism characteristic of most of the Ritter Range pendant (Hanson et al., 1993; Sorensen et al., 1998) and may be related to late deformation on the shear zone (Sharp et al., 2000).
Deformation on the Gem Lake shear zone began after emplacement of the 100-Ma (Bateman, 1992) Rush Creek granodiorite and continued until at least 93 Ma, the age of the syntectonic Kuna Crest granodiorite (Coleman et al., 2004) in which strong solid-state fabric is locally developed due to shear-zone deformation (Tikoff and Greene, 1997). 40Ar/39Ar dating of peak and retrograde metamorphic mineral growth suggests that regional cleavage development in the Koip sequence had ceased by 82–80 Ma, before the region cooled through the biotite closure temperature (Sharp et al., 2000). Thus, shear-zone deformation may have spanned up to 20 m.y. (Bentley, 2004).
Cleavage and Microstructures outside the Gem Lake Shear Zone
Tobisch (1984) examined cleavage development outside the Gem Lake shear zone. We use Tobisch's results as a reference against which to compare observations of cleavage development inside the shear zone. In lithic-lapilli–bearing volcanic rocks of the Koip sequence, Tobisch (1984) recognized two sequential stages of fabric development. The first stage corresponds to relatively low-strain deformation in which the primary mechanism through which lapilli accommodated strain was rigid body rotation. However, as strain increased and lapilli rotated into general parallelism with the XY plane of the strain ellipsoid (and therefore with the cleavage plane), rotation progressively became less important. Lapilli deformation was then accommodated primarily by intracrystalline strain and to a lesser degree by solution-precipitation processes.
Strain in the matrix was accommodated throughout deformation by progressive rotation and recrystallization of mica grains, along with minor solution-precipitation. In relatively undeformed samples, a weak shape-preferred orientation of mica grains exists about the poorly defined cleavage direction. As bulk strain increased, mica grains became progressively better aligned. Tobisch (1984) attributed the development of this strong shape-preferred orientation to a combination of rotation toward and recrystallization of mica grains within the XY plane of the strain ellipsoid.
Cleavage and Microstructures inside the Gem Lake Shear Zone
Cleavage is better developed inside the Gem Lake shear zone than outside. Even in rocks with no macroscopic markers (e.g., aphanitic andesite flows), variations in the intensity of cleavage development allow the gradational boundaries of the shear zone to be mapped (Fig. 2). As we discuss at greater length later, cleavage orientation and intensity are not homogeneous within the shear zone. Rather, these characteristics vary between stratigraphic layers.
Comparisons of thin-section observations of lapilli deformation behavior inside and outside the shear zone indicate different deformation conditions. For example, Figure 4A shows moderate ductile deformation of clasts from outside the shear zone, while Figure 4B shows a clast of similar composition within the shear zone that is fractured and extended, and provided space for precipitation of oxide minerals, presumably from metamorphic fluids. Such fractures occasionally occur in feldspar lithic fragments and feldspar-rich clasts in layers of volcaniclastic rock affected by the shear zone. In contrast, most clasts flowed through a combination of crystal-plastic processes and rotation, as described by Tobisch (1984) for similar rocks outside the shear zone. Grain boundary sliding is commonly difficult to recognize in thin section but may be another important deformation mechanism in clasts and particularly in the matrix.
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These fabric variations both within and outside the Gem Lake shear zone qualitatively demonstrate the heterogeneity of deformation in the region at several scales. Relating observations of heterogeneous deformation at one scale to observations at other scales requires a quantitative, scale-independent measure of deformation. Finite strain provides one such measure, and we now consider deformation at the centimeter, meter, and kilometer scales from a finite-strain perspective.
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CENTIMETER-SCALE ANALYSIS |
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TOPABSTRACTINTRODUCTIONGEOLOGY OF THE EAST-CENTRAL...CENTIMETER-SCALE ANALYSISMETER-SCALE ANALYSISKILOMETER-SCALE ANALYSISCONCLUSIONSAPPENDIX 1. BOOTSTRAP RESAMPLINGAPPENDIX 2. INCLINED...REFERENCES CITED |
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0.5 cm to more than 10 cm. All clast types except pumice were sufficiently abundant to produce reliable results at all outcrops. Pumice shards do not accurately record finite strain because of large variations in primary shape (Tobisch et al., 1977) and because they undergo significant volume loss during deformation (Ragan and Sheridan, 1972). We therefore present results of pumice finite strain only for comparison with results from the other clast populations that more accurately record deformation.
Strain Analysis Methodology
We calculated two-dimensional finite strain for each clast population on each tracing using the Rf/
method (Ramsay, 1967; Dunnet, 1969; Lisle, 1985). The method uses the final aspect ratios (Rf) and orientations () of a population of marker clasts to calculate the direction of maximum stretching (mean) and an amount of strain (Rs) recorded by the population. This method assumes passive behavior of clasts in bulk pure shear and constant-area deformation with shortening perpendicular and elongation parallel to the local cleavage orientation. The method does not assume initially spherical clast shapes or an initial random distribution of clast orientation (Dunnet and Siddans, 1971) and can be used to estimate the strength of any preexisting fabric. Thin-section observations of foliation bending around clasts demonstrate that the assumption of passive clast behavior is incorrect (Fig. 4). Because the clasts (excluding pumice) are more competent than the bulk rock, the Rf/ analysis produces a minimum estimate of the strain experienced by each clast population.
To test the internal consistency of Rf/ results, we conducted bootstrap resampling of the data for each clast population on each measured face (see Appendix 1). To calculate three-dimensional finite strain from these two-dimensional results, each clast population's mean and Rs values for each face were combined into a three-dimensional strain ellipsoid using the method of Robin and Launeau (Robin, 2002; Launeau and Robin, 2005). Results for each ellipsoid include the eigenvectors and eigenvalues of the three principal finite-strain axes. The eigenvectors describe the orientation of the principal strain axes in geographic space. Estimated errors derived from bootstrap analysis result in orientation variability of less than 2° at the 95% confidence level. The eigenvalues are used to calculate a finite-strain magnitude, 
s where s = 0 describes a sphere and values increase as ellipsoid shapes grow more distorted (Nadai, 1963; Hsu, 1966; Hos-sack, 1968; Owens, 1974; Brandon, 1995). This parameter is useful because it allows comparison of strain magnitude from deformations with different strain paths. Estimated errors derived from bootstrap analysis result in magnitude variability of 5% at the 95% confidence level. Eigenvalues are also used to calculate a shape parameter, 
(Nadai, 1963; Hsu, 1966; Hossack, 1968; Owens, 1974; Brandon, 1995). Shape parameter values range from = –1, a perfectly prolate ellipsoid, to = +1, a perfectly oblate ellipsoid. A value of = 0 describes a plane strain ellipsoid.
Matrix Strain
We attempted to calculate finite strain in the matrix using the Fry method (Fry, 1979) and the normalized Fry method (Erslev and Ge, 1990; McNaught, 2002). Results from these methods, however, were unreliable for both thin-section–scale and outcrop-tracing–scale analyses. Calculated matrix strain axes were commonly oriented at highly oblique angles to observed field fabrics. Additionally, calculated strain magnitude was frequently lower than clast strain calculated with the Rf/ technique.
We ascribe the unreliability of our matrix strain estimates to several characteristics of the rocks that violate the assumptions of the method: (1) clasts had some initial fabric; (2) some clasts deformed in a brittle-ductile manner; and (3) clasts occasionally interact. These complications were compounded by the relatively small number of clasts (30–125) measured on each face. While 30 clasts are sufficient for the Rf/ technique (Lisle, 1985, p. 10), center-to-center strain analysis methods work best with 200 or more objects (Erslev and Ge, 1990). We do not consider our matrix strain results further.
Clast Population Strain
Three-dimensional finite-strain results for all clast populations at each outcrop are shown in Table 1 and on Figure 5. Strain orientation, magnitude, and shape are shown on Figure 5. Orientations of calculated lineations and poles to foliation are plotted on equal area net projections. Magnitude and shape are shown on Nadai-Hsu plots of s versus . For comparison, orientations of field-measured clast- and mineral-stretching lineation and foliation are plotted on the equal area net projections on Figure 5.
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10°. Average strain magnitude for all clasts is s = 0.82. This value is comparable to the strain magnitude of s = 0.77 measured in similar rocks 3 km southwest of the Gem Lake shear zone (Tobisch et al., 1977).
Inside the Gem Lake shear zone, the calculated XY plane of the strain ellipsoid for all clast types is consistently subparallel (<5°) to field-measured cleavage and clast-stretching foliation orientation (Fig. 5), which strikes a few degrees more easterly and dips a few degrees more steeply than outside the shear zone. The calculated lineation pitches moderately NW, in good agreement with field measurements, although variation of up to 70° exists between different clast populations at some sites (e.g., GL5).
Strain magnitude inside the shear zone varies with both clast type and stratigraphic layer composition. In the volcaniclastic conglomerate layers (GL6, 9, and 48), average clast strain magnitude varies from s = 0.54–1.18, consistently lower than values in the clast-rich tuff (s = 1.24–1.46). Felsic volcanic clasts record less strain (average s = 0.92) than quartz or intermediate volcanic clasts (average s = 1.39 and 1.46, respectively). Pumice clasts frequently record appreciably higher strain magnitudes than other clast types (e.g., GL6 and GL9), probably due in part to volume loss.
Strain ellipsoid shape shows no clear trends relative to clast type, layer composition, or bulk finite strain. At some outcrops, the strain ellipsoid is consistent for all clast types (e.g., oblate at GL7, prolate at GL9). At other outcrops, we observe no consistent strain ellipsoid geometry (GL4).
Constraints on Clast Effective Viscosity Variation
The different magnitudes of finite strain recorded by different clast populations provide evidence of their relative effective viscosities (Gay, 1968a; Lisle et al., 1983; Treagus and Treagus, 2002). Following Treagus (1999), we use the term effective viscosity to refer to the bulk flow behavior of a body of rock over a finite period of time.
For example, the observation that all clast types record strain magnitudes that vary by substantially less than an order of magnitude suggests that the range of effective viscosities is restricted to an order of magnitude or less, assuming Newtonian rheological behavior. This estimate agrees with previous estimates of the range of effective viscosities displayed by various rock types, which is generally 10 or less (Gay, 1968b; Gay and Fripp, 1976; Huber-Aleffi, 1982; Lisle and Savage, 1982; Lisle et al., 1983; Roday et al., 1990; Kanagawa, 1993; Treagus and Treagus, 2002), although some workers have reported contrasts of up to 125 between quartz veins and fine-grained sedimentary rocks (Shimamoto and Hara, 1976). We note that the relatively small range of apparent clast effective viscosities lends support to the idea that some rocks deform in a Newtonian or nearly Newtonian manner (Treagus, 1999; Treagus and Treagus, 2002). If clast deformation were appreciably non-Newtonian, the range of apparent effective viscosities would likely be much larger.
We can also use measured clast finite-strain values to create a rough estimate of the bulk strain in the Gem Lake shear zone. Gay (1968a) provides the following equation relating two-dimensional bulk strain (Rbulk) to clast strain (Rclast) for a given clast/bulk-rock viscosity ratio (V), assuming bulk pure shear and Newtonian rheologies:
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Using the minimum and maximum measured three-dimensional strain values in the shear zone, respectively s = 0.54 in volcaniclastic conglomerate and s = 1.46 in tuff, we calculate equivalent two-dimensional sectional Rclast values. Assuming a clast/bulk-rock viscosity ratio of V = 10, we use Equation (1) to calculate minimum and maximum Rbulk values. Converting the results back to s values, we arrive at a rough estimate of bulk strain in the shear zone in the range of 2.45 
s 2.90.
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METER-SCALE ANALYSIS |
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TOPABSTRACTINTRODUCTIONGEOLOGY OF THE EAST-CENTRAL...CENTIMETER-SCALE ANALYSISMETER-SCALE ANALYSISKILOMETER-SCALE ANALYSISCONCLUSIONSAPPENDIX 1. BOOTSTRAP RESAMPLINGAPPENDIX 2. INCLINED...REFERENCES CITED |
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Cleavage Orientation Analysis
Detailed examination of cleavage data indicates that orientation varies in different stratigraphic layers, both inside and outside the shear zone (Table 2). In general, layers in which cleavage is closely parallel to bedding tend to be finer grained with few or no clasts (e.g., clast-poor tuff, Fig. 4B). In coarser grained layers with larger angles between cleavage and bedding, mica is less abundant, and foliation is less well developed and is deflected around competent clasts (Fig. 4C).
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5° and less than 15° in layers affected by the shear zone (Table 2). These observations suggest that, although specific stratigraphic layers responded differently to the same bulk deformation, the range of deformation behavior shown by layers was relatively restricted. To place quantitative constraints on the different deformation behaviors of the stratigraphic layers, we use a model of strain refraction and cleavage development to interpret our cleavage orientation observations.
Comparison with Cleavage Refraction Model
Treagus (1983) presents a quantitative model of finite-strain refraction in layered media. Her results indicate that both orientation and magnitude of finite strain differ in adjacent layers of different effective viscosity subjected to the same boundary conditions. Using this model to study cleavage orientation requires several assumptions. First, we assume that cleavage represents a reasonable approximation of the XY plane of the finite-strain ellipsoid (Sorby, 1853; Siddans, 1972; Wood, 1974). Although cleavage orientation does not always precisely reflect finite strain (Williams, 1976, 1977; Hobbs et al., 1982), angular differences are usually less than 5° (Ghosh, 1982). This assumption is justified by the observation that measured finite-strain orientations in the shear zone are invariably subparallel to cleavage (within measurement error). Second, we assume constant Newtonian viscosities for all rock layers throughout deformation. Third, we assume bulk constant-volume deformation. Fourth, we assume strain compatibility between layers; contacts cannot be faults or other discontinuities. Finally, we assume plane strain deformation. Although deformation was demonstrably non-plane strain in the Gem Lake shear zone, we seek only first-order estimates of relative effective viscosity, and this assumption does not appreciably affect such estimates (Treagus, 1983).
We now present an overview of Treagus's (1983) model. Figure 6A schematically shows two layers, A and B, with different finite-strain magnitudes and orientations (represented by different cleavage orientations). The layers have Newtonian viscosities 
A and B. The viscosity ratio is V = B/A Cleavage orientation in each layer is measured with respect to the contact between the layers (bedding) and is described by angles 
A' and B', respectively. Figure 6B shows the relationship between cleavage orientation in layers A and B for various values of V, for the case when layer A has a finite-strain magnitude of s = 0.7 (R 
4). For example, the line for V = 0.2 on Figure 6B describes the relationship between cleavage orientations when layer A is five times stiffer than layer B. Figure 6C shows cleavage orientations for the case when finite-strain magnitude in layer A has increased to s = 1.4 (R 16).
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A' and B' from 0 to 20°. Additionally, we take the average cleavage/bedding angle of 15° in the porphyry layers as our reference (A' = 15°). Other layers have more intensely developed cleavage; therefore, we infer that they have lower effective viscosities than the porphyry. Consequently, on Figures 6D and 6E, we show only curves for V 1.
The range of observed cleavage/bedding angles in layers affected by the Gem Lake shear zone (A' = 15°, B' from 5° to 15°) is plotted as a gray box on Figures 6D and 6E. Comparing this shaded region with relative viscosity curves on Figure 6D, we estimate a maximum relative effective viscosity contrast between 10 and 100 (0.1 
V 0.01). We note, however, that the strain magnitude in layer A for which these curves are calculated is quite low (s = 0.7) and that actual strain in this layer is likely higher (cf. Table 1). Therefore, in Figure 6E, we show curves calculated for a bulk strain in layer A of s = 1.4, which is more compatible with our observations of clast strain. Again considering the data from layers affected by the shear zone, we estimate a maximum effective viscosity contrast of between 2 and 5 (0.5 V 0.2). Thus, as modeled bulk layer strain increases to realistic values, our estimates of effective viscosity contrast decrease (compare Figs. 6D and 6E). Consequently, we consider our cleavage-refraction–based estimate of effective viscosity contrast of 10 to be a maximum value.
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KILOMETER-SCALE ANALYSIS |
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TOPABSTRACTINTRODUCTIONGEOLOGY OF THE EAST-CENTRAL...CENTIMETER-SCALE ANALYSISMETER-SCALE ANALYSISKILOMETER-SCALE ANALYSISCONCLUSIONSAPPENDIX 1. BOOTSTRAP RESAMPLINGAPPENDIX 2. INCLINED...REFERENCES CITED |
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Transpression Models
The obliquely convergent nature of Late Cretaceous deformation of the east-central Sierra Nevada can be described by a transpressional tectonic model. Several variations of transpression have been proposed (see the following discussion). All of these models use an angle of oblique convergence, 
, which is measured from the planar boundary between two converging blocks. This angle can be related to the instantaneous relative rates of contraction and wrenching distributed throughout the deforming zone between the blocks. An angle of = 0° describes perfect strike-slip motion between blocks, = 90° describes orthogonal convergence between plates, and intermediate values describe oblique block convergence.
Most models of transpression predict vertical foliations (e.g., standard transpression of Sanderson and Marchini [1984] and Fossen and Tikoff [1993]; triclinic transpression of Jones and Holdsworth [1998] and Lin et al. [1998]). Only the inclined transpression model of Jones et al. (2004) predicts both the inclined foliations and lineations observed in the Gem Lake shear zone. Consequently, we use this model to place constraints on regional deformation kinematics.
Jones et al. (2004) demonstrate that the following deformation matrix describes deformation in an inclined zone during bulk oblique convergence:
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The coordinate system for this matrix is defined relative to the rigid inclined walls of the deforming zone. On Figure 8A, shear-zone coordinates Xs, Ys, Zs are distinct from geographic coordinates Xg, Yg, Zg. The Xs axis is horizontal within the inclined shear plane and points in the direction of wrenching. The Zs axis points updip within the inclined shear plane, and the Ys axis is perpendicular to the shear plane. The 
y term is calculated from the amount of shortening S within the zone: y = 1 – S, with 0 S 1. Thus, y = 1 is the original zone width (shortening value S = 0), and y decreases during oblique convergence. To conserve volume, this shortening is balanced by inclined extrusion of material parallel to Ys. The wrenching component of deformation in an inclined transpression zone is resolved into two simple shearing terms, one in the Xs direction as a function of Ys position (
xy), and the other in the Zs direction as a function of Ys position (zy).
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Several assumptions are inherent in forward modeling of finite strain. First, we assume geometric steady-state deformation, in which the rate of deformation may have varied in time but the bulk kinematics remained constant. This is distinct from kinematic steady-state deformation in which both the rate and kinematics of deformation remain constant over time. Second, we assume observed foliation and lineation provide a reasonable measure of finite-strain ellipsoid orientation. Third, we assume finite strain measured both inside and outside the Gem Lake shear zone records bulk finite strain experienced at the analysis locations. Fourth, we assume bulk strain reflects the kinematics of transpressional deformation and is not appreciably affected by local modifications of the regional strain field like those produced by some actively intruding plutons (e.g., McNulty et al., 2000; Paterson et al., 1998; Vigneresse et al., 1999). Fifth, the model requires strain incompatibilities between blocks (Fig. 7B), a simplification that could be resolved through use of gradual transitions (e.g., Robin and Cruden, 1994) that are beyond the scope of this analysis. Finally, we assume the region has undergone only minor (<2°) tilting and vertical axis rotation since the Late Cretaceous based on paleotopographic (Unruh, 1991) and paleomagnetic (Frei, 1986) analyses.
Finite strain outside the shear zone constrains initial conditions for the model. The XY plane of the strain ellipsoid outside the shear zone strikes 152° and dips 64° SW. Lineation pitches 80° SE on the foliation plane. Strain has an average magnitude of s = 0.82. To constrain the final conditions of the model, we approximate strain within the shear zone using the average orientation of observed strain and an estimate of the average bulk finite strain. Thus, the XY plane of the strain ellipsoid inside the shear zone strikes 147° and dips 78° SW. Lineation pitches 45° NW. Strain has an average magnitude of s = 1.34. Details of model implementation are described in Appendix 2.
Model Results
Results of the modeling are shown on Figure 8. Modeled strain magnitudes range from s 1.5–4.5 (Fig. 8B), and shapes are all moderately oblate ( +0.5). Models producing the observed strain orientation have 0° < 50° (Fig. 8C) and 0.2 < S < 0.8 (Fig. 8D).
Comparing the observed strain with the modeled strain, two points are clear. First, only models with relatively low strain magnitude match observed strain magnitude. Second, observed strain shape is more generally prolate than modeled strain. Both of these observations can be explained by the competent nature of the clasts used as strain markers, a point we consider further in the Discussion.
Taking these relationships between observed and modeled strain into consideration, we can further constrain the most likely boundary conditions for the shear zone. Modeled strain ellipsoids with relatively low magnitude (s) values best match the strain observed in the shear zone. Using the estimated bulk rock finite strain from the centimeter-scale analysis as a rough guide, we take s = 2.5 as an upper limit of possible values. These low strain magnitude models all have angles of oblique convergence of 0 < 25° (black histogram bars on Fig. 8C). Additionally, the low strain magnitude models have shortening values of 0.2 S 0.6 (black histogram bars on Fig. 8D). These further constraints on Late Cretaceous deformation in the Gem Lake shear zone suggest that the effective angle of oblique convergence inside the zone was = 15 ± 10° and that shortening inside the shear zone was 0.2 S 0.6. These results provide an estimate of the additional deformation partitioned into the shear zone, beyond that accommodated by the rest of the Ritter Range region.
Late Cretaceous Strike-Slip Partitioning and Effective Viscosity Variation
We can use these kinematic constraints to develop a better understanding of Late Cretaceous regional deformation. Assuming geometric steady-state deformation, the angle of oblique convergence describes the bulk kinematics of regional finite deformation, bulk. This angle does not, however, accurately describe the specific kinematics of deformation in the various zones within a distributed strike-slip partitioned system: partitioning of the strike-slip component of deformation results in distinct angles of oblique convergence inside and outside the shear zone. We use the angle in to describe deformation in the Gem Lake shear zone and the angle out to describe deformation in the rest of the Ritter Range region.
Farallon-North America bulk kinematics at the latitude of central California during the time period when the Gem Lake shear zone was active (less than 100 Ma to at least 83 Ma) can be approximately described by bulk = 70 ± 10° (Engebretson et al., 1985; Kelley, 1993; Kelley and Engebretson, 1994). This estimate of bulk assumes that Farallon-North America plate motion described regional deformation. Tikoff and Teyssier (1994) discuss the validity of this assumption for the present-day Sumatra arc. Although the specific estimate of bulk = 70 ± 10° cannot be explicitly corroborated, Farallon-North America relative motion gradually changed from sinistral to dextral oblique convergence during the Early Cretaceous, ca. 120 Ma (Engebretson et al., 1985; Kelley, 1993; Kelley and Engebretson, 1994), and the regional bulk was therefore most likely much greater than our estimate of = 15 ± 10° for the Gem Lake shear zone. These distinct values can be explained, if a relatively large proportion of the strike-slip component of regional displacement was partitioned into the shear zone (e.g., Tikoff and Teyssier, 1994; Jones and Tanner, 1995; Teyssier et al., 1995).
Having recognized the likelihood of strike-slip partitioning, we can use additional observations to place further constraints on the degree of regional partitioning. The Ritter Range pendant is 30 km across (Fig. 1). The 1-km–wide Gem Lake shear zone is therefore 3% the width of the entire region (Fig. 7B). Tobisch et al. (1995) estimate a minimum of 30% shortening for the Ritter Range region. We use this value to describe Late Cretaceous shortening for the region, and we use the results from our inclined transpression modeling to estimate total shortening inside the shear zone. Using our shortening estimate of 0.2 S 0.6, we calculate that the shear zone shortened between 44% and 73%, while the rest of the Ritter Range pendant shortened 30% during the Late Cretaceous. We then use trigonometry to create a regional displacement budget and propagate uncertainties in regional angle of oblique convergence (bulk = 70 ± 10°), estimated angle of oblique convergence inside the Gem Lake shear zone (in = 15 ± 10°), and total shortening inside the shear zone (44%–73%). Following this procedure, we estimate that the angle of oblique convergence in the Ritter Range pendant (outside the shear zone) was between 60° out < 90°. This variation in inside and outside the shear zone requires that strain rates inside the shear zone were 6–17 times faster than outside. Assuming Newtonian rheologies, this implies that effective viscosity inside the Gem Lake shear zone was 6–17 times lower than that in the rest of the Ritter Range pendant.
Discussion
We have demonstrated that Late Cretaceous deformation in the east-central Sierra Nevada was heterogeneous at several scales of observation. Figure 9 is a summary diagram that schematically demonstrates how this heterogeneity is manifested at the centimeter, meter, and kilometer scales. Together with our data, this diagram allows us to consider several topics: (1) Which material properties contribute to heterogeneous deformation at each scale? (2) How is deformation behavior at a given scale of observation related to material properties at different scales? (3) How much does relative effective viscosity vary at each scale of observation?
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Previous work provides insight that allows us to interpret the complex strain population orientations and shapes we observe. Hutton (1979) observed variations in strain in deformed pelites and quartzites adjacent to a fault but did not interpret the data in the context of competence. Freeman (1987) used numerical modeling to predict that a competent non-rigid ellipsoid in a less viscous matrix deforms into a more prolate shape and records lower strain magnitude than is imposed by boundary conditions. Piazolo and Passchier (2002) observed this behavior in analog experimental deformation of competent clasts in a matrix of lower viscosity.
Thus, field observations, along with predictions from numerical and physical models, suggest that measured strain in clast populations varies in shape and orientation depending on a wide range of parameters, including bulk strain kinematics and magnitude, the effective viscosity of clasts relative to the matrix, and clast shape. As bulk finite strain increases, all clast populations tend to rotate into alignment with the principal stretching directions. The rate of this rotation is dependent on the effective viscosity of the clast relative to the matrix and also on clast shape (e.g., prolate versus oblate, axi-symmetric versus non-axisymmetric, small versus large aspect ratio).
Therefore, detailed analysis of orientation differences between clast populations at each station is not possible without more detailed data on clast shape and viscosity contrast. We can conclude, however, that the general alignment of different clast populations at each station (Fig. 5) is the result of rotation toward the principal stretching directions. Additionally, Piazolo and Passchier's (2002) experiments provide support for our hypothesis of moderate effective viscosity contrast between clasts. They demonstrated that clasts with effective viscosities that differ by an order of magnitude or more have distinct deformation behaviors (e.g., low-magnitude pulsating strain in highly competent clasts versus constantly increasing strain in moderately competent clasts. Our observations are most consistent with the latter situation.
Meter-Scale Localization
The different amounts of finite strain recorded within separate stratigraphic layers affected by the shear zone record meter-scale localization of deformation. Layers with a relatively coarse-grained matrix (e.g., GL2, volcaniclastic conglomerate) record less finite strain than layers with a finer grained matrix (e.g., GL6, lithic-lapilli tuff). Competent stratigraphic layers inside the shear zone sometimes record less strain than incompetent layers outside the shear zone. For example, average strain magnitude values in volcaniclastic sediments are as low as s = 0.54 inside the shear zone, while lithiclapilli tuff, which is incompetent relative to volcaniclastic conglomerate, has an average s = 0.82 outside the shear zone.
These observations corroborate studies (e.g., Schmid et al., 1977; Etheridge and Vernon, 1981; Walker et al., 1990; Stünitz and FitzGerald, 1993; Karner et al., 2005) linking fine-grained rocks with relatively high strain rates compared to coarser grained rocks. Etheridge and Vernon (1981) attributed this relationship to the fact that for small grain sizes grain boundary deformation mechanisms (e.g., grain boundary sliding) accommodate bulk rock strain more efficiently than intracrystalline mechanisms.
Clast abundance may also contribute to the differences in competence between different stratigraphic layers. Clast-matrix numerical modeling suggests that (1) in clast-poor rocks, bulk rock strength is controlled by matrix viscosity, and (2) that as clast abundance increases, bulk rock strength becomes dominated by clast viscosity (e.g., Gay, 1969; Treagus and Treagus, 2002). Groome et al. (2006) observed this phenomenon in amphibolite facies schists in which layers relatively rich (up to 30% by volume) in andalusite porphyroblasts were estimated to have an effective viscosity 2–3 times higher than adjacent clast-poor layers. Rocks in the Gem Lake region are almost exclusively matrix-supported, with clast abundance ranging from less than 10% in the clast-rich tuff up to 25% on rare occasions in volcaniclastic conglomerate. These relatively low clast abundances suggest that the matrix is the primary control on bulk rock strength in these rocks. Thus, the coarse-grained nature of the matrix in the volcaniclastic conglomerate may by the dominant factor making it the most competent rock type in the region.
Kilometer-Scale Localization
The distinct difference in foliation and lineation orientations inside and outside the shear zone demonstrates that these areas deformed differently over time, despite having experienced the same regional deformation history. Our numerical model provides a quantitative estimate of how Late Cretaceous deformation varied spatially.
The cause of localization of the Gem Lake shear zone in its present position is not immediately apparent. Although the shear zone formed at the unconformable contact between metased-imentary and metavolcanic rocks, this boundary juxtaposes rock types that appear to be of roughly equivalent competence when viewed side-by-side in the field. The contact, however, appears to be a mechanical boundary of regional importance, as demonstrated by the fact that the Sierra Crest shear-zone system is located at this contact along much of its length within the Gem Lake and Rosy Finch shear zones. One explanation may be that the contact acted as a conduit for metamorphic fluids. Fluid-rock interaction can lead to reaction-enhanced ductility (White and Knipe, 1978; Etheridge et al., 1984; McCaig, 1984; O'Hara, 1988; FitzGerald and Stünitz, 1993; Wintsch et al. 2005), and may therefore have played an important role in localizing the Gem Lake shear zone and perhaps the entire Sierra Crest shear-zone system. The relative abundance of metamorphic veins inside the shear zone supports this hypothesis.
However, a more likely first-order cause of shear-zone localization may be the proximity of the thermal axis of the Sierra Nevada volcanic arc. Throughout the Late Cretaceous evolution of the arc, plutonism migrated eastward at an average rate of 2.7 mm/yr (Chen and Moore, 1982). The location of active shear-zone deformation has mimicked this eastward migration (Tobisch et al. 1995;
°. Shear-zone coordinates Xs, Ys, Zs (described in the text) are defined with respect to shear-zone orientation and the direction of simple shearing. The zone starts with a width of 1 and shortens during deformation by a proportion S. (B) Nadai-Hsu plot showing magnitude and shape of model results matching strain-orientation observations inside the shear zone. A total of 1346 filled dots indicate results, all of which have oblate shapes. Shaded region indicates finite-strain observation in the shear zone. (C) Histogram showing 