Tectonophysics 342 (2001) 371–388 www.elsevier.com/locate/tecto

Thermo-rheological, shear heating model for leucogranite generation, , and deformation during the Trans-Hudson , , South Dakota

Peter I. Nabelek*, Mian Liu, Mona-Liza Sirbescu

Department of Geological Sciences, University of Missouri-Columbia, Columbia, MO 65211, USA Accepted 20 June 2001

Abstract

This paper evaluates thermotectonic models for metamorphism and leucogranite generation during the Proterozoic Trans- Hudson orogeny, as recorded in rocks exposed in the Black Hills, SD. Intrusion of the Harney Peak and associated pegmatites at 1715 Ma occurred at the waning stages of regional deformation and staurolite-grade regional metamorphism. Published Consortium for Continental Reflection Profiling (COCORP) results indicate that Proterozoic sedimentary rocks were thrust over the Archean Wyoming province during the Trans-Hudson collision. Isotopic compositions of the Harney Peak Granite suggest that the exposed Proterozoic and Archean metasedimentary rocks in the Black Hills represent source rocks of the . Numerical simulations of the regional metamorphism and Harney Peak Granite generation, assuming crustal thickening by thrusting coupled with erosion, show the following: (1) Doubling of the crust with normal distribution of radioactive elements does not yield sufficiently high temperatures to cause anatexis anywhere in the crust or growth of in the now exposed part of the crust; (2) a 35-km drop-off length for internal heat production can yield sufficient temperature for garnet growth at the current erosion level; it is, however, insufficient to produce staurolite, and melting can occur only in the deepest parts of the crust; (3) temperatures in crust with stable 70 km thickness for 40 Ma and 35 km drop-off length for heat production could become sufficient to produce staurolite at the current erosion level, and subsequent rapid denudation of the crust could potentially trigger decompression-melting of lower crustal rocks. Although this model could potentially explain the observed temporal relationship between regional metamorphism and leucogranite generation, it is inconsistent with melting of upper crustal Proterozoic source rocks that is indicated by isotopic compositions of the granites, with lack of evidence for rapid denudation of the Trans-Hudson orogen, and with confinement of the leucogranites to the deformed Proterozoic metapelitic rocks. Production of the Harney Peak Granite and its relationship to regional metamorphism of the country rocks are best explained by shear heating at the interface between the Wyoming province and overthrusted sedimentary rocks. We suggest that with reasonable rheologic properties of metapelites and rates of plate convergence, shear heating sufficiently perturbs locally the geotherms to cause anatexis in a deep shear zone system and growth of staurolite in the overlying crust. Modeling rheology of the lithologically stratified thickened crust, with granitic and metapelitic upper plate shows that the currently exposed part of the crust and the granite source region were ductile through much of the orogeny, which explains regional folding of the schists and predicts ductile shear zones in the granite source region. Because of the lithologic stratification, the granitic

* Corresponding author. E-mail address: [email protected] (P.I. Nabelek).

0040-1951/01/$ - see front matter D 2001 Elsevier Science B.V. All rights reserved. PII: S 0040-1951(01)00171-8 372 P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 basement is likely to become significantly weaker during crustal thickening than the upper crust dominated by schists. A weak basement under a folded upper crust is likely to contribute to the observed relatively flat topography of high plateaus over thickened orogens. D 2001 Elsevier Science B.V. All rights reserved.

Keywords: Shear heating; Leucogranites; Numerical modeling; Rheology; Black Hills; Anatexis; Metamorphism

1. Introduction phism has been focused on the Himalayas where leucogranites constitute an integral part of the orogen The source of heat leading to leucogranite gen- (e.g., Le Fort et al., 1987; Harris and Massey, 1994; eration from crustal rocks in thickened convergent Treloar, 1997; Harrison et al., 1998; Huerta et al., orogens is a major unresolved issue. Although under- 1998; Vance and Harris, 1999). However, analogous plating of the crust or intrusion of mafic leucogranites in terms of composition, mode of em- could potentially trigger crustal anatexis, there is a placement, source and host-rock compositions, and lack of chemical and physical evidence for intrusion structural context occur in other regions where crus- of mantle-derived magmas into the source regions of tal collisions have occurred, including the Appala- leucogranites (Le Fort et al., 1987; Scaillet et al., chian Mountains of Maine (Tomascak et al., 1996; 1990; Krogstad and Walker, 1996; Tomascak et al., Pressley and Brown, 1999) and the Black Hills, SD 1996; Nabelek and Bartlett, 1998; Pressley and (Redden et al., 1990; Nabelek et al., 1992a; Krogstad Brown, 1999). Furthermore, partial melting of crustal and Walker, 1996; Nabelek and Bartlett, 1998). This protoliths requires intrusion of at least an equivalent suggests that there may be a common process lead- mass of basalt, which is likely to lead to hybrid- ing to leucogranite generation during crustal colli- ization (Grunder, 1995). Without intrusion of mafic sion. In this paper, we explore possible models for magmas, thermal relaxation within thickened crust generation of the Harney Peak Granite (HPG) in the with typical concentration of radioactive elements Black Hills during the Proterozoic Trans-Hudson cannot by itself give temperatures necessary to melt orogeny, which was responsible for coalescence of metasedimentary source rocks by dehydration-melt- much of the North American craton. Previously ing reactions, except in lower parts of the crust (e.g., published geological, geochemical, thermobaromet- England and Thompson, 1984; Thompson and Con- ric, and chronological data for the metamorphism nolly, 1995). Although pressure–temperature–time and granite generation in the Black Hills provide ( P–T–t) paths in thick orogens may intersect wa- stringent constraints for numerical models of leucog- ter-present solidus of metapelites during exhumation, ranite generation. We conclude that shear heating of thermometry, compositions, and phase relationships pelitic schists during synorogenic thrusting was most of leucogranites suggest that most were high-temper- likely responsible for generation of the HPG. The ature ( > 750 C) magmas that formed by muscovite similarity of scales and processes in the Trans-Hud- or biotite dehydration-melting reactions in metasedi- son orogen to other large orogens suggests that shear mentary rocks (Harris and Inger, 1992; Nabelek et heating may be important for petrogenesis of leucog- al., 1992b; Nabelek and Bartlett, 1998; Patin˜o-Douce ranites in collisional settings. and Harris, 1998). Therefore, to explain the leucog- ranites, modifications of simple crustal thickening- erosion models, including decompression melting of 2. Metamorphism in the Black Hills lower-crustal rocks or deep burial of heat-producing lithologies, have been proposed (e.g., Harris and The Proterozoic Trans-Hudson orogen extends over Massey, 1994; Ruppel and Hodges, 1994; Huerta et several thousand kilometers from the southern edge of al., 1998; Jamieson et al., 1998). the Wyoming craton to northern Quebec. Following Much of the debate about the heat source for erosion and covering by Phanerozoic sediments, part leucogranite generation and associated metamor- of it was uplifted during the Laramide orogeny and is P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 373 now exposed in the core of the Black Hills (Fig. 1a). calated gabbro sills and felsic tuffs (Redden et al., The orogenic events that are recorded by the Pre- 1990). It is likely that these sequences represent what cambrian rocks in the Black Hills have traditionally Baird et al. (1996) inferred to be a wedge of arc rocks been ascribed to collision of the Archean Superior that were thrust over the Wyoming province (Fig. 1). province with the Wyoming province. However, a The Precambrian terrane also includes exposures of a recent Consortium for Continental Reflection Profil- small Archean leucogranite body and metapelites at ing (COCORP) transect across the orogen south of Bear Mountain along the western margin of the terrane the U.S.–Canada border indicates instead that there and of a highly deformed Archean Little Elk Creek may have been a small crustal block, named the granite near the eastern margin of the terrane to the Dakota block, that collided directly with the Wyom- north of the area shown in Fig. 2 (Redden et al., 1990). ing province (Baird et al., 1996; Fig. 1b). It is thus evident that the Archean rocks, probably Metamorphic rocks and leucogranites in the Black belonging to the Wyoming province, were imbricated Hills are the products of events that occurred during with the Proterozoic formations. the orogeny. The metamorphic rocks are dominated by The metasedimentary rocks have undergone two quartzite, metapelite, and metagraywacke (Fig. 2) that regional deformation events (Redden et al., 1990). The originated as platform to deep-marine sequences de- first event resulted in northeast-trending F1 folds that posited 2100–1880 Ma ago, based on ages of inter- show little penetrative deformation. This event may be

Fig. 1. (a) Map showing the relationship of the Black Hills, SD, to major cratonic blocks and the Trans-Hudson orogen (after Hoffman, 1990). The darkest numbers are model mantle extraction ages (in Ga), based mostly on Sm–Nd isotopic data, for Precambrian rocks within each tectonic province. Inset shows location of the map within North America. (b) Baird et al.’s (1996) interpretation of the COCORP transect indicated in part (a). 374 P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388

Fig. 2. Geologic map of Proterozoic terrane in southern Black Hills. Heavy lines are faults; heavy dash lines are isograds: St — staurolite, S — first sillimanite, SK—second sillimanite, K—kyanite. A tuffaceous shale unit (now schist) is shown to highlight major fold structures. Short- dash line within the main body of the Harney Peak Granite marks boundary between mostly B-rich (outside) and Ti-rich granites (inside; Nabelek et al., 1992b). Regions with high abundance of pegmatites are noted. Small exposures of Archean granites and schists occur at the western margin of the Proterozoic terrane and off the map to the northeast of the terrane. related to accretion of island arcs from the south as and Friberg, 1990). There appears to be a progression expressed in the Cheyenne belt of southeastern Wyom- of garnet dates to 1720 Ma with closer proximity to the ing (Dahl et al., 1999). The second deformation, HPG (Dahl et al., 1998). related to the Trans-Hudson collision, resulted in the The latter date approximately corresponds to NNW-trending F2 folds with steeply dipping foliation emplacement of the HPG and its satellite plutons. that dominate the structure of the Black Hills. Sub- The granites were emplaced as thousands of dikes vertical faults that juxtaposed contrasting lithologies (Duke et al., 1990). Indeed, the metamorphic rocks to have similar orientation and are thought to have been the southwest and northwest of the main pluton were active during and after folding (Redden et al., 1990). intruded by hundreds of granite dikes and pegmatites The earliest date for F2 folding is 1760 ± 7 Ma, based (Norton and Redden, 1990). The mineralogy of the 207 206 on combined Pb/ Pb step-leach ages on syn-F2 granites and pegmatites is dominated by , sodic garnet and staurolite from the western portion of the plagioclase, microcline, muscovite, tourmaline or bio- Precambrian terrane near the kyanite isograd (Dahl and tite. Major pegmatite intrusions are often concentrated Frei, 1998). Barometry on from the same area near the major NNW-string faults, suggesting that the indicates pressures of approximately 7.5 kbar (Terry faults may have been pathways for migration of P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 375 leucogranitic melts. Redden et al. (1990) obtained a therefore, only a relevant summary is presented here. 1728 ± 4 Ma U–Pb crystallization age for the HPG The HPG is highly peraluminous and has trace ele- based on two highly discordant zircons and a con- ment characteristics that indicate derivation from cordant 1715 ± 3 Ma age on a monazite from a sill metapelitic or metagraywacke sources. In general, within in the core of the main pluton. the core of the HPG is more Ti-rich and has biotite Krogstad and Walker (1994) obtained concordant as the dominant ferromagnesian , whereas its 1704 to 1700 Ma U–Pb ages on apatites from the flanks and satellite plutons are B-rich and contain Tin Mountain pegmatite located near the western more tourmaline than biotite. Production of the high-B margin of the exposed Proterozoic terrane. The range and high-Ti melts is attributed to muscovite and of ages for the leucogranites may reflect uncertainty biotite dehydration-melting reactions, respectively, as due to inheritance, discordance, or differences in muscovite is the dominant B-containing phase in closure temperatures of the analyzed . On metapelites, whereas biotite is the dominant Ti-con- the other hand, the range may also indicate an ex- taining phase (Nabelek et al., 1992a; Nabelek and tended duration of magmatism. For simplicity, in this Bartlett, 1998). These reactions are consistent with paper we refer to all leucogranite intrusions and relative REE and Th concentrations in the two suites, pegmatites in the Black Hills as the HPG. with depletion of these elements in the B-rich suite Whether the HPG was emplaced rapidly or over a and enrichment in the Ti-rich suite. The depletion in period of millions of years, the radiometric data the former suite is attributed to disequilibrium melting indicate that its emplacement post-dated initial garnet involving monazite, which remained armored by sta- growth in the exposed portion of the crust by several ble biotite in the residue (Nabelek and Glascock, tens of millions of years. Indeed, combined 40Ar/39Ar 1995). Oxygen isotope fractionations among minerals data on hornblende and micas from the metamorphic in the granites indicate crystallization temperatures of rocks suggest that they already cooled to < 500 Cby >750 C for both granite suites, consistent with the time of granite intrusion (Holm et al., 1997). dehydration-melting reactions in the source region Emplacement of the post-F2 HPG appears to have (Nabelek et al., 1992b). Furthermore, calculated water superimposed the first and second sillimanite iso- content of the HPG , based on composition of grads on the regional metamorphism, which may primary magmatic fluid inclusions, is 3.5 wt.%, explain in part the youngest garnet ages (Dahl et also consistent with dehydration-melting reactions al., 1998). Moreover, the emplacement resulted in rather than fluid-present melting (Nabelek and Ternes, flattening of the steeply dipping regional foliation 1997). around the main pluton and some satellite intrusions. Isotopic data show that the granites were generated At the time of granite emplacement, the country from heterogeneous sources. The tourmaline-contain- rocks were at 3.5–4 kbar based on garnet–alumino- ing granites and pegmatites have similar Early Proter- silicate–quartz–plagioclase barometry (Helms and ozoic Nd and Pb model TDM ages and the same range Labotka, 1991). Thus, the metamorphic rocks that of whole rock d18O values (12.3–13.6%)asthe are at the present erosion level were exhumed from country rock schists (Nabelek et al., 1992b; Krogstad 25 to 13 km between the times of initial garnet et al., 1993; Krogstad and Walker, 1996). This indi- growth (1760 Ma) and granite emplacement (1728– cates that the schists are equivalent to the source rocks 1715 Ma). of this granite suite. In contrast, the Ti-rich granites have mostly Archean TDM ages, similar to TDM ages of the Archean Little Elk Creek granite, implying that 3. Conditions of HPG generation and nature of its the primary source rocks for this suite probably source rocks belonged to the Wyoming craton. d18O values of this suite, ranging from 10.8% to 12.8%, indicate that the The conditions of HPG generation and nature of its sources also included a pelitic component. Overall, source rocks were addressed in previous papers the isotopic data suggest that the HPG melts were (Nabelek et al., 1992a,b; Krogstad et al., 1993; Krog- generated at the interface between the Wyoming stad and Walker, 1996; Nabelek and Bartlett, 1998); craton and overlying Proterozoic schists. The interface 376 P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 was likely imbricated as suggested by the occurrence volumetric radioactive heating, Ar, and shear heating, of Archean granites and metapelites within the dom- As. inantly Proterozoic sequences in the Black Hills, and We solved Eq. (1) using the finite difference the overlapping isotopic values of the two suites method in a two-dimensional, 30 by 125 grid (Liu (Krogstad and Walker, 1996). and Furlong, 1993). We assumed that the crust was thickened by stacking a 35-km sequence of relatively cold oceanic sediments over a 90 km lithosphere with 4. Thermotectonic models a 35 km crust (Fig. 3). Stacking of such a thick sedimentary pile has occurred, for example, during A successful thermotectonic model for metamor- thrusting of the Central Maine Belt pelitic sequences phism and leucogranite generation during the Trans- over the Bronson Hill basement during the Devonian Hudson orogeny as expressed in the Black Hills must (Brown and Solar, 1998a). The thrusting in the Trans- be consistent with the following observations and Hudson orogen was assumed to have occurred along a data: (1) a source region that included mixed Archean single horizontal boundary and after some time period and Proterozoic metapelites, (2) melting temperatures (Table 1) was accompanied by unroofing with diffu- that were sufficiently high for muscovite and biotite sive thermal relaxation. Advection of heat during dehydration-melting reactions, (3) granite generation thrusting was included in the calculation. However, that occurred tens of millions of years following initial because we ignored any possible lateral heterogene- garnet growth and folding of the now exposed meta- ities, the model is equivalent to a one-dimensional morphic rocks, (4) the presence of metamorphic rocks model, which permits easy illustration of evolving in the currently exposed portion of the crust that geotherms and pressure–temperature–time paths. decompressed from about 7.5 to 3–4 kbar prior to One-dimensional models for thermal structures of granite generation, (5) lack of evidence for intrusion the crust are potentially amenable to analytical sol- of mafic magmas into the crust which could have utions (e.g., Mancktelow and Grasemann, 1997). caused heat advection, and (6) constraints imposed by However, because in our models we included erosion the COCORP profile of Baird et al. (1996) (Fig. 1). of internal heat-generation profiles and non-steady Here we examine several potential models that have state erosion rates, simple analytical solutions are been advanced for leucogranite generation in thick- not available. Numerical calculations permit more ened orogens without advection of heat from the flexible examination of non-steady state parameters. mantle by mafic magmas and that could potentially be applicable to metamorphism and HPG generation 4.1. Model parameters during the Trans-Hudson orogeny. The transient thermal evolution during crustal Model parameters that were the same in all thickening and unroofing can be written as: numerical experiments are listed in Table 1. Some parameters merit discussion. The initial crustal  @T L@f thickness of 70 km was estimated from the current 1 þ ¼ kr2T À u ÁrT thickness of the crust in the Trans-Hudson orogen @t C @T p ( 45 km; Fig. 1), plus 25 km of eroded crust as 1 given by barometry of the exposed metapelites. We þ ðAr þ AsÞð1Þ Cp evaluated four different models: thermal relaxation with erosion and normal distribution of internal heat (Liu and Furlong, 1993). Parameter T is temperature generation (model 1), effect of high internal heat and the term uÁrT is thermal advection associated production (model 2), decompression melting with with thickening and erosion, in which u is the velocity high internal heat production (model 3), and shear vector. Parameter t is time, k is thermal diffusivity,  is heating (model 4). In models where shear heating is density, Cp is specific heat, L is latent heat of fusion, not considered, thermal evolution is mainly con- and f is melt fraction. Our numerical simulations were trolled by thermal relaxation and unroofing. Except focused on examination of the last two parameters, in model 3, unroofing was assumed to start 10 Ma P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 377

Fig. 3. Initial geometry and temperature distribution for numerical simulations. Lithospheric properties are listed in Table 1. The model assumes thickening of the crust along a thrust fault at depth of 35 km. The Moho is at depth of 70 km and bottom of the lithosphere at 125 km. Maximum initial temperature of overthrusted sedimentary rocks is assumed to be 250 C. A 15-km drop-off length for heat production was assumed for the initial temperature distribution in the underlying lithosphere in models 1 and 4 (solid profile) and a 35-km drop-off length was assumed for models 2 and 3 (dashed profile). In model 4, the boundary between overthrusted sedimentary rocks and underlying basement is assumed to be a 4-km-wide shear zone. Position of the metapelite solidus is shown for reference. after initiation of thrusting to allow sufficient time mantle to the base of the lithosphere rather than to for thickening of the upper plate and for the crust to the base of the crust. become unstable. The average unroofing rate of 0.3 Internal heat generation depends on concentration mm year À 1 is given by the time it took for the and distribution of heat producing elements in the exposed schists to decompress from 25 km at 1760 crust. We used 2 10 À 6 WmÀ 3 for volumetric in- Ma to 12 km at 1715 Ma, as indicated by thermo- ternal heating near the surface (A0), which is based on barometry and geochronology (Terry and Friberg, the average concentration of radioactive elements in 1990; Dahl and Frei, 1998). the Black Hills schists (Nabelek and Bartlett, 1998). The initial total thickness of the lithosphere in the The value is normal for crustal rocks, which generally models is 125 km. Temperature at the surface of the have heat production in the range of 0.5 10 À 6 to thickened lithosphere is held at 0 C and at the base at 3 10 À 6 WmÀ 3 (Spear, 1993). For initial condi- 1300 C. Although our main interest is in the thermal tions, we assumed exponential decrease in heat pro- conditions in the crust, we chose fixed temperature at duction with depth in both the upper and lower plates, À Z/D the base of the lithosphere because both temperature A(Z)=A0e , where Z is depth and D is drop-off and heat flux at the base of the crust are transient length (Lachenbruch, 1970). The initial heat produc- variables during orogeny. Models that assume a fixed tion profile was assumed to erode during denudation mantle flux at the base of the crust (e.g., Peacock, of the crust. 1989; Zen, 1995) require an artificial rise in the The initial geotherms in the lower plate (Fig. 3) are mantle temperature to keep a constant thermal gra- defined by the parameters listed in Table 1. For dient across the Moho, as Fourier’s law requires heat models 1 and 4, D of 15 km was used, and in models flux to be proportional to the thermal gradient (Liu 2 and 3, D of 35 km was used. In contrast, the and Furlong, 1993). Our assumption has the more maximum initial temperature of the upper plate was realistic implication of convective stirring of the arbitrarily set at 250 C so that incipient metamor- 378 P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388

Table 1 Lithospheric properties and model parameters All models Depth of thrust fault (km) 35 Total thickness of lithosphere (km) 125 Temperature at top (C) 0 Temperature at bottom (C) 1300 Density of crust (kg m À 3) 2900 Radiogenic heat production at top (W m À 3)2 10 À 6 Thermal diffusivity (m2 s À 1)1 10 À 6 Thermal conductivity (W m À 1 K À 1) 2.25 Coefficients for specific heat a: 276 b: 68.3 10 À 3 c: 87.5 105

Model 1 Model 2 Model 3 Model 4 Drop-off length for heat production (km) 15 35 35 15 Beginning of unroofing (Ma) 10 10 50 10 Rate of unroofing (mm year À 1) 0.3 0.3 1.0 0.3 Duration of thrusting (Ma) n.a. n.a. n.a. 55 Rate of thrusting (cm year À 1) n.a. n.a. n.a. 4.0 Shear stress at thrust (MPa) n.a. n.a. n.a. 35 phism of thrust-up sedimentary sequences could be age schist were used for all assumed lithologies in the approximated. It is noted, however, that within about models. 10 Ma, the thermal structure becomes essentially independent of the choice of the initial geotherm in 4.2. Model 1: thermal relaxation of thickened crust the upper crust. with erosion Latent heat of fusion was invoked in the calcula- tions when temperature reached the muscovite or For reference purposes, we first present a simple biotite + muscovite dehydration-melting reactions, model in which evolving geotherms (Fig. 4a) and which as noted above are indicated by high crystal- pressure–temperature–time ( P–T–t) paths (Fig. 4b) lization temperatures and inferred water content of the in a thickened crust were controlled mainly by thermal HPG (Nabelek et al., 1992a; Nabelek and Ternes, relaxation and erosion. Fig. 4a shows that nowhere in 1997). Given that the trace element characteristics of the crust temperature becomes sufficiently high to the HPG indicate dominance of muscovite dehydra- reach the fluid-absent metapelite solidus, as indicated tion-melting rather than biotite-dehydration melting by the depth–time path of the Moho. Moreover, only (Nabelek and Bartlett, 1998), we assumed that melting in the vicinity of the thrust fault is the temperature occurred over a 20 C interval and melt fraction was sufficient to produce garnet in metamorphic rocks, 25% as allowed by the average composition of the whereas in the currently exposed part of the crust Black Hills schists (Nabelek and Bartlett, 1998). The (initial depth 25 km), the maximum temperatures value for latent heat of fusion is that for albite would have been 100 C below the garnet isograd (Stebbins et al., 1983). (Fig. 4b). Within reasonable range of model parame- Specific heat of the crustal rocks was assumed to ters, we find that thermal relaxation in the crust À 2 vary with temperature, with Cp = a + bT ÀcT . The coupled with continuous erosion cannot explain the applied coefficients (Table 1) are based on the average grade of metamorphism and granite generation in the mineralogy of the schists. For example, at 25 C heat Black Hills. Similar conclusions about achievable capacity is 726 J kg À 1 and at 700 C it is 1223 J kg À 1. metamorphic grade in upper parts of an eroding Heat capacities of granite and olivine vary similarly thickened crust has been reached previously by others with temperature; therefore, coefficients for the aver- (e.g., Thompson and Connolly, 1995). P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 379

Chamberlain and Sonder, 1990; Ruppel and Hodges, 1994; Royden, 1993; Huerta et al., 1998; Jamieson et al., 1998). Because we have no good reason to assume a higher volumetric heat production at the surface than 2 10 À 6 WmÀ 3, in model 2 we only tested the effect of deep burial of heat-producing lithologies by assuming a 35-km drop-off length for heat production in both upper and lower plates. Compared to model 1, geotherms are elevated, espe- cially in the lower crust (Fig. 5a). Although the temperature at the erosion level (25 km initial depth) almost reaches the garnet isograd, it is insufficient to explain the syn-F2 staurolite-grade metamorphism (Fig. 5b). Moreover, nowhere in the upper crust does the temperature become sufficiently high to reach the

Fig. 4. Model 1—thermal relaxation of thickened crust with erosion. Input parameters are discussed in the text and listed in Table 1. Erosion begins at 10 Ma. (a) Diagram showing the initial and evolving geotherms in 10 Ma intervals (times noted on the bottom right). Depths–temperature paths of the thrust fault and Moho with time are indicated. (b) Corresponding pressure – temperature–time ( P–T–t) paths for four sections of the thickened crust. Numbers at each path indicate initial model depths and dots indicate 10 Ma intervals. Garnet and staurolite-in isograds (Spear and Cheney, 1989) are appropriate for compositions of minerals in the Black Hills schists. Relevant fluid-absent solidi of metapelites (Le Breton and Thompson, 1988; Patin˜o-Douce and Harris, 1998), and stability fields for aluminosilicate polymorphs (Holdaway, 1971) are also shown. Section of the crust that began at 25 km is at the present level of exposure. Section of the crust that began at 45 km represents the Wyoming basement. Note that in this model melting does not occur anywhere in the crust and temperatures in the upper crust are insufficient to explain the regional metamorphic grade that is observed in the Black Hills.

Fig. 5. Model 2 — effect of high internal heat production. All 4.3. Model 2: effect of high internal heat production parameters are the same as in model 1, except that here the drop-off depth for radioactive heat production is increased to 35 km. (a) Several authors have previously argued that Evolving geotherms which show that melting occurs only in the bottom portion of the lower crust. (b) P–T–t paths showing that increased concentration of heat producing elements maximum temperatures in the upper crust are higher than in model in the upper crust or deep burial of heat-producing 1, but insufficient to explain the regional metamorphic grade in the material can result in partial melting in the crust (e.g., Black Hills. 380 P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 metapelite solidus. This is because of the cooling effect of erosion, especially in the upper crust, as shown by the P–T–t paths. Only in the lower half of the lower plate temperatures become sufficiently high for melting of metapelites. This conclusion agrees with other two-dimensional models that assumed deep burial of heat-producing material (Huerta et al., 1998; Jamieson et al., 1998). It is very unlikely, however, that the HPG was generated in such a deep part of the crust as the likely lithologies in the deep crust are mafic rocks or felsic , not meta- pelites. Furthermore, confinement of melting to deep rocks of the Wyoming province would produce magmas with only Archean TDM ages. We conclude, therefore, that a thickened heat-producing layer in the upper crust alone cannot explain the regional metamorphic grade in the currently exposed part of the crust and HPG generation from Proterozoic metapelites.

4.4. Model 3: decompression-melting coupled with high internal heat production

Harris and Massey (1994) argued that the High Himalayan leucogranites were generated by decom- Fig. 6. Model 3 — decompression-melting coupled with high in- pression-melting of metasedimentary rocks. This re- ternal heat production. All parameters are the same as in model 2, except that rapid erosion of 1.0 mm year À 1 is assumed to start 40 quires a rapid, near-adiabatic decompression of source Ma after thickening. (a) Evolving geotherms showing that melting is rocks so that dehydration-melting reactions can be be possible only in the lower part of the lower crust. (b) P–T–t intersected. We modeled this process assuming a 35- paths showing that in the upper crust, thermal conditions could km drop-off length for concentration of heat-produc- potentially have been sufficient for grade of metamorphism that is ing isotopes and beginning of erosion delayed to 40 observed in the Black Hills. Ma after beginning of thermal relaxation of the thickened crust. The assumed erosion rate is 1.0 mm genesis of the HPG as there were with model 2. First, year À 1. Extensive period of stable crustal thickness this model again requires the presence of metapelites permits elevation of geotherms throughout the crust to at depths greater than 45 km, which is inconsistent higher temperatures than would occur if erosion began with barometry of the schists in the Black Hills, and earlier. The results show that sufficiently high temper- the likely occurrence of granulites and more mafic atures to produce garnet and staurolite are reached in rocks at such great depths. Second, this model can the upper crust and melting of metapelites could occur plausibly only explain the high-Ti granites from the if they ascended from a depth greater than 45 km in Archean Wyoming basement. It cannot account for the lower crust (Fig. 6a,b). Harris and Massey (1994) the high-B granites that were generated from Proter- also concluded that rapid decompression would per- ozoic sedimentary rocks thrust over the Wyoming mit melting only of source rocks coming from similar province. Third, 40Ar/39Ar analysis of hornblende depths. and micas from the Black Hills are not consistent This model could potentially explain both the early with rapid denudation of the orogen (Holm et al., growth of garnet at the erosion level and the subse- 1997). Fourth, the model implies a random distribu- quent intrusion of granites. However, there are similar tion of melt production in the lower crust rather than problems with application of this model to petro- its confinement to subhorizonal shear zones in shal- P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 381 lower, mid-crustal levels that appears to be the case in collisional orogens (Brown, 1994). Therefore, we do not favor rapid denudation of the Trans-Hudson orogen as the dominant mechanism leading to gen- eration of the HPG. It is noted that for melting to occur in this model, high internal heat production in both the upper and lower plates is required, as for example implemented here by assumption of the 35- km drop-off length. Assumption of a more typical 10–15 km drop-off length (Lachenbruch, 1970) does notleadtosufficienttemperaturestoexplainthe metamorphic grade at the erosion level or melting anywhere in the crust.

4.5. Model 4: shear-heating coupled with erosion

Our preferred model for metamorphism and granite generation in the Black Hills includes shear heating in shear zones as a significant component of heat gen- eration in the crust (Fig. 7). Shear heating contribution to leucogranite generation has been controversial, largely because of potential for self-regulation with increasing temperature and during melting (Yuen et al., 1978) and poor constraints on rheology of plau- sible source rocks at high temperatures. Shear heating Fig. 7. Model 4 — effect of shear heating. The parameters are the was proposed as a possible mechanism for granite same as in model 1, but shear heating is included. The shear zone is 4 km wide with center at 33 km depth (shaded region in part b). (a) generation in the High Himalayas by Le Fort (1975), Diagram showing the initial and evolving geotherms. A thermal but its significance was discounted by Tokso¨z and anomaly is produced in the shear zone until thrusting ceases. Note Bird (1977), because they thought the source rocks that the metapelite solidus is reached in the shear zone and deeper. may become too weak at temperatures approaching (b) P–T–t paths showing that the metapelite solidus is reached in anatexis to sustain sufficiently high stress for shear the shear zone and temperatures in the overlying crust can explain the observed metamorphic conditions. heating to have an appreciable thermal effect. Shear heating has regained some prominence with recogni- tion that it may be required to explain inverted low-pressure metamorphism and elevated geotherms metamorphic gradients below major thrust faults and in collisional orogens (Hochstein and Reneauer-Lieb, shear zones (England and Molnar, 1993; Treloar, 1998; Stu¨we, 1998). Here we further consider the role 1997), although the relatively high values of shear of shear heating in shear zones as a process leading to stress (100–1100 MPa) that England and Molnar granite generation in light of thermo-rheological con- (1993) empirically obtained are thought unreasonable straints. by many. Zhu and Shi (1990) and Harrison et al. The rate of volumetric shear heating in strained (1997, 1998) argued that shear-heating along thrust rocks is given by As = tn/dz, where t is shear stress, n faults, assuming moderate shear stress of 30–50 MPa, is thrusting velocity, and dz is the width of shear zone could explain generation of the High-Himalaya gran- (Liu and Furlong, 1993). For n we assumed 4 cm ites and we have proposed a similar preliminary year À 1, consistent with the currently observed rates model for generation of the HPG (Nabelek and Liu, of plate convergence. Although the value is probably 1999). In an analogous fashion, some have advocated larger than a typical rate of motion across shear zones, that homogeneous shear associated with deformation the plate convergence rate is likely partitioned across of large crustal sections may lead to high-temperature, the width of the shear zone, which we account for by 382 P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388

fabric orientation, is much smaller than that of a dry granite below the brittle–ductile transition. Fig. 8 shows shear strength values (t) for a mica schist and a granite assuming t = ss/2, where ss is the differential stress s1 À s3. We assumed power law behavior for ss: :  " 1=n H s ¼ exp ð2Þ s A nRT

: (Kirby and Kronenberg, 1987). Parameter " is the strain rate (10 À 15 s À 1), A is a constant, H is the enthalpy of activation, R is the gas constant, and T is temperature (K). Values of these parameters are Fig. 8. Thermal dependence of shear strength of dry granite and listed in Table 2. It is apparent from Fig. 8 that in schist based on power-law rheological parameters given in Table 2. contrast to granite, shear strength values for schist Granite is much stronger than a schist at low temperatures. remain relatively high at 35 MPa even at near- However, schist retains its strength at high temperatures, whereas granite becomes very weak. solidus temperatures. Therefore, for shear stress we used this value to calculate the contribution of shear heating. dz. Furthermore, we assumed that the effect of shear The model results show that temperatures in the heating decreased in a Gaussian fashion away from shear zone and deeper reach the metapelite solidus center of the shear zone. The width of the shear zone 30–40 Ma after the initiation of thrusting, in spite is assumed to be 4 km with its center 2 km above the of the cooling effect of erosion (Fig. 7a). At the plate boundary. The 4-km width is crudely consistent depth of the currently exposed part of the crust, the with spacing of faults in the Black Hills. In any case, garnet isograd is reached about 10 Ma after initia- the results are relatively insensitive to dz values tion of thrusting (Fig. 7b). Thus, in the model, between 1 and 10 km. The assumption of distributed there is an approximately 30 Ma delay between shear heating across a finite shear zone is a better initial garnet growth at the level of exposure (ini- approximation for imbricate thrusting than an assump- tially at 25 km) and granite generation in the shear tion of heat generation along a single fault. It is zone. According to the model, at the level of consistent with occurrence of shear zones in pelitic exposure garnet may have grown for 20–30 Ma rocks that are thrust over basements during collisions until peak metamorphism at staurolite-grade condi- (Brown and Solar, 1998b). The duration of thrusting tions. This model reproduces well the duration of was assumed to be 55 Ma, accounting for the time regional garnet growth in the southern Trans-Hud- needed for rocks at 7.5 kbar to reach the garnet son orogen and its timing relative to intrusion of isograd ( 10 Ma; Fig. 7) plus the time difference the HPG. (45 Ma) between initial garnet growth and HPG intrusion. A common criticism of shear heating is that the Table 2 crust in the ductile region may have insufficient Parameters for power-law behavior of stress strength to support significant shear stress. The Schista Graniteb Olivinec criticism may be related to the common assumption H (kJ mol À 1) 98 123 420 of granite rheology for the crust. A granitic crust A (MPa À n s À 1) 1.3 10 À 67 1.6 10 À 9 1.9 103 indeed becomes weak below the brittle–ductile tran- n 31 3 3 sition (see below). However, as shown in experiments a Shea and Kronenberg (1992). by Shea and Kronenberg (1992), the dependence of b Kirby and Kronenberg (1987). mica schist rheology on temperature, irrespective of c Rutter and Brodie (1988). P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 383

5. Crustal rheology tively high strength below the transition in contrast to mica poor rocks (c.f., Shea and Kronenberg, 1992). Parallel to calculating evolving geotherms and P– The ductile behavior of the deep parts of the schist T–t paths in model 4, we computed the evolving yield layer provides an explanation for the development of strength of the lithosphere assuming three rheologi- F2 folds that are observed in the Black Hills, while cally distinct layers (Fig. 9). The top layer was maintenance of high shear strength permits enhance- assumed to be a schist, the second layer a dry granite, ment of temperatures in the ductile shear zone until and the third layer an olivine mantle. These layers the time of partial melting. According to the model, represent Proterozoic metasedimentary sequences, the the currently exposed part of the crust should have underlying Wyoming craton, and the mantle litho- remained in the ductile zone through the time of HPG sphere, respectively. Yield strength at each depth is intrusion, which is consistent with flattening of the F2 the minimum stress for brittle or ductile deformation. foliation by the pluton. However, by 60 Ma this Brittle strength is given by Byerlee’s law: t = msn, part of the crust may have reached the brittle–ductile where m is the frictional coefficient (0.6) and sn is the transition. normal stress on the fault (Byerlee, 1978). By assum- In contrast to the upper schist layer, the granitic ing that fractures occur in all orientations, sn can be middle layer and the mantle lithosphere become replaced by the lithospheric stress at each depth. relatively weak early after thickening. Such rheologic Ductile strength was calculated using Eq. (2) assum- behavior is likely to lead to gneissic morphology of ing t = ss/2 and flow parameters in Table 2. granitic rocks in the deep crust. An evidence for such The model results show an early development of a behavior in the Wyoming crust during the Trans- relatively shallow brittle–ductile transition in the Hudson orogeny may be in the distinctly gneissic upper schist layer. However, the schist retains a rela- fabric of the Archean Little Elk Creek granite and, to a

Fig. 9. Calculated rheology of a layered lithosphere at 20 Ma intervals during relaxation and erosion. Note that scale of the abscissa for the initial and subsequent time intervals is different. Layer 1 represents a schist, layer 2 a dry granite, and layer 3 olivine mantle. The schist layer retains relatively high strength, even in the ductile part, through the duration of thermal relaxation, in contrast to granitic lower crust and the mantle. Shear zone and current erosion level remain within the ductile region of the upper crust. However, at 60 Ma the present surface approaches the brittle–ductile transition due to erosion. 384 P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 lesser extent, in the granite at Bear Mountain (Redden suggests a causal relationship between thrusting and et al., 1990). Another result of a weak ductile granitic melt production, although others have argued essen- crust may be the development of topographically tially the opposite, that melts within the crust pro- relatively flat plateaus over thickened orogens as the mote movement of major faults and exhumation of lower crust will have a tendency to creep and there- orogens (e.g., Hollister, 1993). fore expand. Although any evidence that such a Because of the similar geologic conditions at the plateau may have existed during the Trans-Hudson level of granite emplacement in the CMB and the orogeny is gone, a weak lower granitic crust could Black Hills, we propose that the HPG was generated potentially explain the flat topography of other pla- in shear zones along imbricate thrusts at the interface teaus, for example the Tibetan plateau (e.g., Bird, between the Wyoming province and overthrusted 1991; Zhao and Morgan, 1987). metasedimentary rocks (Fig. 10). The model is con- sistent with the COCORP results (Fig. 1; Baird et al., 1996). Generation of small magma batches at an 6. Discussion imbricated Archean and Proterozoic interface would have lead to intrusion of isotopically heterogeneous In the thermo-rheologic model that best explains leucogranitic dikes that reflect the range of composi- generation of the HPG, partial melting is assumed to tions of the exposed potential source rocks. Further- occur in a crustal shear-zone system. Although the more, as shown in Fig. 7b, melting in shallower parts granite’s source region is not accessible, there is of the shear zone would more likely lead only to evidence from other collisional terranes that leucog- muscovite-dehydration melting giving rise to the B- ranite melts are generated in shear zones and then, at rich granite suite, while melting in the hotter deeper least partly, migrate along listric faults to higher part of the shear zone system would have also levels in the crust. For example, Brown and Solar involved biotite, thus leading to the Ti-rich HPG suite. (1998a,b) and Solar et al. (1998) documented mig- We suggest that melts generated in the shear zone matites in subhorizonal shear zones in metasedimen- system migrated along a listric faults to the current tary rocks of the Central Maine Belt (CMB), New level of erosion. The NNW-striking faults in the Black England, that were thrust upon Proterozoic Bronson Hills may be an expression of the upper structural Hill basement during the Devonian. The CMB is a level of the fault system. high-T, low-P metamorphic belt, analogous to the A potential consequence of melt generation by Proterozoic terrane in the Black Hills. These authors shear heating is that shear stress in the shear zone proposed that melts were extracted from the migma- may drop once melt forms. Conversely, as an active titic source region and then migrated along the shear part of the shear zone weakens, shear stress may be zone system to higher levels in the crust due to amplified in other parts of the shear zone system, in a pressure gradients generated by buoyancy and tec- manner similar to stress amplification due to viscous tonic stresses. Leucogranites and pegmatites that relaxation within the ductile crust (Kusznir and Bott, occur in the CMB are isotopically heterogeneous 1977). Furthermore, after melts are extracted, shear like the granites and pegmatites in the Black Hills stress in the source region may again increase. On the (Tomascak et al., 1996; Pressley and Brown, 1999), other hand, in many convergent orogens, including reflecting extraction and migration of small melt the Black Hills and the CMB, granite generation batches from the source region. Similarly, the iso- occurred at the waning stages of deformation in topically heterogeneous High Himalaya leucogranites orogenic cycles. This may indicate that once melt occur within metasedimentary sequences that lie in forms, strain is accumulated in the partially molten the hanging wall of the Main Central Thrust (Deniel zones reducing deformation elsewhere (Brown and et al., 1987; Guillot and Le Fort, 1995). Zhu and Shi Solar, 1998b). However, at the level of granite (1990) and Harrison et al. (1997, 1998) proposed emplacement in upper parts of a listric system closer that the granites were generated because of shear to the brittle–ductile transition, the crystallized gran- heating along the thrust fault. The occurrence of ites may not be deformed as strain there is likely to be leucogranites and their sources in shear zone systems lower. P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 385

Fig. 10. Schematic drawing showing the presumed source region of the HPG within a ductile shear zone at the interface between Proterozoic metasedimentary rocks thrust over the Archean Wyoming basement. Granitic melts migrated within the shear zone and other weak structural zones to the present erosion level. The metasedimentary rocks were folded mostly prior to melting. The drawing is based on the diagram of Solar et al. (1998) illustrating ascent of melts in the Central Maine Belt.

Leucogranites such as the HPG and the Maine thermal conditions are likely to be older than crystal- granites have often been interpreted as post-tectonic, lization age of granites. Thus, the granites may appear largely because of general lack of deformation in the post-tectonic, when in fact they are not. granites and differences between mineral ages in host metamorphic rocks and granite crystallization ages (e.g., Holm et al., 1997; Dahl and Frei, 1998; Nabelek 7. Conclusions and Bartlett, 1998). In addition, granite emplacement at high levels in the crust has been advocated as cause We propose that shear heating during thrusting of of high-T, low-P metamorphism (e.g., Moench and Proterozoic metasedimentary rocks over the Archean Zartman, 1976; Lux et al., 1986; De Yoreo et al., Wyoming province during the Trans-Hudson orogeny 1991). Our thermotectonic model shows, however, contributed significantly to generation of the HPG. By that granites can appear syn-collisional or post-colli- using published values for shear strength of schists sional depending on the depth of the crust where and reasonable convergence rates, we have shown that metamorphic and crystallization ages are obtained sufficient heat can be generated in ductile shear zones and on the metamorphic minerals that are dated. Near in middle portions of thickened crusts to cause partial the source region, dates for peak metamorphism, melting. Our model reproduces well the timing of migmatites, and arrested granite plutons, as recorded regional deformation and metamorphism prior to for example by monazite, may be similar. However, granite intrusion in the Black Hills. In contrast to age of early garnet growth may be older than anatexis other thermal models for crustal melting that require associated with peak metamorphism. In contrast, in unusually high concentrations of radioactive elements shallower parts of the crust where metamorphic rocks or very high rates of decompression-melting, our may have already cooled down from peak thermal model is consistent with the observed concentration conditions prior to granite generation at a greater of heat-producing isotopes in the Black Hills and the depth because of unroofing, even regional metamor- common association of migmatites and leucogranites phic ages recorded by a mineral that grew during peak with shear zones in convergent orogens. Our model 386 P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 also resolves the issue of the occurrence of apparently Deniel, C., Vidal, P., Fernandez, A., Fort, L.P., Peucat, J.J., 1987. post-tectonic granites in convergent orogens, as these Isotopic study of the Manaslu granite (Himalaya, Nepal): infer- ences on the age and source of Himalayan leucogranites. 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