lable at ScienceDirect

Journal of Structural Geology 84 (2016) 14e30

Contents lists avai

Journal of Structural Geology

journal homepage: www.elsevier .com/locate/ jsg

Bulk arc strain, crustal thickening, magma emplacement, and massbalances in the Mesozoic Sierra Nevada arc

Wenrong Cao a, b, *, Scott Paterson a, Jason Saleeby c, Sean Zalunardo a

a Department of Earth Sciences, University of Southern California, 3651 Trousdale, Parkway, Los Angeles, CA 90089-0740, USAb Department of Earth Science, Rice University, 6100 Main St. MS-126, Houston, TX 77005, USAc Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA

a r t i c l e i n f o

Article history:Received 15 June 2015Received in revised form29 October 2015Accepted 3 November 2015Available online 15 January 2016

Keywords:Finite strainCrustal thickeningMagma emplacementMass balanceMesozoic Sierra Nevada arc

* Corresponding author. Current address: DepartUniversity, MS-126, 6100 Main Street, Houston, TX 77

E-mail addresses: caowenrong@gmail.com (W(S. Paterson), jason@gps.caltech.edu (J. Saleeby)(S. Zalunardo).

http://dx.doi.org/10.1016/j.jsg.2015.11.0020191-8141/© 2016 Elsevier Ltd. All rights reserved.

a b s t r a c t

Quantifying crustal deformation is important for evaluating mass balance, material transfer, and theinterplay between tectonism and magmatism in continental arcs. We present a dataset of >650 finitestrain analyses compiled from published works and our own studies with associated structural,geochronologic, and geobarometric information in central and southern Sierra Nevada, California, toquantify the arc crust deformation. Our results show that Mesozoic tectonism results in 65% arc-perpendicular bulk crust shortening under a more or less plane strain condition. Mesozoic arc mag-matism replaced ~80% of this actively deforming arc crust with plutons requiring significantly greatercrustal thickening. We suggest that by ~85 Ma, the arc crust thickness was ~80 km with a 30-km-thickarc root, resulting in a ~5 km elevation. Most tectonic shortening and magma emplacement must beaccommodated by downward displacements of crustal materials into growing crustal roots at the esti-mated downward transfer rate of 2e13 km/Myr. The downward transfer of crustal materials must occurin active magma channels, or in “escape channels” in between solidified plutons that decrease in sizewith time and depth resulting in an increase in the intensity of constrictional strainwith depth. We arguethat both tectonism and magmatism control the thickness of the crust and surface elevation with slightmodification by surface erosion. The downward transported crustal materials initially fertilize the MASHzone thus enhancing to the generation of additional magmas. As the crustal root grows it may potentiallypinch out and cool the mantle wedge and thus cause reduction of arc magmatism.

© 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Quantitative mass balances in continental margin arcs, duringorogeny, mountain building, magma emplacement, growth of deepcrustal roots, and lower crustal delamination have been difficult tocalculate for four main reasons: 1) the addition of large volumes ofmagma either overprints or entirely removes large volumes of pre-existing crust, thus removing significant geologic evidence abouthost rock displacements; (2) lower crustal sections of continentalarcs are rarely exposed; (3) the strong deformation and meta-morphism present in these environments masks evidence of dis-placements, and (4) widespread markers of finite strain and/or

ment of Earth Science, Rice005, USA.. Cao), paterson@usc.edu, seanzalunardo@gmail.com

regional displacements are needed and not always available inthese settings. However there remains a strong motivation tocollect such data in order to address a series of interrelated ques-tions: (1) Canwe better quantify both strain and bulk shortening incontinental arcs to clarify their role in mountain building, devel-opment of crustal roots, and delamination? (2) How is local spacemade for the emplacement of plutons? (3) Can we better constraincrustal thickening through time and thus determine towhat degreetectonic processes are linked to the “tempos” of non-steady statemagmatism (e.g., Ducea, 2001; DeCelles et al., 2009; Paterson andDucea, 2015)?

Over the past 40 years a number of studies have completedextensive dating of both plutonic and metamorphic rocks andcollected strain data in or near the Sierra Nevada batholith of Cal-ifornia (e.g. Tobisch et al., 1977; Paterson et al., 1989; Saleeby, 1990;Busby-Spera and Saleeby, 1990; Tobisch et al., 1995; Mundil et al.,2004; Schweickert and Lahren, 2006; Saleeby et al., 2008; Memetiet al., 2010; Barth et al., 2012; Chapman et al., 2012; Paterson et al.,

W. Cao et al. / Journal of Structural Geology 84 (2016) 14e30 15

2014; Cao et al., 2015). Over the past 10 years, we have renewedthese efforts by continuing modern U/Pb dating of both plutonicand metavolcanic units, plus detrital zircon dating of metasedi-mentary units, measuring strains in a wide variety of rock types,and integrating our structural studies to estimate a temporal his-tory of bulk shortening throughout the Mesozoic. Below, afterintroducing Sierran geology, we present an integration of over 650finite strain analyses across the central and southern Sierra Nevadawith our recent structural and geochronologic data to quantify thestrain and mass balances.

2. Geological background

2.1. Sierra Nevada arc

The Sierra Nevada in California (Fig. 1A) represents a long-lived(~170 million years) Mesozoic continental arc formed by subduc-tion between Farallon and North American plates. The plutonic partof the arc is referred to as the Sierra Nevada Batholith, a collectiveterm for mainly intermediate plutons of Mesozoic age (Fig. 1B).Episodic magmatism in the Sierra Nevada arc is well documented,and three magmatic flare-ups bounded by four magmatic lulls arerecognized (Ducea, 2001; DeCelles et al., 2009; Paterson and Ducea,2015).

Host rock pendants representing the Mesozoic volcanic andsedimentary carapace of the Sierra Nevada arc are locally pre-served. In the central Sierra Nevada (36.5� N to 38.5� N), strain datahave been collected and compiled from nine stratigraphicallyrelated but spatially disconnected pendants (Fig. 1C): PiuteMeadow, Saddlebag Lake, Ritter Range, Jackass Lake, Iron Moun-tain, Mountain Morrison, Mountain Goddard, Oak Creek and

Fig. 1. (A) Map of California with Sierra Nevada Batholith highlighted in black. (B) Sierra Nevmap of central Sierra Nevada. Boxes show the areas where strain data are collected. Gray isPaleozoic rocks. Light blue is sedimentary rock of various ages. WMB¼Western MetamorphBelt, SCT¼ Sullivan Creek Terrane, CAL¼ Calaveras Complex, SFF¼ Shoo Fly Formation, PMJL ¼ Jackass Lake pendant, IM¼ Iron Mountain pendant, MM ¼ Mountain Morrison pendpendant, LIS ¼ Lake Isabella pendant, PL¼ Piute Lookout pendant, S¼ Sonora Intrusive ComWhitney Intrusive Complex, SF¼ San Francisco, LA ¼ Los Angeles. Index of shear zone/fault:Foothills suture; 4 ¼ Melones fault; 5 ¼ Bear Mountain fault. (For interpretation of the refearticle.)

Boyden Cave. Lithology of these strata is mainly andesitic to rhyo-dactic, clastic volcanic rocks with local, intra-arc sedimentary rocks.(e.g. Brook, 1977; Tobisch and Fiske, 1982; Greene and Schweickert,1995; Tobisch et al., 2000; Sharp et al., 2000; Schweickert andLahren, 2006). The paleo-depths at which these host rock pen-dants are preserved range from 2 to 4 kbar, approximately 7e14 km(3.64 km/kbar, assume density 2.75 g/cm3) (Anderson et al., 2008;Paterson et al., 2014; Nadin and Saleeby, 2008; Chapman et al.,2012).

In the southern Sierra Nevada (36�N to ~ 35.8�N), deeper levelsof the arc are progressively exposed southwards to ~10 kbar(Pickett and Saleeby, 1993; Saleeby et al., 2003; Nadin and Saleeby,2008; Chapman et al., 2012). Extreme transposition and migmati-zation are pervasive in pendant rocks at >7 kbar levels, therebyinhibiting strain measurements. Strain data have been collectedfrom two host rock pendants, Lake Isabella and Piute Lookout(Fig. 1B). Both of these pendants underwent peak metamorphismand deformational conditions during ca. 100e90 Ma magmatism,Lake Isabella at ~4 kbar conditions (Dixon,1995; Ague and Brimhall,1988a; Saleeby, unpubl.) and Piute Lookout at ~7 kbar conditions(Saleeby et al., 2008).

These host rock pendants in the central and southern SierraNevada had experiencedmultiple phases of deformation during theMesozoic. Field evidence of arc-perpendicular shortening, andvertical stretching are found in many host rock pendants. Thisregional strain pattern is responsible for the NW-striking, steeplydipping bedding, regional foliation, and steeply plunging lineation(e.g. Tobisch and Fiske,1982; Sharp et al., 2000; Saleeby et al., 2003;Schweickert and Lahren, 2006) (Fig. 2). The tilted bedding andmetamorphic foliation and lineation are formed time-transgressively during the Mesozoic (Tobisch and Fiske, 1982; Cao

ada Batholith with four Late Cretaceous Intrusive Complexes highlighted. (C) SimplifiedWestern Metamorphic Belt. Green is Mesozoic arc-related volcanic rock. Dark blue areic Belt, WFB¼Western Foothill Belt, CFB¼ Central Foothill Belt, EFB ¼ Eastern Foothill¼ Puite Meadow pendant, SL¼ Saddlebag Lake pendant, RR ¼ Ritter Range pendant,ant, MG ¼ Mountain Goddard pendant, BC¼ Boyden Cave pendant, OC¼Oak Creekplex, T ¼ Tuolumne Intrusive Complex, MP ¼ Mono Pass Intrusive Complex, MW ¼ Mt.1 ¼ Sierra Crest Shear Zone; 2 ¼ potential Mojave-Snow Lake fault; 3 ¼ Permo-Traissicrences to colour in this figure legend, the reader is referred to the web version of this

Fig. 2. Field photos showing strain markers. (A) Triassic volcanic breccia from Sullivan Creek Terrane. (B) Pebbly mudstone from Calaveras Complex. (C) Late Triassic Cooney Lakeconglomerate from Saddlebag Lake pendant. (D) Cooney Lake conglomerate cut by a Middle Jurassic pluton. Black lines show the intrusive contact. (E) Late Triassic volcaniclasticrocks from Saddlebag Lake pendant. (F) Jurassic conglomerate from Saddlebag Lake pendant. (G) Cretaceous volcanic breccia from Saddlebag Lake pendant. (H) Cretaceous volcanicrocks from Saddlebag Lake pendant with steep bedding cut by a Cretaceous pluton.

W. Cao et al. / Journal of Structural Geology 84 (2016) 14e3016

et al., 2015). SW- or NW-vergent thrusts and strike-slip faults (e.g.Lahren and Schweickert, 1995; Tobisch et al., 2000; Schweickertand Lahren, 2006; Cao et al., 2015) also developed during theMesozoic. Dextral transpressional shear zones (e.g. Sierra CrestShear Zone) developed in the Late Cretaceous as the subductionbetween Farallon and North America plates become more oblique(e.g. Greene and Schweickert, 1995; Tikoff and Saint-Blanquat,1997; Nadin and Saleeby, 2008). Host rock pendants also under-went sub-greenschist to amphibolite facies regional meta-morphism and local contact metamorphism in pluton aureoles

(Tobisch et al., 1977; Barton and Hanson, 1989; Hanson et al., 1993;Albertz, 2006).

2.2. Western Metamorphic Belt

The Western Metamorphic Belt (WMB, Fig. 1C) is a belt ofmetamorphic rocks along the western edge of the Sierra Nevada.TheWMB consists of terranes accreted to thewesternmargin of theNorth American continent and/or formed along the continentalmargin and infolded with North American derived marine

W. Cao et al. / Journal of Structural Geology 84 (2016) 14e30 17

sediments (Clark, 1964; Edelman and Sharp, 1989; Schweickertet al., 1999; Snow and Scherer, 2006). Terrane accretion began inthe Permo-Triassic and ceased by Middle or Late Jurassic (e.g. Snowand Scherer, 2006; Dickinson, 2008; Saleeby, 2011). The accretionresulted in a major boundary, Permo-Triassic Foothills suture,separating displaced continental passive margin fragments fromaccreted terranes and several intra-arc thrust faults, the LateJurassic Melones fault and Bear Mountain fault separating differenttectonic regimes (Fig. 1C, e.g. Clark, 1964; Schweickert et al., 1977;Miller and Paterson, 1991; Saleeby and Dunne, 2015). In this pa-per, the WMB in the central Sierra is divided into the Foothills andEastern Belts (Fig. 1C).

3. Description of datasets

3.1. Sample locations

Strain data are mainly collected from host rocks across thecentral Sierra Nevada with a small subset collected in the southernSierra Nevada. Boxes in Fig. 1B and c show the area where straindata were collected. Compiled strain data and references of datasource are provided in the Supporting Materials.

3.2. Methods of finite strain measurement

The strain measurements compiled in this paper have beenobtained by a number of different people using several differentmethods (e.g., Tobisch et al., 1977, 2000; Longiaru, 1987; Patersonet al., 1989; Albertz, 2006; Horseman et al., 2008). A great major-ity of the strains were determined from clastic objects that can beapproximated by ellipsoidal shapes (e.g., pebbles in conglomerates,lithic fragments and pumice lapilli in volcanics, sand grains insandstones). These were analyzed using one of the following twoapproaches:

1. When logistically feasible, oriented samples with clastic objectswere collected and brought back to the lab. Three perpendicularsurfaces either parallel to principal planes (Tobisch et al., 1977)or arbitrary (Paterson et al., 1989) were cut in each sample andthen labeled with sample coordinate axes. In each 2D surfacethe orientation of the long axis of clasts relative to the samplecoordinates axes and the long axis/short axis ratio of least~25e50 objects per surface were measured (by hand in olderstudies and digitally from images of the surface in recentstudies). Rf/f techniques (e.g., Shimamoto and Ikeda, 1976; Lisle,1979,1985) were used to determine the shape and orientation of2D ellipses for each surface and then combined into a single 3Dellipsoid (Shimamoto and Ikeda, 1976; Miller and Oertel, 1979).The orientations of 3D ellipsoids were reoriented to truegeographic orientations using the sample orientation data.Given sufficient sample sizes, precision errors are in the range of5e10% (see Miller and Oertel, 1979 for error estimates).

2. When not feasible to collect oriented samples, surfaces axialratios and orientations of clastic objects were obtained onprincipal planes. Since each two principal planes share one axisof strain, a 3D ellipsoid (X� Y� Z) can be determined by settingZ ¼ 1 and determining the ratios of X/Z and Y/Z from the 2Daverages (Ramsay, 1967; Lisle, 1977; Paterson, 1983). Strainellipsoid orientations for these field determinations areassumed to be parallel to the cleavage (XeY plane) and mineralor clast lineation (X-axis). Precision errors using this approachwere in the range of 5e20% when fitting 2D surfaces to 3Dresults.

The above approaches assume constant volume strain at the

scale of individual clasts. In most cases we see little evidence oflarge volume changes (e.g., fibers in pressure shadows or dissolu-tion of clasts), thus supporting the above assumption. These ap-proaches also ignore the existence of any primary fabrics insamples, which may be present if clasts were even weakly alignedduring deposition and burial. Lisle (1979), Paterson et al. (1989) andPaterson and Yu (1993) discuss approaches for correcting finalstrains for the presence of primary fabrics. Note that many primaryfabric ellipsoids have small axial ratios (Paterson et al., 1995). Sincethese corrections are only available for some of the data discussedin this paper, we only use and compare uncorrected data. Finally Rf/f techniques assume that there is no difference in the viscosity ofclasts andmatrix and thus clast strain equals bulk strain of the rock.Any effect of viscosity differences decrease as the percent of clastsin samples increase and as the sample becomes clast supported(i.e., at around >50% clasts). The existence of viscosity contrasts canbe evaluated by examining whether the cleavage is deflectedaround clasts or passes undeflected through them. Most samples inthis study show little evidence of significant viscosity contrasts.

Strains in slate and phyllite samples from the WMB weredetermined by Paterson et al. (1989) using the March method(March, 1932; Oertel, 1983). Precision errors are in the range of5e10%. These samples record different strains than nearby (at cm tom scale) samples measured by Rf/f techniques and are interpretedto include a component of flattening strain formed during burialand dewatering (Oertel, 1983; Paterson et al., 1989, 1995).

A very few of the strains presented in this paper were deter-mined using the Fry method (Crespi, 1986; Erslav, 1988). In thismethod 3 perpendicular cuts are made in oriented samples and foreach face the distance and direction between centers of objects aremeasured and used to construct an “all-objects-separation” plot.The inner cut-off of plotted points is used to determine the ratioand orientation of 2D ellipses. These ellipses are combined into a3D ellipsoid using both Shimamoto and Ikeda (1976) andMiller andOertel (1979) techniques. Precision errors for Fry data are in therange of 5e20% depending on the number of objects used (seeCrespi, 1986 for error estimates).

3.3. Geochronologic data

Numerous studies have determined absolute ages of plutonsand host rocks in the central Sierra Nevada (e.g. Bateman andChappell, 1979; Busby-Spera and Saleeby, 1990; Schweickert andLahren, 1993; Tobisch et al., 1995; Schweickert and Lahren, 2006;Saleeby et al., 2008; Memeti et al., 2010; Chapman et al., 2012;Barth et al., 2012; Paterson et al., 2014; Cao et al., 2015). Wecompiled these ages and integrated themwith the strain datawhenavailable. We focused on U/Pb zircon ages of plutons and volcanicsor interpreted ages of deposition for sedimentary units based onyoungest age peaks of detrital zircons. For host rocks without datedabsolute ages, we assign approximate ages based on stratigraphiccorrelations. Mesozoic rock ages are binned into age groups (seeSection 4.4). While the majority of rock ages in our dataset areMesozoic, a few Paleozoic ages were included from continentalmargin tectonic slices now residing in the Sierra Nevada.

3.4. Geobarometric data

The Aluminum-in-hornblende barometer (Johnson andRutherford, 1989; Schmidt, 1992; Holland and Blundy, 1994;Anderson and Smith, 1995) was used to determine emplacementpressure/depth of plutons in the central Sierra Nevada (e.g. Agueand Brimhall, 1988a, 1988b; Ague and Brandon, 1992; Pickett andSaleeby, 1993; Ague, 1997; Saleeby et al., 2003, 2008; Nadin andSaleeby, 2008; Anderson et al., 2008; Chapman et al., 2012;

W. Cao et al. / Journal of Structural Geology 84 (2016) 14e3018

Paterson et al., 2014). We compiled the geobarometric data andintegrated them with the strain data when available and used theemplacement pressure of nearby intruding plutons as themaximum paleo-depth of host rocks. Paleo-depths are then binnedinto different groups (see Section 4.5). The rocks of shallowerpaleo-depth (1e3 kbars) are from the central Sierra Nevadawhereas rocks of deeper paleo-depth (4e7 kbars) are from thesouthern Sierra Nevada.

4. Characteristics of finite strain in Mesozoic Sierra Nevada

4.1. Orientations of metamorphic foliation and lineation in centralSierra Nevada

Metamorphic foliation and lineation are well developed in theWMB and host rock pendants in the central Sierra Nevada. Foliationtype varies from slaty cleavage to schistosity to mylonitic in ductileshear zones. Mineral lineations are defined by aligned stretchedclasts, pebbles, and mineral grains. Fig. 3 shows the metamorphicfoliation and lineation from the WMB and several host rock pen-dants in the central Sierra Nevada. The measurements are fromboth Paleozoic and Mesozoic rocks but the great majority are fromMesozoic rocks. The cylindrical best fits are calculated(Allmendinger et al., 2012; Cardozo and Allmendinger, 2013).Regional foliations in most of the areas dip steeply and strike NW toNNWparallel to the trend of the arc. The foliation best fits only vary

Fig. 3. Lower hemisphere, equal area projections of metamorphic foliations and lineations fcontours with 2.0 sigma contour interval (C.I.) are added. Dots in the red shade are polesNF¼Number of foliation, NL¼Number of lineation. Cylindrical best fits are calculated usinAllmendinger, 2013). (For interpretation of the references to colour in this figure legend, th

within 17� between most areas except in the Iron Mountain andJackass Lake areas, where the foliation best fits strike slightly morenortherly. Lineations in all areas are steeply plunging(plunge > 70�). We interpret the foliations and lineations toapproximate the XeY planes and X-axes of finite strain ellipsoids(X, Y, Z are the longest, intermediate, and shortest axes of a strainellipsoid, respectively). Comparisons of calculated XeY planes andX-axes of strain from samples analyzed in the lab support thisassumption (e.g., Paterson et al., 1989). The consistent orientationsof regional foliation and lineation across the central Sierra Nevadasuggest a more or less co-axial arc-perpendicular ductile short-ening during Late Paleozoic and Mesozoic, or approximate theshear plane orientations of arc-parallel shear zones and thus theXeY plane of high shear related strains, which is consistent withobservations from many other researchers (e.g. Tobisch and Fiske,1982; Greene and Schweickert, 1995; Sharp et al., 2000; Tobischet al., 2000; Albertz, 2006; Horsman et al., 2008; Cao et al., 2015).

4.2. General patterns of finite strain in Mesozoic Sierra Nevada

We plotted 612 strain measurements with age constraints on aHsu diagram (Hsu, 1966; Hossack, 1967) (Fig. 4). Most measure-ments plot at a strain magnitude less than 1.8 with a few, typicallyin shear zones, ranging up to 3.4. Lode's ratios (Lode,1926) are quitevariable with most between�0.75 and 1. Triassic and Jurassic rocksshow slightly higher magnitudes with very few (4 points) > 3.0. All

rom Western Metamorphic Belt and host rock pendants in central Sierra Nevada. Kambto the metamorphic foliation and dots in the blue shade are metamorphic lineation.g Stereonet 9.0 and 95% confidence ellipses (Allmendinger et al., 2012; Cardozo ande reader is referred to the web version of this article.)

Fig. 4. (A) Hus plot (Hus, 1966; Hossack, 1967) of all 612 data with age constraints. Yellow part is the zoomed area shown in plot (B). Hus plots are made using the programdeveloped by Mookerjee and Nickleach (2011). Points are color-coded by rock ages. Lode's ratio is calculated based on Lode (1926). (For interpretation of the references to colour inthis figure legend, the reader is referred to the web version of this article.)

W. Cao et al. / Journal of Structural Geology 84 (2016) 14e30 19

Cretaceous rocks show magnitudes less than ~2.1. The data areslightly concentrated in the flattening region (g > 0) but show anoverall symmetrical distribution.

We also plotted strain measurements in the space of X- and Z-extension percent (Fig. 5). The central bold red curve (Y ¼ 0) rep-resents the relationship between X- and Z-extension under planestrain. The thin curves on either side of the central bold curve showthe relation between X- and Z-extension if volume loss and/or Y-extension occurred during deformation. Fig. 5 shows that the ma-jority of data clustering about the red curves with X-directionextension ranging from <5% to about 500%. Most data cluster in thespace defined by 25%e150% X-direction extension, 20%e70% Z-di-rection shortening, and between Y ¼ 0% and Y ¼ 20% extension

Fig. 5. Finite strain measurements plotted in the space of X- and Z-extension percent(negative value ¼ shortening; X, Y, Z are the longest, intermediate and shortest axes ofa finite strain ellipsoid). Each dot represents an individual strain measurement. Thecentral coarse red curves represent the relation between X- and Z-extension if thedeformation is plane strain. The thin red curves represent the relation between X- andZ-extension if there is volume loss or Y-extension during deformation. Measurementsfrom slates are shown as yellow dots, whose finite strain ellipsoids are likely to beaffected by primary compaction during sedimentation and lithification. The plot sug-gests that the host rocks in the central Sierra Nevada are strained at about 50% inaverage with <15e20% Y-direction length change and/or potential volume changes.(For interpretation of the references to colour in this figure legend, the reader isreferred to the web version of this article.)

curves. Average Z-direction shortening is 49.4% with a standarddeviation of 16.7%. Since the volume change has not been deter-mined by strain measurements in the present study, the deviationof points plotted off the central “plane strain” curve in Fig. 5 isinterpreted as the results of length change along the Y-direction. Inreality, both length change along the Y-direction and volumechange can cause the deviation from the plane strain. Most of themeasurements from slate fall in the flattening field on the diagram,which is interpreted as recording primary compaction during burialand dewatering (Pfiffner and Ramsay, 1982; Paterson et al., 1995).This is consistent with the observation in slates that cleavage iscommonly parallel to bedding. If we correct for this earlycompaction, the resulting tectonic strains shift upwards andapproach the central “plane strain” curve (Paterson et al., 1989).

In summary, Fig. 5 suggests that although Sierran strain mea-surements have a wide range of X- and Z-direction length change,most points are within the Y ¼ 0 ± 20% range suggesting roughlyplane strain at the arc scale. Since the Y-Z plane parallels regionalNW-striking foliation and X-direction parallels lineation (Figure 3),Figure 5 suggests the finite ductile strain in these pendant rocks is50% arc-parallel shortening, ~100% vertical thickening and limitedarc-parallel length and/or volume change.

4.3. Strain vs. rock types

To investigate the relationship between strain and rock type inthe central Sierra Nevada, we plot strain data from 9 major rocktypes (pebbly mudstone, sandstone, conglomerate, slate/phyllite,andesite, rhyolite/dacite, tuff/lapilli stone, volcanic breccia, andunclassified volcanics) on Hsu diagrams (Fig. 6). The strain plot ofpebbly mudstone (Fig. 6A) shows strain magnitude below 1.8 andvariable strain shape. Sandstone (Fig. 6B) shows a concentrateddistribution in strain magnitude less than 1.2 and variable strainshape. Conglomerate (Fig. 6C) shows two groups: one with strainmagnitudes less then 1.8 and with slightly more flattening shape,the second with higher strain magnitudes higher than 2.1 andconstrictional strain shape. The strain measurements in the firstand second groups are from conglomerates in the central andsouthern Sierra Nevada, respectively. Slate and phyllite (Fig. 6D)cluster in the flattening regime, probably due to compaction duringsedimentation and lithification or volume loss during plane strain

Fig. 6. Hsu plots of 9 major rock types from Western Metamorphic Belt and central Sierra Nevada. Strain magnitude (ε) contour interval is 0.3. Lode's ratio (g) contour interval is0.25.

W. Cao et al. / Journal of Structural Geology 84 (2016) 14e3020

deformation (Ramsay and Wood, 1973; Pfiffner and Ramsay, 1982).Andesite (Fig. 6E) shows strain magnitudes �1.5 based on 12 datapoints. Rhyolite and dacite (Fig. 6F), and tuff-lapilli stone (Fig. 6G)show slightly concentrated distribution along the Lode's ratio ¼ 0line suggesting that these rocks are deformed close to “planestrain”. Volcanic breccia (Fig. 6H) shows higher strain magnitudeswith many points above 1.8, plotting slightly in the flatteningregime. Fig. 6I shows volcanic rocks that are not classified intocomposition groups. Strain magnitudes of these volcanic rocks aremostly below 2.1 and are slightly more distributed in the flatteningregimes.

In summary, Fig. 6 shows that rock type affects strain magnitudeand strain shape but not significantly. Strain magnitude is typicallyless than 1.8. Strain shape is generally evenly distributed in con-strictional and flattening regions but for some rock types (slate andphyllite, volcanics unclassified), flattening, presumably due tocompaction during lithification, is more common.

4.4. Strain vs. rock ages

To investigate the relationship between strain and rock age inthe central Sierra Nevada, we plot the strain magnitude and Lode'sratio against rock ages (Fig. 7).

Notice the age of a rock is only an upper limit of the age ofdeformation but can still be used to bin data into different lengthsof time.

Strain magnitudes (Fig. 7A) of Triassic, Jurassic, and Cretaceousrocks are fairly scattered but the overall trend is a slight decrease instrain magnitude with younging. The trend of decreasing strainmagnitude with younging can be seen both from the distribution ofindividual data and the trend of averaged magnitudes. Triassicrocks of 220e230 Ma ages have strain magnitude average between1.0 and 1.5 while Jurassic rocks fluctuate around 1.0. Early Creta-ceous rocks (145e100 Ma) show strain magnitude average no morethan 1.0. Average strain magnitude of Late Cretaceous rocks

Fig. 7. Strain magnitude (ε) and Lode's ratio (g) plotted against rock age. Averages of strain magnitudes and Lode's ratios of rocks of the same/similar ages are plotted as filled circles.Red bars show 2 standard deviations. Individual measurements are plotted as empty squares. The arrows show the interpreted trends. Strain magnitude deceases from Triassic rocksto Early Cretaceous rocks and it spreads in Late Cretaceous rocks (100e80 Ma). Lode's ratio slightly increases from Triassic rocks to Early Cretaceous rocks and its range spreads inLate Cretaceous rocks (100e80 Ma). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

W. Cao et al. / Journal of Structural Geology 84 (2016) 14e30 21

(100e80 Ma) show a wider spread ranging from 0.6 to 1.7. Thetrend confirms that older rocks are on average more deformedalthough local exceptions occur for Late Cretaceous rocks. Fig. 7Balso shows a scattered pattern but the averages of Lode's ratioslightly increases from Triassic to Jurassic. Since most slate andphyllite are Jurassic, the Jurassic Lode's ratios are likely to beaffected by the flattening during compaction and lithification.

4.5. Strain vs. paleo-depths

To investigate the relationship between strain and rock ages inthe central Sierra Nevada, we plot the strain magnitude and Lode'sratio against the paleo-depths of rocks (Fig. 8). The paleo-depths ofhost rocks are represented by the paleo-depth of plutons intrudingthe host rocks. Thus the paleo-depths of host rocks do not give fullinformation about the change in a rock's vertical position throughtime: A rock may be displaced vertically prior or subsequent to thelocking in at the emplacement depth. We report paleo-depths aspressure in units of kilobar (kbar). A conversion constant of3.64 km/kbar can be used to transform pressure to depth.

Fig. 8A shows that the average strain magnitude generally in-creases from 0.7 at 1 kbar to 1.2 at 3 kbars except the lower

Fig. 8. Strain magnitude (ε) and Lode's ratio (g) plotted against paleo-depth of rock (paleo-dratios of rocks of same paleo-depths are plotted as filled circles. Red bars show 2s errors. Intrends. Strain magnitude generally increases from 1 kbar to 3 kbars then sharply increases1.5e3 kbars then sharply decrease to �0.65 at 7 kbars. Notice that the uncertainty associat

magnitude (εz 1.0) of rocks at 2.5 kbars. Strain magnitude averageincreases to 2.3 and 2.4 of the rocks at 4 kbars and 7 kbars,respectively. Fig. 8B shows that the average Lode's ratio has thehighest value at 1 kbar (g z 0.38) and drops to gz 0.2 for rocks at1.5e3 kbars. The average Lode's ratio then sharply decreasesto �0.3 and �0.65 at 4 kbars and 7 kbars, respectively. The overallpattern of Lode's ratio suggests rocks at 1e3 kbars have more planeto flattened shapes while the rocks at deeper paleo-depths typicallybecome more constrictional. These data sets (Fig. 8A and B) alsosuggest that there is a general negative correlation between strainmagnitude and Lode's ratio as the paleo-depth increases. At shal-lower depth, strain magnitude averages are small (ε< 1.5) andLode's ratio averages are positive (g>0). Strain magnitude averageincreases to greater values and Lode's ratio average decreases tonegative values at greater depth indicating that rocks at deeperpaleo-depths are associated with higher strain magnitude andmore constrictional strain shape.

4.6. Strain near pluton margins

One challenge in studying finite strain in continental arcs is todifferentiate strain caused by regional tectonism from strain caused

epth is expressed in the unit of kilobar, kbar). Averages of strain magnitudes and Lode'sdividual measurements are plotted as empty squares. The arrows show the interpretedat 4 kbars. Lode's ratio has the highest value at 1 kbar and decreases to about 0.2 ated with barometry data is usually about ± 1 kbar.

W. Cao et al. / Journal of Structural Geology 84 (2016) 14e3022

by pluton emplacement. A pluton potentially generates a localizedstructural aureole in which strain in the host rocks is higher thanstrain outside the aureole (e.g., Paterson and Vernon, 1995). In or-der to constrain strain related to pluton emplacement, we compiledLode's ratios, strain magnitudes, and Z-shortening in host rockagainst the distance from the nearest contact of the CretaceousTuolumne Intrusive Complex in the central Sierra Nevada (Fig. 9).Locations of transects are shown in Fig. 1C.

As shown in the plot of Lode's ratio vs. distance from plutoncontact (Fig. 9A), there is no clear correlation between strain shapeand distance to the contact: Strain can be flattening (g > 0), orconstrictional (g < 0), or close to plane strain (g z 0) at any dis-tance. Maximum strain magnitudes (Fig. 9B) and Z-shortening(Fig. 9C) suggest that higher strain in host rocks only locally occurwithin <200 m distance from the Tuolumne Intrusive Complex.Furthermore, pluton aureole strain can be evaluated by examining

Fig. 9. (A) Lode's ratio (g), (B) strain magnitude (ε), and (C) Z-shortening plotted againsteastern and northern contacts are shown in Fig. 1.

the deflection of host rockmarkers (e.g., bedding, contacts, and pre-emplacement dikes, faults and foliations) as pluton margins areapproached. We have used this approach while mapping a numberof pluton aureoles throughout the central Sierra and find that zonesof increased strain near the margin are rare and only locallydeveloped and large sections of the pluton margin are quitediscordant to host rock bedding and foliations indicating little to nostrain increase towards the pluton margin. Such observationssuggests that even for a pluton of a fairly large size as the TuolumneIntrusive Complex, higher host rock strain may be absent or quitelocalized within a few hundred meters from the contact.

4.7. Rate estimation of downward transport of host rocks

Downward transfer of host rocks is proposed by some re-searchers to solve the “space problem” during pluton emplacement

the distance from intrusive contacts of Tuolumne Intrusive Complex. The locations of

W. Cao et al. / Journal of Structural Geology 84 (2016) 14e30 23

(e.g. Saleeby, 1990; Tobisch et al., 2000; Paterson and Farris, 2008).The evidence supporting downward transport of host rocks in-cludes the subvertical host rock stretching lineation and magmaticlineation in plutons (Saleeby et al., 2003; Paterson and Farris, 2008;Cao et al., 2015; this study), stoped blocks in plutons, and plutonrim and roof synclines and monoclines in adjacent host rocks (e.g.Paterson and Vernon, 1995; Paterson and Farris, 2008). Plutonsintruding older volcanic rocks or sedimentary rocks (Fig. 2D, H)suggest that these supracrustal materials must be transporteddownwards to emplacement levels, which range from 2 to 3 kbarsin the central Sierra Nevada to 9e10 kbars in the southern SierraNevada (Saleeby, 1990; Chapman et al., 2012).

With the geobarometry and geochronology data sets, we areable to estimate the minimum rate of downward transport of hostrocks (mm/yr or km/Myr). The transported distance can be calcu-lated using the emplacement pressure of pluton and the time in-terval is the age difference between host rocks and intrudingpluton. Fig.10 shows the estimatedminimum rates in different hostrock pendants: most of them show rates of 2e13 mm/yr with fasterrates found in the Cinko Lake, Jackass Lake and Eagle Peak areas,where upper crust plutons (~3 kbars) intrude slightly older (<1Ma)volcanic rocks suggesting a absolute rate of >10 mm/yr. Thecalculated absolute rates are the minimum values since supra-crustal materials can stay at surface until a pluton intruded later.This might be the case for some apparent slower rates found inRitter Range, Green Lake and Saddlebag Lake areas.

5. Discussion

5.1. Possible first-order mechanisms contributing to finite bulk arcstrain

Before we establish a comprehensive model of first-ordermechanisms of strain, we will first examine two end member

Fig. 10. Plot shows the minimum downward transport rates of host rocks in thesouthern and central Sierra. The horizontal axis is the age difference in million yearsbetween the host rocks and intruding plutons. The vertical axis is the emplacementdepth in kilobar (kbar) of the hosting plutons determined by Aluminum-in-Hornblende barometry. The background color shows the absolute downward trans-port rates. The rate varies from 2 to 13 km/Myr for most of the data. Location is givennear the data points, which are color-coded by the age of plutons. (For interpretation ofthe references to colour in this figure legend, the reader is referred to the web versionof this article.)

models and their resulting strain implications (Fig. 11). Model A(Fig. 11-A1) shows a crust only strained by homogenous, constantvolume tectonic shortening and thickening with no magmatism.Above the brittleeductile transition, crustal shortening occurs bybrittle thrust faults, tilting of bedding, and duplex structures. Belowthe brittleeductile transition, crustal shortening occurs by regionalductile strain and localized ductile shears, which also rotatebedding. Since the deformation is constant volume, plane strain,shortening will be balanced by crustal thickening. Development ofLS-fabrics are predicted below the brittleeductile transition underplane strain condition. (Sullivan, 2013). If some Y-direction lengthchange or volume loss occurs, strain shape will deviate away fromplane strain and become slightly flattening (Fig. 11-A2). In a ho-mogenous crust, strain shape and magnitude should be the samethroughout the crustal column and plot as a horizontal line in thestrain shape vs. depth (Fig. 11-A2) and strain magnitude vs. depthplots (Fig. 11-A3).

Model B (Fig. 11-B1) shows a crustal column being intruded bypulses of ascending magma but with no tectonic deformation.During magma ascent and trapping (e.g., emplacement) structuralaureoles remain small or non-existent. Little to no evidence ofregional lateral displacement of host rock units exists. This leavesthe likelihood that complex processes within laterally growingplutonic bodies and narrow aureoles drive vertical displacements.Regional stress fields generated during emplacement of magmasmay also drive host rock tilting and vertical displacements. As thearc matures the volume of plutonic rocks increases and a greateramount of magma are preferentially trapped at increasing depths(Saleeby, 1990; Paterson and Ducea, 2015). The magmas begin lifeas low viscosity bodies (with dike, sheet, diapir, or irregular shapes)but over the short timescales of crystallization become highstrength objects that are mechanically part of the host rock. Severalprocesses deserve consideration. First there is a clear mass balanceissue: as plutons emplace, an equal volume of host rock must bedisplaced to make the room. Structural and strain patterns requirevertical motion either in or immediately next to the magma col-umns or in volumetrically decreasing “host rock channels” betweensolidified plutons (Fig. 11-B1). In the Sierran arc greater than 80% oforiginal host rock is now displaced requiring almost doubling of thecrustal thickness. Second, strain within host rocks will increase inintensity and will become more constructional with depth as hostrock is displaced downwards through increasingly narrow channels(Fig. 11-B2, B3). Host rocks are forced to “escape” vertically, throughthese “escape channels” either within magma columns or boundedby solidified plutonic bodies. The downward escape of host rock ispotentially complicated by dragging forces, up or downwardswithin narrow, discontinuous aureoles. Similar shear forces alongthe magma-host rock contact had been proposed to contribute tohost rock bedding rotation (Tobisch et al., 2000) and constrictionalstrain of host rocks in pluton aureoles (Paterson and Farris, 2008).

We propose that together Model A and B depict many but not allaspects of the deformation and observed strain patterns in the Si-erra Nevada. The LS-fabrics (Fig. 3) in host rock pendant in centralSierra Nevada as well as strain plots (Figs. 4 and 5) suggest thatplane strain dominates the deformation in shallower arc crust.Minor Y-extension and/or volume loss may shift the strain towardto a slightly more flattening strain regime. Such strain patterns canbe explained by Model A. The increase of strain and more con-strictional strain with depth can only be explained by theincreasing number of plutons and magma with depth as predictedin Model B. Combining Model A and B, Model C (Fig. 11-C1) shows acrust undergoing simultaneous tectonism and magmatism. In thismodel, combined tectonic and magmatic stresses result in complexhorizontal shortening and vertical thickening that must accom-modate both tectonic and magma addition mass balance

Fig. 11. Three proposed models for ductile straining mechanisms. Model A is homogenous tectonic thickening only. Model B only has the magmatism. Model C combines tectonismand magmatism. A1, B1, and C1 show the cartoon illustrating the corresponding models. A2, B2, and C2 show predicted trends of Lode's ratio (g), or strain shape, changing withdepth. A3, B3, and C3 show predicted trends of strain magnitude (ε) changing with depth. See text for full discussion. BDT¼ Brittle-ductile transition.

W. Cao et al. / Journal of Structural Geology 84 (2016) 14e3024

requirements. Magmatic bodies may be internally strained andhave their shapes influenced by tectonism. Solidified plutons willact as a “plutonic framework”. As the crust is tectonically shortened,the distances between plutons may decrease resulting a moreconstrictional strain in host rocks with depth. We propose Model Ccould depict the observed strain patterns in both shallower anddeeper parts of crust (Fig. 11-C2, C3).

Fig. 12 shows crustal column of Sierra Nevada arc withincreasing strain magnitude and constrictional shapes with depthbased on Model C. The limited increase in Mesozoic surface ele-vations and upper crustal exhumation (discussed in next section)requires major downwards transfer of host rocks to balance thecrustal shortening and emplacement of plutons. The downwardtransported host rocks may spread laterally during growth of largeorogenic roots resulting in the vertical constructional strainsevolving to plane to flattening strains in the lower crust (Fig. 12).And as descending host rocks enter the MASH zone (Hildreh andMoorbath, 1988), they may be disaggregated, partly assimilatedand recycled into new ascending magma batches (e.g. Zellmer andAnnen, 2008).

The goal of our models (Figs. 11 and 12) is to give a first-orderapproximation of processes that need evaluation as crust isstrained during magmatism and tectonism. We recognize thatmore complicated processes occur during arc deformationincluding structures that broke through the Mesozoic Sierran arc,

such as regional strike-slip faults, ductile shear zones, and low-angle normal faults (e.g. Lahren and Schweickert, 1989; Kistler,1990; Saleeby and Busby, 1993; Nadin and Saleeby, 2008;Chapman et al., 2015; Saleeby and Dunne, 2015). Since moststrike slip faults trend ~ parallel to the arc, they may shuffle unitsparallel to the arc but not significantly affect the overall shorteningand thickening. Dip slip faults/shears are less common but at timesmay play a greater role in arc deformation and strain that deservesgreater attention in future studies. These structures will also aid inthe overall arc shortening/thickening and tilt of units discussed inthis paper and may add localized concentrated increments of strainto the arc crust. When possible such strain increments are includedin the finite bulk arc strain. The model shown in Fig. 12 of course isnot a prefect explanation for arc strain. We do not fully understandsome observed strain patterns. For example, the spread of theaverage strain magnitude and Lode's ratio in Late Cretaceous rocks(mainly volcanic rocks of 100e80 Ma in age) (Fig. 7A and B). Wesuspect such temporally restricted strain variations might be aconsequence of volumetrically large addition of magma in the LateCretaceous leading to a rheologically very heterogeneous crust.

5.2. The finite bulk arc strain, mass balance and crustal thickening

Above we concluded that the ductile strain in the WMB andSierran host rock pendants resulted in about 50% arc-perpendicular

Fig. 12. A possible model for Mesozoic Sierra Nevada based on the Models C shown in Fig. 11. An arc crustal column is shown with tectonic shortening, ascending magma bodies,and crystallized plutons. Above the brittleeductile transition, thrusts, duplex structures and as well as other host rock drop-down processes (e.g. stoping, ridge bedding rotation)accommodate the tectonic shortening strain and transport supracrustal materials downwards. The majority part of the arc crust below the brittleeductile transition is deformed inthe ductile fashion. Host rocks are forced to transport downward through escape channels. Strain magnitude increases and strain become more constrictional towards depth. Thedownward transported host rocks may enter the MASH zone at lower crust at about 70 km, where host rocks might be desegregated and assimilated. The thickness of the crustshown here is based on the discussion in Section 5.2.

W. Cao et al. / Journal of Structural Geology 84 (2016) 14e30 25

shortening in a more or less plane strain style. In the field, at thepaleo-depths of 5e10 km, different packages of ductilely deformedrocks are commonly separated by Mesozoic NE- or SW-vergentthrust faults (Tobisch et al., 2000; Schweickert and Lahren, 2006;Cao et al., 2015), which have been subsequently rotated withbedding to a sub-vertical orientation. To estimate the bulk defor-mation in host rocks, other deformation mechanisms need to beevaluated as well. Tobisch et al. (2000) proposed that thrust-relatedduplex structures can rotate the bedding to 45� at maximum,whichcorrespond to about 30% shortening along horizontal direction (Caoet al., 2015). Since both ductile and brittle strain suggest the sameNEeSW shortening kinematics, we combine 50% ductile shorteningwith 30% shortening caused by thrust-related duplex, for a finiteshortening strain is about 65% shortening (1�[1e0.5[1e0.3] ¼ 0.65).

To estimate the finite bulk arc strain and crustal thickening, inaddition to the host rocks, one has to take the plutons into account.Sierran plutons record multiple strain events caused by both in-ternal magma flow and external tectonic shortening (Patersonet al., 1998; Zak et al., 2007) The tectonic strain in plutons arerepresented by the ~NW-striking magmatic-subsolidus foliationand subvertical lineation (e.g. Zak et al., 2007; Cao et al., 2015).Strain in plutons is difficult to retrieve quantitatively due to the lackof strain markers. In a few cases, strain can be estimated using thefolded veins/dikes within the plutons. Our estimates of averagedtectonic strains in plutons range from 0 to 30% shortening with acommon average around 10% shortening (e.g., Paterson et al., 2014).Others have suggested that pluton shapes may reflect tectonic

strains (e.g. Weinberg et al., 2004). Some plutons in central SierraNevada have more or less circular shapes whereas others havelength/width ratios of up to 3/1. However neither show internaltectonic fabrics that are more intense than discussed above. Nor dothey show evidence at their NWor SE “ends” of expansion in eitherthe plutons or host rocks. Thus we suspect that plutons haven'tbeen significantly strained by regional shortening. Even so for ourfirst-order calculations below, we assume the plutons have beentotally shortened ~20% of which the fabrics record about half.

In an active continental arc, the thickening of crust is caused by(1) tectonic thickening compensating the tectonic shortening and(2) magmatic intrusion (e.g. Allmendinger et al., 1997; Karlstromet al., 2014; Lee et al., 2015). To calculate the final crustal thick-ness, a Matlab script (see Supporting Materials) is written toexplore the simultaneous incremental addition of magmatism andincremental regional strain to a crust. For the Sierra Nevada, weassume an initial crust thickness of ~25 km when the arc started(~250 Ma) and that the pluton fraction in the crust is about 0.8 by~85 Ma. The calculation also assumes 20% shortening in plutonsand 20% volume loss/Y-direction extension of host rocks into ac-count. Fig. 13 shows the final crustal thickness in a parameter spaceof host rock strain (εH) and pluton fraction (b) for a given initialcrustal thickness of 25 km. When εH ¼ �0.65 and b ¼ 0.8, the finalcrustal thickness is ~97 km. Next, we consider how erosion andexhumation modifies the crustal thickness.

In the central Sierra Nevada, Al-in-Hornblende barometer onMesozoic plutons establishes that Triassic plutons in the easternSierra emplaced at ~3.2 kbars are juxtaposed by Late Cretaceous

Fig. 13. Crustal thickness determined by host rock strain (εH) and pluton volumefraction (b). The initial thickness of the crust is assumed to be 25 km and the calcu-lation takes 20% shortening in plutons and 20% volume loss/length change along Y-direction of host rocks into account. If εH ¼ -0.65 and b ¼ 0.8, the resulting thickness ofcrust is ~97 km. The crustal thickness show in this plot does not include exhumation.Exhumation will reduce the thickness to 77e87 km for Late Cretaceous Sierra Nevada(see text).

Fig. 14. Cartoon showing that exhumation based on barometry of plutons may only give aTime 1, Pluton A was emplaced at 10 km depth and at Time 2, Pluton B was emplaced at 8equals to the thickness of rock eroded. (B) is the case when there is crustal thickening. At Ti8 km depth. The difference between emplacement depth of Pluton A and B is less than the

W. Cao et al. / Journal of Structural Geology 84 (2016) 14e3026

(~86 Ma) plutons at ~2 kbars, suggesting a Mesozoicexhumation< 5 km (Cao et al., 2015). In theWMB, Triassic volcanicsand Jurassic marine sediments are exposed at the surface and showlower to upper greenschist grades of metamorphism. In addition,Late Jurassic plutons in the WMB (e.g., the Guadalupe IgneousComplex) intruded these sedimentary rocks at shallow levels cor-responding to 1e2 kbars (Haeussler and Paterson, 1993; Putirkaet al., 2014) and are intruded by Late Cretaceous plutons withslightly higher Al-in-hornblende pressures of ~3 kbars (Ague andBrimhall, 1988a; Haeussler and Paterson, 1993), which suggeststhat large exhumation did not occur in the WMB early in theMesozoic and if anything depths increased in the Cretaceous, thelatter consistent with Cretaceous crustal thickening.

In the southern Sierra, Early Triassic plutons emplaced at10e15 km depth are intruded by Middle Jurassic and Late Creta-ceous plutons emplaced at 5e6 km depth (Nadin and Saleeby,2008; Saleeby and Dunne, 2015), suggesting that mid-crustalexhumation from Early Triassic to Late Cretaceous in southern Si-erra is ~10 km. Exhumation in the southern Sierra along the KaweakRiver based on barometry in plutons indicates an average 0.5 mm/yr exhumation between ~100 Ma and 85 Ma although the westernand eastern parts of the southern Sierras have different exhumationrates (Saleeby and Sousa, personal communication).

In summary, the by ~85 Ma, the exhumation of southern Sierra

minimum value of exhumation. (A) is the case when there is no crustal thickening. Atkm depth. The difference between emplacement depth of Pluton A and B is 2 km andme 1, Pluton A was emplaced at 10 km depth and at Time 2, Pluton B was emplaced atthickness of rock eroded.

Fig. 15. Elevation as a function of crustal thickness and arc root thickness if crust isisostastically balanced (Eq. (3)). For the estimated crustal thickness range of SierraNevada at 80 Ma (~80 km), the elevation will be 4.5e5.7 km if the arc root is 30 km.The area between horizontal dashed lines is the elevation range of Puna-Altiplanoplateau of the central Andes (4e5 km, Allmendinger et al., 1997). This calculation as-sumes the crust density rc ¼ 2.9 g/cm3, mantle density rm ¼ 3.3 g/cm3, and arc rootdensity rr ¼ 3.5 g/cm3 based on Lee et al. (2015). This calculation also assumes that0 km elevation when the crust is 25 km thick.

W. Cao et al. / Journal of Structural Geology 84 (2016) 14e30 27

is larger (~10 km) than the exhumation in the central Sierra(<5 km). However, the exhumation based on barometry only givesa minimum value of rocks eroded (Fig. 14). The correction ofexhumation with respect of crustal thickening should be made. Inthis paper, for a first-order approximation, we use a more generousrange of 10e20 km for the amount of removed crust duringMesozoic thickening of the Sierra Nevada. Since we earlier esti-mated that crustal thickness is ~97 km at 85 Ma, surface erosionwill reduce the Late Cretaceous crustal thickness to ~77e87 km.

5.3. Implications on downward transfer of host rocks, paleo-elevation and arc behaviors

As we discussed in the previous sections, downward transfer ofhost rocks satisfy the strain patterns observed and helps both thetectonically driven thickening and root development and the“space problem” during magma ascent and emplacement (e.g.Saleeby, 1990; Paterson and Farris, 2008; Anderson et al., 2010;Chapman et al., 2014). The downward transfer of host rocks isrequired to make the mass balance in the arc crust: about ~50-km-thickmaterials have to be transported downwards to accommodatethe thickened crust if the initial crust thickness is 25 km. Theminimum rates of such processes are shown in Fig. 10. In a 10 Myrinterval, 20e130 km of downward transport of host rock material isfeasible given these rates. Although this is a rough estimate, itshows that materials can be displaced downward by tens-of-kilometers during the duration of a magmatic flare event, makingenough space for emplacement of voluminous magma.

Downward transport of host rocks can potentially play a role inregulating Sierran magmatism and arc tempos: It transportssupracrustal materials downward, fertilizing the MASH in thelower crust and upper mantle in addition to crustal inputs from thefore-arc, retro-arc and downgoing plate (e.g. Kay et al., 2005;Ducea, 2001; DeCelles et al., 2009; Hacker et al., 2011; Chapmanet al., 2013, 2014). d18O and ε Nd results suggest that crustal sour-ces have contributed up to 50% of Sierran magmatic sources (Duceaand Barton, 2007). The isotopic data cannot constrain the exactsource of supracrustal materials, but leaves open the possibilitythat intra-arc downward transfer of host rocks is one likely source.Crustal thickening not only introduces greater crustal componentsto the arc magma source regime, but it also places greater verticalintervals of the source regime in both the plagioclase out andgarnet in stability fields favoring the accumulation of an eclogiticresidue along the base of the crust (Saleeby et al., 2003). Thefoundering of such high-density arc roots into asthenosphericmantle may further introduce supracrustal materials (e.g. crustalisotopic signatures) into the mantle and contribute to thegeochemical heterogeneity of the mantle.

The estimated 77 to 87 km-thick crust at ~85 Ma will build ahigh elevation in the Sierra Nevada as a result of isostasy. Elevation(h) is a function of crustal thickness (H) and arc root thickness (R) ifcrust is isostastically balanced (Eq. (3), modified from Lee et al.,2015):

h ¼ h0 þ�1� rc

rm

�$ðH � H0Þ þ

�1� rr

rm

�$R (3)

h0 is the initial elevation and H0 is the initial crustal thickness. rc,rm, and rr are the densities of crust, asthenospheric mantel and arc

root, respectively. Note that�1� rc

rm

�>0 while

�1� rr

rm

�<0,

which means that thickened crust will positively contribute to theelevation while the arc root will reduce the elevation. Fig. 15 showsthe how the elevation changes with crustal thickness (H) and arcroot thickness (R) assuming h0 ¼ 0 and H0 ¼ 25 km. If the arc root is

30 km thick, the elevation of Sierra Nevada at ~85 Ma will be4.5e5.7 km, close to the Puna-Altiplano plateau of central Andes(4e5 km, Allmendinger et al., 1997).

The thickened crust also influences the asthenospheric mantlewedge and magma production. Fig. 16 shows a subduction zonebefore and after magmatism and deformation. Before magmatismand deformation started (Fig. 16A), the crust is 25 km thick andmantle flow is not impeded. After magmatism and deformationstarted (Fig. 16B), the crust is thickened to ~80 km with a 30-km-thick arc root. Mantle flow will be impeded and as a result, arcmagmatism will potentially migrate inboard (Karlstrom et al.,2014). Chin et al. (2012, 2015) also suggested that such thickenedcrust also cools down the mantle wedge causing the reduction ofthe production of new magmas. The impeded mantel flow, litho-spheric mantle cooling effect, and the slab flattening that started~90e85 Ma (Saleeby, 2003) in Sierra Nevada may eventually cooland thus reduce magma generation in the Sierra Nevada area andcause the eastward migration of magmatism.

6. Conclusions

A compiled dataset of >650 finite strain analyses from centraland southern Sierra Nevada, California are used to help quantify thearc crust deformation in Sierra Nevada. Our results show that theoverall Mesozoic tectonism results in 65% arc-perpendicular bulkcrust shortening under a more or less plane strain condition withductile strain recording about 50% shortening. The tectonism leadsto at least >100% crustal thickening. Since Mesozoic magmatismreplaced ~80% of the crust, this mass balance exchange droveadditional thickening. We estimated that the arc crust has beensignificantly thickened to ~80 km by ~85 Ma due to the combinedeffects of tectonism and magmatism. A 30-km-thick arc root wasgenerated and surface elevation of ~5 km at this same time. Usingconstraints on exhumation, most crustal materials must be trans-ported downwards to accommodate the crustal thickening atestimated rates of 2e13 km/Myr. The downward transfer of crustalmaterials must occur in locations of active magma channels, or in

Fig. 16. Cartoon shows how magmatism and deformation thicken the crust. (A) is the geometry of an arc system before magmatism and deformation. The initial thickness of crust(H0) is 25 km and elevation (h0) is at sea level (0 km). The mantle flow is not impeded. (B) is the geometry of the arc system after magmatism and deformation and it may apply tothe Sierra Nevada arc at ~85 Ma. Crust is thickened (H') to ~80 km and elevation (h') is ~5 km. The total thickness of crust and arc root extending into mantle wedge is ~80 km.Mantle flow is impeded. The thickened crust could also cool down the mantle wedge. The impeded mantle flows, cooling effect, and the slab flattening are likely to contribute to themigration of magmatism.

W. Cao et al. / Journal of Structural Geology 84 (2016) 14e3028

“escape channels” in between solidified plutons that decrease insize with time and depth resulting in an increase in the intensity ofconstrictional strain with depth. The crustal thickness and surfaceelevation are thus controlled by both tectonism and magmatismbut are slightly modify the surface erosion. On the one hand, thedownward transported crustal materials may fertilize the MASHzone thus enhancing the generation of additional magmas. How-ever, as the crustal root grows it may potentially pinch out and coolthe mantle wedge and thus cause reduction of arc magmatism.

Acknowledgments

Paterson acknowledges support from NSF grants EAR-1019636,EAR-0537892 and EAR-0073943 and U.S. Geological Survey EDMAPgrants G13AC00120 (supporting Sean Hartman) and 03HQA0038(supporting Vali Memeti) for work in and around the TIC. WenrongCao acknowledges support from EDMAP Grant G12AC20178 andGeological Society of America Graduate Student Research Grants.We thank USC undergraduate student Emily Van Guilder for theinitial strain data compilation. Snir Attia, Sean Hartman, KatieArdill, and Babsi Ratschbacher, are gratefully thanked for theirdiscussions and comments on the manuscript. Cin-Ty Lee, JulingZhang and Xun Yu are thanked for the discussion on isostasy andcrustal thickening. Alan Chapman and an anonymous reviewer arethanked for their critical comments, which greatly help to improvethe quality of the manuscript. We also thank Editor Toru Takeshitafor handling the submission.

Appendix A. Supplementary data

Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.jsg.2015.11.002.

References

Ague, J.J., 1997. Thermodynamic calculation of emplacement pressures for batho-lithic rocks, California: implications for the aluminum-in-hornblende barom-eter. Geology 25, 563e566.

Ague, J.J., Brandon, M.T., 1992. Tilt and northward offset of Cordilleran batholithsresolved using igneous barometry. Nature 360, 146e149.

Ague, J.J., Brimhall, G.H., 1988a. Magmatic arc asymmetry and distribution ofanomalous plutonic belts in the batholiths of California: effects of assimilation,crustal thickness, and depth of crystallization. Geol. Soc. Am. Bull. 100, 912e927.

Ague, J.J., Brimhall, G.H., 1988b. Regional variations in bulk chemistry, miner-alogy,and the compositions of mafic and accessory minerals in the batholiths of

California. Geol. Soc. Am. Bull. 100, 891e911.Albertz, M., 2006. Relationships between melt-induced rheological transitions and

finite strain: observations from host rock pendants of the Tuolumne IntrusiveSuite, Sierra Nevada, California. J. Struct. Geol. 28, 1422e1444.

Allmendinger, R.W., Cardozo, N.C., Fisher, D., 2012. Structural Geology Algorithms:Vectors & Tensors. Cambridge University Press, Cambridge, UK.

Allmendinger, R.W., Jordan, T.E., Kay, S.M., Isacks, B.L., 1997. The evolution of theAltiplano-Puna plateau of the Central Andes. Annu. Rev. Earth Planet. Sci. 25,139e174.

Anderson, J.L., Barth, A.P., Wooden, J.L., Mazdab, F., 2008. Thermometers and ther-mobarometers in granitic systems. Rev. Mineral. Geochem. 69, 121e142.

Anderson, J.L., Paterson, S.R., Memeti, V., Zhang, Tao, Economos, R., Barth, A.,Pignotta, G., Mundil, R., Foley, B., Schmidt, K., 2010. Episodic downward crustalflow during Triassic to Cretaceous magma surges in the central Sierra arc. Geol.Soc. Am. Abstr. Progr. 42, 51.

Anderson, J.L., Smith, D.R., 1995. The effects of temperature and fO2 on the Al-in-hornblende barometer. Am. Mineral. 80, 549e559.

Barth, A.P., Feilen, A.D.G., Yager, S.L., Douglas, S.R., Wooden, J.L., Riggs, N.R.,Walker, J.D., 2012. Petrogenetic connections between ash-flow tuffs and agrandioritic to granitic intrusive suite in the Sierra Nevada arc, California.Geosphere 8, 250e264.

Barton, M.D., Hanson, R.B., 1989. Magmatism and the development of low-pressuremetamorphic belts: Implications from the western United States and thermalmodeling. Geol. Soc. Am. Bull. 101, 1051e1065.

Bateman, P.C., Chappell, B.W., 1979. Crystallization, formation, and solidification ofthe Tuolumne intrusive series, Yosemite National Park, California. Geol. Soc.Am. Bull. 99, 465e482.

Brook, C.A., 1977. Stratigraphy and structure of the Saddlebag Lake roof pendant,Sierra Nevada, California. Geol. Soc. Am. Bull. 88, 321e334.

Busby-Spera, C.J., Saleeby, J.B., 1990. Intra-arc strike-slip fault exposed at batholithiclevels in southern Sierra Nevada, California. Geology 18, 255e259.

Cao, W., Paterson, S.R., Memeti, V., Mundil, R., Anderson, L., Schmidt, K., 2015.Tracking paleo-strain field in a continental arc: a study of incremental and finitestrain in Mesozoic plutons and host rocks, respectively in central Sierra Nevada,California. Lithosphere 7, 296e320.

Cardozo, N., Allmendinger, R.W., 2013. Spherical projections with OSXStereonet.Comput. Geosci. 51, 193e205.

Chapman, A.D., Ernst, W.G., Gottlieb, E., Powerman, V., Metzger, E.P., 2015. Detritalzircon geochronology of NeoproterozoiceLower Cambrian passive-marginstrata of the White-Inyo Range, east-central California: implications for theMojaveeSnow Lake fault hypothesis. Geol. Soc. Am. Bull. http://dx.doi.org/10.1130/B31142.1. B31142e1.

Chapman, A.D., Saleeby, J.B., Eiler, J., 2013. Slab flattening trigger for isotopicdisturbance and magmatic flare- up in the southernmost Sierra Nevada bath-olith, California. Geology 41, 1007e1010. http://dx.doi.org/10.1130/G34445.1.

Chapman, A.D., Saleeby, J.B., Wood, D.J., Piasecki, A., Kidder, S., Ducea, M.N.,Farley, K.A., 2012. Late Cretaceous gravitational collapse of the southern SierraNevada batholith, California. Geosphere 8, 314e341.

Chapman, A.D., Ducea, M.N., Kidder, S., Petrescu, L., 2014. Geochemical constraintson the petrogenesis of the Salinian arc, central California: implications for theorigin of intermediate magmas. Lithos 200e201, 126e141. http://dx.doi.org/10.1016/j.lithos.2014.04.011.

Chin, E.J., Lee, C.-T.A., Luffi, P., Tice, M., 2012. Deep lithospheric thickening andrefertilization beneath continental arcs: case study of the P, T and compositionalevolution of peridotite xenoliths from the Sierra Nevada, California. J. Petrol. 53,477e511. http://dx.doi.org/10.1093/petrology/egr069.

W. Cao et al. / Journal of Structural Geology 84 (2016) 14e30 29

Chin, E.J., Lee, C.-T.A., Blichert-Toft, J., 2015. Growth of upper plate lithospherecontrols tempo of arc magmatism: constraints from Al-diffusion kinetics andcoupled Lu-Hf and Sm-Nd chronology. Geochem. Persp. Let. 1, 20e32. http://dx.doi.org/10.7185/geochemlet.1503.

Clark, L.D., 1964. Stratigraphy and Structure of Part of the Western Sierra NevadaMetamorphic Belt, California. U. S. Geological Survey Special Paper 410. U. S.Govt. Print. Off.

Crespi, J.M., 1986. Some guidelines for the practical application of Fry's method ofstrain analysis. J. Struct. Geol. 24, 799e808.

DeCelles, P.G., Ducea, M.N., Kapp, P., Zandt, G., 2009. Cyclicity in Cordilleranorogenic systems. Nat. Geosci. 2, 251e157.

Dickinson, W.R., 2008. Accretionary MesozoiceCenozoic expansion of the Cordil-leran continental margin in California and adjacent Oregon. Geosphere 4,329e353.

Dixon, E.T., 1995. An Evaluation of Hornblende Barometry, Isabella to TehachapiRegion, Southern Sierra Nevada, California. M.S. thesis. University of Michigan,Ann Arbor, p. 150.

Ducea, M., 2001. The California Arc: thick granitic batholiths, eclogitic residues,lithospheric-scale thrusting, and magmatic flare-ups. GSA Today 11, 4e10.

Ducea, M.N., Barton, M.D., 2007. Igniting flare-up events in Cordilleran arcs. Geology35, 1047e1050. http://dx.doi.org/10.1130/G23898A.1.

Edelman, S.H., Sharp, W.D., 1989. Terranes, early faults, and pre-Late Jurassicamalgamation of the western Sierra Nevada metamorphic belt, California. Geol.Soc. Am. Bull. 101, 420e1433.

Erslev, E.A., 1988. Normalized center-to-center strain analysis of packed aggregates.J. Struct. Geol. 10, 201e209.

Greene, D.C., Schweickert, R.A., 1995. The Gem Lake shear zone: Cretaceous dextraltranspression in the northern Ritter Range pendant, eastern Sierra Nevada,California. Tectonics 14, 945e961. http://dx.doi.org/10.1029/95TC01509.

Hacker, B.R., Kelemen, P.B., Behn, M.D., 2011. Differentiation of the continental crustby relamination. Earth Planet. Sci. Lett. 307, 501e516. http://dx.doi.org/10.1016/j.epsl.2011.05.024.

Haeussler, P.J., Paterson, S.R., 1993. Post-emplacement tilting and burial of theGuadalupe igneous complex, sierra Nevada, California. Geol. Soc. Am. Bull. 105,1310e1320.

Hanson, R.B., Sorensen, S.S., Barton, M.D., Fiske, R.S., 1993. Long-term evolution offluiderock interactions in magmatic arcs: evidence from the Ritter Rangependant, Sierra Nevada, California, and numerical modeling. J. Petrol. 34,23e62.

Holland, T., Blundy, J., 1994. Non-ideal interactions in calcic amphiboles and theirbearing on amphibole-plagioclase thermometry. Contrib. Mineral. Petrol. 116,433e447.

Hildreth, W., Moorbath, S., 1988. Crustal contributions to arc magmatism in theAndes of central Chile. Contrib. Mineral. Petrol. 984, 455e489.

Horsman, E., Tikoff, B., Czeck, D., 2008. Rheological implications of heterogeneousdeformation at multiple scale in the Late Cretaceous Sierra Nevade, California.Geol. Soc. Am. Bull. 120, 238e255.

Hossack, J.R., 1967. Pebble deformation and thrusting in the Bygdin Area (southernNorway). Tectonophysics 5, 315e339.

Hsu, T.C., 1966. The characteristics of coaxial and non-coaxial strain paths. J. StrainAnalysis Eng. Des. 1, 216e222.

Johnson, M.C., Rutherford, M.J., 1989. Experimental calibration of an Aluminum-in-hornblende geobarometer with application to Long Valley caldera (California)volcanic rocks. Geology 17, 837e841.

Kay, S.M., Gody, E., Kurz, A., 2005. Episodic arc migration, crustal thickening, sub-duction erosion and magmatism in the south-central Andes. Geol. Soc. Am. Bull.117, 67e88. http://dx.doi.org/10.1130/B25431.1.

Karlstrom, L., Lee, C.-T.A., Manga, M., 2014. The role of magmatically driven litho-spheric thickening on arc front migration. Geochem. Geophys. Geosystems 15.http://dx.doi.org/10.1002/2014GC005355.

Kistler, R.W., 1990. Two different lithosphere types in the Sierra Nevada, California.Geol. Soc. Am. Memoirs 174, 271e282.

Lahren, M.M., Schweickert, R.A., 1989. Proterozoic and lower Cambrian passivemargin rocks of snow Lake pendant, Yosemite-Emigrant Wilderness, sierraNevada, California: evidence for major early cretaceous dextral translation.Geology 17, 156e160.

Lahren, M.M., Schweickert, R.A., 1995. Continuation of the Snow Lake block intowestern Nevada and speculations on the geometry and tectonics of the Mojave-Snow Lake fault. Geol. Soc. Am. Abstr. Progr. 27, 58.

Lee, C.T.A., Thurner, S., Paterson, S.R., Cao, W., 2015. The rise and fall of continentalarcs: Interplays between magmatism, uplift, weathering, and climate. EarthPlanet. Sci. Lett. 425, 105e119.

Lisle, R.J., 1977. Estimation of the tectonic strain ratio from the mean shape ofdeformed elliptical markers. Geol. Mijnb. 56, 140e144.

Lisle, R.J., 1979. Strain analysis using deformed pebbles: the influence of initialpebble shape. Tectonophysics 60, 263e277.

Lisle, R.J., 1985. Geological Strain Analysis: a Manual for the Rf/q Technique. Per-gamon Press, Oxford.

Lode, W., 1926. Versuche uber den Einfluss der mittleren Hauptspannung auf dasFliessen des Metalle Eisen, Kupfer, und Nickel. Zieitschrift Phys. 36, 913e939.

Longiaru, S., 1987. Tectonic Evolution of Oak Creek Volcanic Roof Pendant, EasternSierra Nevada, California. Ph.D. thesis. University of California Santa Cruz.

March, A., 1932. Mathematische Theorie der Regelung nach der Korngestalt. Z. Krist.81, 285e297.

Memeti, V., Gehrels, G.E., Paterson, S.R., Thompson, J.M., Mueller, R.M., 2010. Re-

evaluating the Mojave-Snow Lake fault hypothesis and origins of central Sierranmetasedimentary pendant strata using detrital zircon provenance analyses.Lithosphere 2, 341e360.

Miller, D.M., Oertel, G., 1979. Strain determination from the measurement of pebbleshapes: a modification. Tectonophysics 55, T11eT13.

Miller, R.B., Paterson, S.R., 1991. Geology and tectonic evolution of the BearMountains fault zone, Foothills terrane, central Sierra Nevada, California. Tec-tonics 10, 995e1006.

Mookerjee, M., Nickleach, S., 2011. Three-dimensional strain analysis using math-ematica. J. Struct. Geol. 33, 1467e1476.

Mundil, R., Nomade, S., Paterson, S., Renne, P.R., 2004. Geochronological Constraints(40Ar/39Ar and U/Pb) on the Thermal History of the Tuolumne Intrusive Suite(Sierra Nevada, California). AGU Fall Meeting Abstract V53A-0616.

Nadin, E.S., Saleeby, J.B., 2008. Disruption of regional primary structure of the SierraNevada batholith by the Kern Canyon fault system, California. Geol. Soc. Am.Special Pap. 438, 1e26.

Oertel, G., 1983. The relationship of strain and preferred orientation of phyllosilicategrains in rocks e a review. Tectonophysics 100, 413e447.

Paterson, S.R., 1983. A comparison of methods used in measuring finite strains fromellipsoidal objects. J. Struct. Geol. 5, 611e618.

Paterson, S.R., Ducea, 2015. Arc magmatic tempos: gathering the evidence. Ele-ments 11, 91e98.

Paterson, S.R., Farris, D.W., 2008. Downward host rock transport and the formationof rim monoclines during the emplacement of Cordilleran batholiths. Trans-actions R. Soc. Edinb. Earth Sci. 97, 397e413.

Paterson, S.R., Fowler, T.K., Schmidt, K.L., Yoshinobu, A.S., Yuan, E.S., Miller, R.B.,1998. Interpreting magmatic fabric patterns in plutons. Lithos 44, 53e82.

Paterson, S.R., Tobisch, O.T., Bhattacharyya, T., 1989. Regional structural and strainanalyses of terranes in the Western Metamorphic belt, central Sierra Nevada,California. J. Struct. Geol. 11, 255e273.

Paterson, S.R., Memeti, V., Anderson, J.L., Cao, Wenrong, Lackey, J.S., Putirka, K.D.,Miller, R.B., Miller, J.S., Mundil, R., 2014. Overview of arc processes and tempos.In: Memeti, V., et al. (Eds.), Formation of the Sierra Nevada Batholith: Magmaticand Tectonic Processes and Their Tempos, Geological Society of America FieldGuide, 34, pp. 87e104.

Paterson, S.R., Vernon, R.H., 1995. Bursting the bubble of ballooning plutons: a re-turn to nested diapirs emplaced by multiple processes. Geol. Soc. Am. Bull. 107,1356e1380.

Paterson, S.R., Yu, H., 1993. Microstructures and primary grain-shape fabrics insandstones: implications for depositional processes and strain analyses.J. Struct. Geol. 16, 505e517.

Paterson, S.R., Yu, H., Oertel, G., 1995. Primary and tectonic fabric intensities inmudrocks. Tectonophysics 247, 105e119.

Pfiffner, O.A., Ramsay, J.G., 1982. Constraints on geological strain rates: Argumentsfrom finite strain states of naturally deformed rocks. J. Geophys. Res. 87,311e321.

Pickett, D.A., Saleeby, J.B., 1993. Thermobarometric constraints on the depth ofexposure and conditions of plutonism and metamorphism at deep levels of theSierra Nevada Batholith, Tehachapi Mountains, California. J. Geophys. Res. SolidEarth (1978e2012) 98, 609e629.

Putirka, K., Canchola, J., Rash, J., Smith, O., Torrez, G., Paterson, S., Ducea, M., 2014.Pluton assembly and the genesis of granitic magmas: insights from the GICpluton in cross section, Sierra Nevada Batholith, California. Am. Mineral. 99,1284e1303.

Ramsay, J.G., 1967. Folding and Fracturing of Rocks. McGraw-Hill, New York.Ramsay, J.G., Wood, D., 1973. The geometric effects of volume changes during

deformation processes. Tectonophysics 16, 263e277.Saleeby, J.B., 1990. Progress in tectonic and petrogenetic studies in an exposed

cross-section of young (~100 Ma) continental crust, southern Sierra Nevada,California. In: Salisbury, M.H., Fountain, D.M. (Eds.), Exposed Cross- Sections ofthe Continental Crust, pp. 137e158.

Saleeby, J.B., 2003. Segmentation of the Laramide slab e evidence from thesouthern Sierra Nevada region. Geol. Soc. Am. Bull. 115, 655e668.

Saleeby, J.B., 2011. Geochemical mapping of the Kings-Kaweah ophiolite belt,southwestern Sierra Nevada Foothills-Evidence for progressive melange for-mation in a large offset transform-subduction initiation environment. In:Wakabayashi, J., Dilek, E. (Eds.), Geological Society of America Special Paper onthe the Nature and Formation of Melanges, Geological Society of AmericaSpecial Paper, 480, pp. 31e73. http://dx.doi.org/10.1130/2011.2480(02).

Saleeby, J.B., Busby, C., 1993. Paleogeographic and tectonic setting of axial andwestern metamorphic framework rocks of the southern Sierra Nevada, Cali-fornia. In: Dunne, G., McDougall, K. (Eds.), Mesozoic Paleogeography of theWestern United States-II: Pacific Section, Society of Economic Paleontologistsand Mineralogists, Book, 71, pp. 197e226.

Saleeby, J.B., Ducea, M.N., Busby, C.J., Nadin, E.S., Wetmore, P.H., 2008. Chronology ofpluton emplacement and regional deformation in the southern Sierra Nevadabatholith, California. Geol. Soc. Am. Special Pap. 438, 397e427.

Saleeby, J.B., Ducea, M.N., Clemens, K.D., 2003. Production and loss of high-densitybatholithic root, southern Sierra Nevada, California. Tectonics 22. http://dx.doi.org/10.1029/2002TC001374, 2003.

Saleeby, J.B., Dunne, G., 2015. Temporal and tectonic rela- tions of early Mesozoicarc magmatism, southern Sierra Nevada, California. In: Anderson, T.H.,Didenko, A.N., John- son, C.L., Khanchuk, A.I., MacDonald Jr., J.H. (Eds.), LateJurassic Margin of the Laurasiada Record of Faulting Accommodating PlateRotation, Geological Society of America Special Paper, 513. http://dx.doi.org/

W. Cao et al. / Journal of Structural Geology 84 (2016) 14e3030

10.1130/2015.2513(05).Schmidt, M.W., 1992. Amphibole composition in tonalite as a function of pressure:

an experimental calibration of the Al-in-hornblende barometer. Contrib. Min-eral. Petrol. 110, 304e310.

Schweickert, R.A., Hanson, R.E., Girty, G.H., 1999. Accretionary tectonics of thewestern Sierra Nevada metamorphic belt. In: Wagner, D.L., Graham, S.A. (Eds.),Geologic Field Trips in Northern California: Sacramento, CA, vol. 119. CaliforniaDepartment of Conservation, Division of Mines and Geology, CentennialMeeting of the Cordilleran Section of the Geological Society of America, SpecialPublication, pp. 33e79.

Schweickert, R.A., Lahren, M.M., 1993. Tectonics of the east-central Sierra Nevada-Saddlebag Lake and northern Ritter Range pendants. In: Lahren, M.M.,Trexler, J.H., Spinoza, C. (Eds.), Crustal Evolution of the Great Basin and theSierra Nevada: Geological Society of America May 1993 Field Trip Guidebook.Department of Geological Sciences, University of Nevada, Reno, pp. 313e352.

Schweickert, R.A., Lahren, M.M., 2006. Geologic evolution of saddlebag Lakependant, eastern sierra Nevada, California: tectonic implications. In: Girty, G.,Cooper, J.D. (Eds.), Using Stratigraphy, Sedimentology, and Geochemistry toUnravel the Geologic History of the Southwestern Cordillera: Pacific Section.SEPM (Society for Sedimentary Geology), Fullerton, pp. 27e56.

Schweickert, R.A., Saleeby, J.B., Tobisch, O.T., 1977. Paleotectonic and paleogeo-graphic significance of the Calaveras complex, western Sierra Nevada, Califor-nia. In: Stewart, J.H., Stevens, C.H. (Eds.), Paleozoic Paleogeography of theWestern United States: Pacific Section. Society of Economic Paleontologists andMineralogists, pp. 381e394.

Sharp, W.D., Tobisch, O.T., Renne, P.R., 2000. Development of Cretaceous trans-pressional cleavage synchronous with batholith emplacement, central SierraNevada, California. Geol. Soc. Am. Bull. 112, 1059e1066. http://dx.doi.org/10.1130/0016-7606(2000).

Shimamoto, T., Ikeda, Y., 1976. A simple algebraic method for strain estimation fromdeformed ellipsoidal objects. 1, Basic theory. Tectonophysics 36, 315e337.

Snow, C.A., Scherer, H., 2006. Terranes of the Western Sierra Nevada foothillsmetamorphic belt, California: a critical review. Int. Geol. Rev. 48, 46e62. http://dx.doi.org/10.2747/0020-6814.48.1.46.

Sullivan, W.A., 2013. L tectonites. J. Struct. Geol. 50, 161e175.Tikoff, B., Saint-Blanquat, M., 1997. Transpressional shearing and strike-slip parti-

tioning in the Late Creta ceous Sierra Nevada magmatic arc, California. Tectonics16, 442e459. http://dx.doi.org/10.1029/97TC00720.

Tobisch, O.T., Fiske, R.S., Sacks, S., Taniguchi, D., 1977. Strain in metamorphosedvolcaniclastic rocks and its bearing on the evolution of orogenic belts. Geol. Soc.Am. Bull. 88, 23e40.

Tobisch, O.T., Fiske, R.S., 1982. Repeated parallel deformation in part of the easternSierra Nevada, California and its implications for dating structural events.J. Struct. Geol. 4, 177e195.

Tobisch, O.T., Fiske, R.S., Saleeby, J.B., Holt, E., Sorensen, S.S., 2000. Steep tilting ofmetavolcanic rocks by multiple mechanisms, central Sierra Nevada, California.Geol. Soc. Am. Bull. 112, 1043e1058.

Tobisch, O.T., Saleeby, J.B., Renne, R.R., McNulty, B., Tong, W., 1995. Variations indeformation fields during development of a large volume magmatic arc, centralSierra Nevada, California. Geol. Soc. Am. Bull. 107, 148e166.

Weinberg, R.F., Sial, A.N., Mariano, G., 2004. Close spatial relationship betweenplutons and shear zones. Geology 32, 377e380.

Zak, J., Paterson, S.R., Memeti, V., 2007. Four magmatic fabrics in the Tuolumnebatholitsh, central Sierra Nevada, California (USA): Implications for interpretingfabric patterns in plutons and evolution of magma chambers in the upper crust.Geol. Soc. Am. Bull. 119, 184e201.

Zellmer, G.F., Annen, C., 2008. An Introduction to Magma Dynamics, 304. GeologicalSociety, London, Special Publications, pp. 1e13.