Thermo-rheological, shear heating model for …web.missouri.edu/~lium/Research/Papers/Nabelek01tectono.pdfThermo-rheological, shear heating model for leucogranite generation, metamorphism,

Thermo-rheological, shear heating model for leucogranite

generation, metamorphism, and deformation during

the Proterozoic Trans-Hudson orogeny,

Black Hills, 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 Granite 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 granites. 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 garnet 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 basement 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

0040-1951/01/$ - see front matter D 2001 Elsevier Science B.V. All rights reserved.

PII: S0040-1951 (01 )00171 -8

* Corresponding author.

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

www.elsevier.com/locate/tecto

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

The source of heat leading to leucogranite gen-

eration from crustal rocks in thickened convergent

orogens is a major unresolved issue. Although under-

plating of the crust or intrusion of mafic magmas

could potentially trigger crustal anatexis, there is a

lack of chemical and physical evidence for intrusion

of mantle-derived magmas into the source regions of

leucogranites (Le Fort et al., 1987; Scaillet et al.,

1990; Krogstad and Walker, 1996; Tomascak et al.,

1996; Nabelek and Bartlett, 1998; Pressley and

Brown, 1999). Furthermore, partial melting of crustal

protoliths requires intrusion of at least an equivalent

mass of basalt, which is likely to lead to hybrid-

ization (Grunder, 1995). Without intrusion of mafic

magmas, thermal relaxation within thickened crust

with typical concentration of radioactive elements

cannot by itself give temperatures necessary to melt

metasedimentary source rocks by dehydration-melt-

ing reactions, except in lower parts of the crust (e.g.,

England and Thompson, 1984; Thompson and Con-

nolly, 1995). Although pressure–temperature–time

(P–T– t) paths in thick orogens may intersect wa-

ter-present solidus of metapelites during exhumation,

thermometry, compositions, and phase relationships

of leucogranites suggest that most were high-temper-

ature ( > 750 �C) magmas that formed by muscovite

or biotite dehydration-melting reactions in metasedi-

mentary rocks (Harris and Inger, 1992; Nabelek et

al., 1992b; Nabelek and Bartlett, 1998; Patino-Douce

and Harris, 1998). Therefore, to explain the leucog-

ranites, modifications of simple crustal thickening-

erosion models, including decompression melting of

lower-crustal rocks or deep burial of heat-producing

lithologies, have been proposed (e.g., Harris and

Massey, 1994; Ruppel and Hodges, 1994; Huerta et

al., 1998; Jamieson et al., 1998).

Much of the debate about the heat source for

leucogranite generation and associated metamor-

phism has been focused on the Himalayas where

leucogranites constitute an integral part of the orogen

(e.g., Le Fort et al., 1987; Harris and Massey, 1994;

Treloar, 1997; Harrison et al., 1998; Huerta et al.,

1998; Vance and Harris, 1999). However, analogous

leucogranites in terms of composition, mode of em-

placement, source and host-rock compositions, and

structural context occur in other regions where crus-

tal collisions have occurred, including the Appala-

chian Mountains of Maine (Tomascak et al., 1996;

Pressley and Brown, 1999) and the Black Hills, SD

(Redden et al., 1990; Nabelek et al., 1992a; Krogstad

and Walker, 1996; Nabelek and Bartlett, 1998). This

suggests that there may be a common process lead-

ing to leucogranite generation during crustal colli-

sion. In this paper, we explore possible models for

generation of the Harney Peak Granite (HPG) in the

Black Hills during the Proterozoic Trans-Hudson

orogeny, which was responsible for coalescence of

much of the North American craton. Previously

published geological, geochemical, thermobaromet-

ric, and chronological data for the metamorphism

and granite generation in the Black Hills provide

stringent constraints for numerical models of leucog-

ranite generation. We conclude that shear heating of

pelitic schists during synorogenic thrusting was most

likely responsible for generation of the HPG. The

similarity of scales and processes in the Trans-Hud-

son orogen to other large orogens suggests that shear

heating may be important for petrogenesis of leucog-

ranites in collisional settings.

2. Metamorphism in the Black Hills

The Proterozoic Trans-Hudson orogen extends over

several thousand kilometers from the southern edge of

the Wyoming craton to northern Quebec. Following

erosion and covering by Phanerozoic sediments, part

of it was uplifted during the Laramide orogeny and is

P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388372

now exposed in the core of the Black Hills (Fig. 1a).

The orogenic events that are recorded by the Pre-

cambrian rocks in the Black Hills have traditionally

been ascribed to collision of the Archean Superior

province with the Wyoming province. However, a

recent Consortium for Continental Reflection Profil-

ing (COCORP) transect across the orogen south of

the U.S.–Canada border indicates instead that there

may have been a small crustal block, named the

Dakota block, that collided directly with the Wyom-

ing province (Baird et al., 1996; Fig. 1b).

Metamorphic rocks and leucogranites in the Black

Hills are the products of events that occurred during

the orogeny. The metamorphic rocks are dominated by

quartzite, metapelite, and metagraywacke (Fig. 2) that

originated as platform to deep-marine sequences de-

posited 2100–1880 Ma ago, based on ages of inter-

calated gabbro sills and felsic tuffs (Redden et al.,

1990). It is likely that these sequences represent what

Baird et al. (1996) inferred to be a wedge of arc rocks

that were thrust over the Wyoming province (Fig. 1).

The Precambrian terrane also includes exposures of a

small Archean leucogranite body and metapelites at

Bear Mountain along the western margin of the terrane

and of a highly deformed Archean Little Elk Creek

granite near the eastern margin of the terrane to the

north of the area shown in Fig. 2 (Redden et al., 1990).

It is thus evident that the Archean rocks, probably

belonging to the Wyoming province, were imbricated

with the Proterozoic formations.

The metasedimentary rocks have undergone two

regional deformation events (Redden et al., 1990). The

first event resulted in northeast-trending F1 folds that

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).

P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 373

related to accretion of island arcs from the south as

expressed in the Cheyenne belt of southeastern Wyom-

ing (Dahl et al., 1999). The second deformation,

related to the Trans-Hudson collision, resulted in the

NNW-trending F2 folds with steeply dipping foliation

that dominate the structure of the Black Hills. Sub-

vertical faults that juxtaposed contrasting lithologies

have similar orientation and are thought to have been

active during and after folding (Redden et al., 1990).

The earliest date for F2 folding is 1760 ± 7 Ma, based

on combined 207Pb/206Pb step-leach ages on syn-F2garnet and staurolite from the western portion of the

Precambrian terrane near the kyanite isograd (Dahl and

Frei, 1998). Barometry on garnets from the same area

indicates pressures of approximately 7.5 kbar (Terry

and Friberg, 1990). There appears to be a progression

of garnet dates to 1720 Ma with closer proximity to the

HPG (Dahl et al., 1998).

The latter date approximately corresponds to

emplacement of the HPG and its satellite plutons.

The granites were emplaced as thousands of dikes

(Duke et al., 1990). Indeed, the metamorphic rocks to

the southwest and northwest of the main pluton were

intruded by hundreds of granite dikes and pegmatites

(Norton and Redden, 1990). The mineralogy of the

granites and pegmatites is dominated by quartz, sodic

plagioclase, microcline, muscovite, tourmaline or bio-

tite. Major pegmatite intrusions are often concentrated

near the major NNW-string faults, suggesting that the

faults may have been pathways for migration of

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.


leucogranitic melts. Redden et al. (1990) obtained a

1728 ± 4 Ma U–Pb crystallization age for the HPG

based on two highly discordant zircons and a con-

cordant 1715 ± 3 Ma age on a monazite from a sill

within migmatites in the core of the main pluton.

Krogstad and Walker (1994) obtained concordant

1704 to 1700 Ma U–Pb ages on apatites from the

Tin Mountain pegmatite located near the western

margin of the exposed Proterozoic terrane. The range

of ages for the leucogranites may reflect uncertainty

due to inheritance, discordance, or differences in

closure temperatures of the analyzed minerals. On

the other hand, the range may also indicate an ex-

tended duration of magmatism. For simplicity, in this

paper we refer to all leucogranite intrusions and

pegmatites in the Black Hills as the HPG.

Whether the HPG was emplaced rapidly or over a

period of millions of years, the radiometric data

indicate that its emplacement post-dated initial garnet

growth in the exposed portion of the crust by several

tens of millions of years. Indeed, combined 40Ar/39Ar

data on hornblende and micas from the metamorphic

rocks suggest that they already cooled to < 500 �C by

the time of granite intrusion (Holm et al., 1997).

Emplacement of the post-F2 HPG appears to have

superimposed the first and second sillimanite iso-

grads on the regional metamorphism, which may

explain in part the youngest garnet ages (Dahl et

al., 1998). Moreover, the emplacement resulted in

flattening of the steeply dipping regional foliation

around the main pluton and some satellite intrusions.

At the time of granite emplacement, the country

rocks were at 3.5–4 kbar based on garnet–alumino-

silicate–quartz–plagioclase barometry (Helms and

Labotka, 1991). Thus, the metamorphic rocks that

are at the present erosion level were exhumed from

� 25 to � 13 km between the times of initial garnet

growth (1760 Ma) and granite emplacement (1728–

1715 Ma).

3. Conditions of HPG generation and nature of its

source rocks

The conditions of HPG generation and nature of its

source rocks were addressed in previous papers

(Nabelek et al., 1992a,b; Krogstad et al., 1993; Krog-

stad and Walker, 1996; Nabelek and Bartlett, 1998);

therefore, only a relevant summary is presented here.

The HPG is highly peraluminous and has trace ele-

ment characteristics that indicate derivation from

metapelitic or metagraywacke sources. In general,

the core of the HPG is more Ti-rich and has biotite

as the dominant ferromagnesian mineral, whereas its

flanks and satellite plutons are B-rich and contain

more tourmaline than biotite. Production of the high-B

and high-Ti melts is attributed to muscovite and

biotite dehydration-melting reactions, respectively, as

muscovite is the dominant B-containing phase in

metapelites, whereas biotite is the dominant Ti-con-

taining phase (Nabelek et al., 1992a; Nabelek and

Bartlett, 1998). These reactions are consistent with

relative REE and Th concentrations in the two suites,

with depletion of these elements in the B-rich suite

and enrichment in the Ti-rich suite. The depletion in

the former suite is attributed to disequilibrium melting

involving monazite, which remained armored by sta-

ble biotite in the residue (Nabelek and Glascock,

1995). Oxygen isotope fractionations among minerals

in the granites indicate crystallization temperatures of

>750 �C for both granite suites, consistent with

dehydration-melting reactions in the source region

(Nabelek et al., 1992b). Furthermore, calculated water

content of the HPG magma, based on composition of

primary magmatic fluid inclusions, is � 3.5 wt.%,

also consistent with dehydration-melting reactions

rather than fluid-present melting (Nabelek and Ternes,

1997).

Isotopic data show that the granites were generated

from heterogeneous sources. The tourmaline-contain-

ing granites and pegmatites have similar Early Proter-

ozoic Nd and Pb model TDM ages and the same range

of whole rock d18O values (12.3–13.6%) as the

country rock schists (Nabelek et al., 1992b; Krogstad

et al., 1993; Krogstad and Walker, 1996). This indi-

cates that the schists are equivalent to the source rocks

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

the primary source rocks for this suite probably

belonged to the Wyoming craton. d18O values of this

suite, ranging from 10.8% to 12.8%, indicate that the

sources also included a pelitic component. Overall,

the isotopic data suggest that the HPG melts were

generated at the interface between the Wyoming

craton and overlying Proterozoic schists. The interface


was likely imbricated as suggested by the occurrence

of Archean granites and metapelites within the dom-

inantly Proterozoic sequences in the Black Hills, and

the overlapping isotopic values of the two suites

(Krogstad and Walker, 1996).

4. Thermotectonic models

A successful thermotectonic model for metamor-

phism and leucogranite generation during the Trans-

Hudson orogeny as expressed in the Black Hills must

be consistent with the following observations and

data: (1) a source region that included mixed Archean

and Proterozoic metapelites, (2) melting temperatures

that were sufficiently high for muscovite and biotite

dehydration-melting reactions, (3) granite generation

that occurred tens of millions of years following initial

garnet growth and folding of the now exposed meta-

morphic rocks, (4) the presence of metamorphic rocks

in the currently exposed portion of the crust that

decompressed from about 7.5 to 3–4 kbar prior to

granite generation, (5) lack of evidence for intrusion

of mafic magmas into the crust which could have

caused heat advection, and (6) constraints imposed by

the COCORP profile of Baird et al. (1996) (Fig. 1).

Here we examine several potential models that have

been advanced for leucogranite generation in thick-

ened orogens without advection of heat from the

mantle by mafic magmas and that could potentially

be applicable to metamorphism and HPG generation

during the Trans-Hudson orogeny.

The transient thermal evolution during crustal

thickening and unroofing can be written as:

@T

@t1þ L@f

Cp@T

� �¼ kr2T � u � rT

þ 1

�CpðAr þ AsÞ ð1Þ

(Liu and Furlong, 1993). Parameter T is temperature

and the term u�rT is thermal advection associated

with thickening and erosion, in which u is the velocity

vector. Parameter t is time, k is thermal diffusivity, � is

density, Cp is specific heat, L is latent heat of fusion,

and f is melt fraction. Our numerical simulations were

focused on examination of the last two parameters,

volumetric radioactive heating, Ar, and shear heating,

As.

We solved Eq. (1) using the finite difference

method in a two-dimensional, 30 by 125 grid (Liu

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

a 35 km crust (Fig. 3). Stacking of such a thick

sedimentary pile has occurred, for example, during

thrusting of the Central Maine Belt pelitic sequences

over the Bronson Hill basement during the Devonian

(Brown and Solar, 1998a). The thrusting in the Trans-

Hudson orogen was assumed to have occurred along a

single horizontal boundary and after some time period

(Table 1) was accompanied by unroofing with diffu-

sive thermal relaxation. Advection of heat during

thrusting was included in the calculation. However,

because we ignored any possible lateral heterogene-

ities, the model is equivalent to a one-dimensional

model, which permits easy illustration of evolving

geotherms and pressure– temperature– time paths.

One-dimensional models for thermal structures of

the crust are potentially amenable to analytical sol-

utions (e.g., Mancktelow and Grasemann, 1997).

However, because in our models we included erosion

of internal heat-generation profiles and non-steady

state erosion rates, simple analytical solutions are

not available. Numerical calculations permit more

flexible examination of non-steady state parameters.

4.1. Model parameters

Model parameters that were the same in all

numerical experiments are listed in Table 1. Some

parameters merit discussion. The initial crustal

thickness of 70 km was estimated from the current

thickness of the crust in the Trans-Hudson orogen

(� 45 km; Fig. 1), plus � 25 km of eroded crust as

given by barometry of the exposed metapelites. We

evaluated four different models: thermal relaxation

with erosion and normal distribution of internal heat

generation (model 1), effect of high internal heat

production (model 2), decompression melting with

high internal heat production (model 3), and shear

heating (model 4). In models where shear heating is

not considered, thermal evolution is mainly con-

trolled by thermal relaxation and unroofing. Except

in model 3, unroofing was assumed to start 10 Ma


after initiation of thrusting to allow sufficient time

for thickening of the upper plate and for the crust to

become unstable. The average unroofing rate of 0.3

mm year� 1 is given by the time it took for the

exposed schists to decompress from 25 km at 1760

Ma to 12 km at 1715 Ma, as indicated by thermo-

barometry and geochronology (Terry and Friberg,

1990; Dahl and Frei, 1998).

The initial total thickness of the lithosphere in the

models is 125 km. Temperature at the surface of the

thickened lithosphere is held at 0 �C and at the base at

1300 �C. Although our main interest is in the thermal

conditions in the crust, we chose fixed temperature at

the base of the lithosphere because both temperature

and heat flux at the base of the crust are transient

variables during orogeny. Models that assume a fixed

mantle flux at the base of the crust (e.g., Peacock,

1989; Zen, 1995) require an artificial rise in the

mantle temperature to keep a constant thermal gra-

dient across the Moho, as Fourier’s law requires heat

flux to be proportional to the thermal gradient (Liu

and Furlong, 1993). Our assumption has the more

realistic implication of convective stirring of the

mantle to the base of the lithosphere rather than to

the base of the crust.

Internal heat generation depends on concentration

and distribution of heat producing elements in the

crust. We used 2 10� 6 W m � 3 for volumetric in-

ternal heating near the surface (A0), which is based on

the average concentration of radioactive elements in

the Black Hills schists (Nabelek and Bartlett, 1998).

The value is normal for crustal rocks, which generally

have heat production in the range of 0.5 10� 6 to

3 10� 6 W m� 3 (Spear, 1993). For initial condi-

tions, we assumed exponential decrease in heat pro-

duction with depth in both the upper and lower plates,

A(Z) =A0e� Z/D, where Z is depth and D is drop-off

length (Lachenbruch, 1970). The initial heat produc-

tion profile was assumed to erode during denudation

of the crust.

The initial geotherms in the lower plate (Fig. 3) are

defined by the parameters listed in Table 1. For

models 1 and 4, D of 15 km was used, and in models

2 and 3, D of 35 km was used. In contrast, the

maximum initial temperature of the upper plate was

arbitrarily set at 250 �C so that incipient metamor-

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.


phism of thrust-up sedimentary sequences could be

approximated. It is noted, however, that within about

10 Ma, the thermal structure becomes essentially

independent of the choice of the initial geotherm in

the upper crust.

Latent heat of fusion was invoked in the calcula-

tions when temperature reached the muscovite or

biotite + muscovite dehydration-melting reactions,

which as noted above are indicated by high crystal-

lization temperatures and inferred water content of the

HPG (Nabelek et al., 1992a; Nabelek and Ternes,

1997). Given that the trace element characteristics of

the HPG indicate dominance of muscovite dehydra-

tion-melting rather than biotite-dehydration melting

(Nabelek and Bartlett, 1998), we assumed that melting

occurred over a 20 �C interval and melt fraction was

25% as allowed by the average composition of the

Black Hills schists (Nabelek and Bartlett, 1998). The

value for latent heat of fusion is that for albite

(Stebbins et al., 1983).

Specific heat of the crustal rocks was assumed to

vary with temperature, with Cp = a + bT�cT� 2. The

applied coefficients (Table 1) are based on the average

mineralogy of the schists. For example, at 25 �C heat

capacity is 726 J kg� 1 and at 700 �C it is 1223 J kg� 1.

Heat capacities of granite and olivine vary similarly

with temperature; therefore, coefficients for the aver-

age schist were used for all assumed lithologies in the

models.

4.2. Model 1: thermal relaxation of thickened crust

with erosion

For reference purposes, we first present a simple

model in which evolving geotherms (Fig. 4a) and

pressure–temperature–time (P–T– t) paths (Fig. 4b)

in a thickened crust were controlled mainly by thermal

relaxation and erosion. Fig. 4a shows that nowhere in

the crust temperature becomes sufficiently high to

reach the fluid-absent metapelite solidus, as indicated

by the depth–time path of the Moho. Moreover, only

in the vicinity of the thrust fault is the temperature

sufficient to produce garnet in metamorphic rocks,

whereas in the currently exposed part of the crust

(initial depth 25 km), the maximum temperatures

would have been � 100 �C below the garnet isograd

(Fig. 4b). Within reasonable range of model parame-

ters, we find that thermal relaxation in the crust

coupled with continuous erosion cannot explain the

grade of metamorphism and granite generation in the

Black Hills. Similar conclusions about achievable

metamorphic grade in upper parts of an eroding

thickened crust has been reached previously by others

(e.g., Thompson and Connolly, 1995).

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� 3) 2900

Radiogenic heat production at top (W m� 3) 2 10� 6

Thermal diffusivity (m2 s� 1) 110� 6

Thermal conductivity (W m� 1 K� 1) 2.25

Coefficients for specific heat a: 276

b: 68.3 10� 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� 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� 1) n.a. n.a. n.a. 4.0

Shear stress at thrust (MPa) n.a. n.a. n.a. 35


4.3. Model 2: effect of high internal heat production

Several authors have previously argued that

increased concentration of heat producing elements

in the upper crust or deep burial of heat-producing

material can result in partial melting in the crust (e.g.,

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� 6 W m � 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; Patino-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

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)

Evolving geotherms which show that melting occurs only in the

bottom portion of the lower crust. (b) P–T– t paths showing that

maximum temperatures in the upper crust are higher than in model

1, but insufficient to explain the regional metamorphic grade in the

Black Hills.


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 granulites, 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-

pression-melting of metasedimentary rocks. This re-

quires a rapid, near-adiabatic decompression of source

rocks so that dehydration-melting reactions can be

intersected. We modeled this process assuming a 35-

km drop-off length for concentration of heat-produc-

ing isotopes and beginning of erosion delayed to 40

Ma after beginning of thermal relaxation of the

thickened crust. The assumed erosion rate is 1.0 mm

year � 1. Extensive period of stable crustal thickness

permits elevation of geotherms throughout the crust to

higher temperatures than would occur if erosion began

earlier. The results show that sufficiently high temper-

atures to produce garnet and staurolite are reached in

the upper crust and melting of metapelites could occur

if they ascended from a depth greater than � 45 km in

the lower crust (Fig. 6a,b). Harris and Massey (1994)

also concluded that rapid decompression would per-

mit melting only of source rocks coming from similar

depths.

This model could potentially explain both the early

growth of garnet at the erosion level and the subse-

quent intrusion of granites. However, there are similar

problems with application of this model to petro-

genesis of the HPG as there were with model 2. First,

this model again requires the presence of metapelites

at depths greater than � 45 km, which is inconsistent

with barometry of the schists in the Black Hills, and

the likely occurrence of granulites and more mafic

rocks at such great depths. Second, this model can

plausibly only explain the high-Ti granites from the

Archean Wyoming basement. It cannot account for

the high-B granites that were generated from Proter-

ozoic sedimentary rocks thrust over the Wyoming

province. Third, 40Ar/39Ar analysis of hornblende

and micas from the Black Hills are not consistent

with rapid denudation of the orogen (Holm et al.,

1997). Fourth, the model implies a random distribu-

tion of melt production in the lower crust rather than

its confinement to subhorizonal shear zones in shal-

Fig. 6. Model 3—decompression-melting coupled with high in-

ternal heat production. All parameters are the same as in model 2,

except that rapid erosion of 1.0 mm year� 1 is assumed to start 40

Ma after thickening. (a) Evolving geotherms showing that melting is

be possible only in the lower part of the lower crust. (b) P–T– t

paths showing that in the upper crust, thermal conditions could

potentially have been sufficient for grade of metamorphism that is

observed in the Black Hills.


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

not lead to sufficient temperatures to explain the

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

was proposed as a possible mechanism for granite

generation in the High Himalayas by Le Fort (1975),

but its significance was discounted by Toksoz and

Bird (1977), because they thought the source rocks

may become too weak at temperatures approaching

anatexis to sustain sufficiently high stress for shear

heating to have an appreciable thermal effect. Shear

heating has regained some prominence with recogni-

tion that it may be required to explain inverted

metamorphic gradients below major thrust faults and

shear zones (England and Molnar, 1993; Treloar,

1997), although the relatively high values of shear

stress (100–1100 MPa) that England and Molnar

(1993) empirically obtained are thought unreasonable

by many. Zhu and Shi (1990) and Harrison et al.

(1997, 1998) argued that shear-heating along thrust

faults, assuming moderate shear stress of 30–50 MPa,

could explain generation of the High-Himalaya gran-

ites and we have proposed a similar preliminary

model for generation of the HPG (Nabelek and Liu,

1999). In an analogous fashion, some have advocated

that homogeneous shear associated with deformation

of large crustal sections may lead to high-temperature,

low-pressure metamorphism and elevated geotherms

in collisional orogens (Hochstein and Reneauer-Lieb,

1998; Stuwe, 1998). Here we further consider the role

of shear heating in shear zones as a process leading to

granite generation in light of thermo-rheological con-

straints.

The rate of volumetric shear heating in strained

rocks is given by As = tn/dz, where t is shear stress, nis thrusting velocity, and dz is the width of shear zone

(Liu and Furlong, 1993). For n we assumed 4 cm

year � 1, consistent with the currently observed rates

of plate convergence. Although the value is probably

larger than a typical rate of motion across shear zones,

the plate convergence rate is likely partitioned across

the width of the shear zone, which we account for by

Fig. 7. Model 4— effect of shear heating. The parameters are the

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)

Diagram showing the initial and evolving geotherms. A thermal

anomaly is produced in the shear zone until thrusting ceases. Note

that the metapelite solidus is reached in the shear zone and deeper.

(b) P–T– t paths showing that the metapelite solidus is reached in

the shear zone and temperatures in the overlying crust can explain

the observed metamorphic conditions.


dz. Furthermore, we assumed that the effect of shear

heating decreased in a Gaussian fashion away from

center of the shear zone. The width of the shear zone

is assumed to be 4 km with its center 2 km above the

plate boundary. The 4-km width is crudely consistent

with spacing of faults in the Black Hills. In any case,

the results are relatively insensitive to dz values

between 1 and 10 km. The assumption of distributed

shear heating across a finite shear zone is a better

approximation for imbricate thrusting than an assump-

tion of heat generation along a single fault. It is

consistent with occurrence of shear zones in pelitic

rocks that are thrust over basements during collisions

(Brown and Solar, 1998b). The duration of thrusting

was assumed to be 55 Ma, accounting for the time

needed for rocks at 7.5 kbar to reach the garnet

isograd (� 10 Ma; Fig. 7) plus the time difference

(45 Ma) between initial garnet growth and HPG

intrusion.

A common criticism of shear heating is that the

crust in the ductile region may have insufficient

strength to support significant shear stress. The

criticism may be related to the common assumption

of granite rheology for the crust. A granitic crust

indeed becomes weak below the brittle–ductile tran-

sition (see below). However, as shown in experiments

by Shea and Kronenberg (1992), the dependence of

mica schist rheology on temperature, irrespective of

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� s3. We assumed power law

behavior for ss:

ss ¼"

A

� �1=nexp

H

nRT

� �ð2Þ

(Kirby and Kronenberg, 1987). Parameter " is the

strain rate (10 � 15 s� 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

listed in Table 2. It is apparent from Fig. 8 that in

contrast to granite, shear strength values for schist

remain relatively high at � 35 MPa even at near-

solidus temperatures. Therefore, for shear stress we

used this value to calculate the contribution of shear

heating.

The model results show that temperatures in the

shear zone and deeper reach the metapelite solidus

30–40 Ma after the initiation of thrusting, in spite

of the cooling effect of erosion (Fig. 7a). At the

depth of the currently exposed part of the crust, the

garnet isograd is reached about 10 Ma after initia-

tion of thrusting (Fig. 7b). Thus, in the model,

there is an approximately 30 Ma delay between

initial garnet growth at the level of exposure (ini-

tially at 25 km) and granite generation in the shear

zone. According to the model, at the level of

exposure garnet may have grown for 20–30 Ma

until peak metamorphism at staurolite-grade condi-

tions. This model reproduces well the duration of

regional garnet growth in the southern Trans-Hud-

son orogen and its timing relative to intrusion of

the HPG.

Fig. 8. Thermal dependence of shear strength of dry granite and

schist based on power-law rheological parameters given in Table 2.

Granite is much stronger than a schist at low temperatures.

However, schist retains its strength at high temperatures, whereas

granite becomes very weak.

Table 2

Parameters for power-law behavior of stress

Schista Graniteb Olivinec

H (kJ mol� 1) 98 123 420

A (MPa� n s� 1) 1.3 10� 67 1.6 10� 9 1.9 103

n 31 3 3

a Shea and Kronenberg (1992).b Kirby and Kronenberg (1987).c Rutter and Brodie (1988).

:

:


5. Crustal rheology

Parallel to calculating evolving geotherms and P–

T– t paths in model 4, we computed the evolving yield

strength of the lithosphere assuming three rheologi-

cally distinct layers (Fig. 9). The top layer was

assumed to be a schist, the second layer a dry granite,

and the third layer an olivine mantle. These layers

represent Proterozoic metasedimentary sequences, the

underlying Wyoming craton, and the mantle litho-

sphere, respectively. Yield strength at each depth is

the minimum stress for brittle or ductile deformation.

Brittle strength is given by Byerlee’s law: t= msn,where m is the frictional coefficient (0.6) and sn is thenormal stress on the fault (Byerlee, 1978). By assum-

ing that fractures occur in all orientations, sn can be

replaced by the lithospheric stress at each depth.

Ductile strength was calculated using Eq. (2) assum-

ing t = ss/2 and flow parameters in Table 2.

The model results show an early development of a

relatively shallow brittle–ductile transition in the

upper schist layer. However, the schist retains a rela-

tively high strength below the transition in contrast to

mica poor rocks (c.f., Shea and Kronenberg, 1992).

The ductile behavior of the deep parts of the schist

layer provides an explanation for the development of

F2 folds that are observed in the Black Hills, while

maintenance of high shear strength permits enhance-

ment of temperatures in the ductile shear zone until

the time of partial melting. According to the model,

the currently exposed part of the crust should have

remained in the ductile zone through the time of HPG

intrusion, which is consistent with flattening of the F2foliation by the pluton. However, by � 60 Ma this

part of the crust may have reached the brittle–ductile

transition.

In contrast to the upper schist layer, the granitic

middle layer and the mantle lithosphere become

relatively weak early after thickening. Such rheologic

behavior is likely to lead to gneissic morphology of

granitic rocks in the deep crust. An evidence for such

behavior in the Wyoming crust during the Trans-

Hudson orogeny may be in the distinctly gneissic

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.


lesser extent, in the granite at Bear Mountain (Redden

et al., 1990). Another result of a weak ductile granitic

crust may be the development of topographically

relatively flat plateaus over thickened orogens as the

lower crust will have a tendency to creep and there-

fore expand. Although any evidence that such a

plateau may have existed during the Trans-Hudson

orogeny is gone, a weak lower granitic crust could

potentially explain the flat topography of other pla-

teaus, for example the Tibetan plateau (e.g., Bird,

1991; Zhao and Morgan, 1987).

6. Discussion

In the thermo-rheologic model that best explains

generation of the HPG, partial melting is assumed to

occur in a crustal shear-zone system. Although the

granite’s source region is not accessible, there is

evidence from other collisional terranes that leucog-

ranite melts are generated in shear zones and then, at

least partly, migrate along listric faults to higher

levels in the crust. For example, Brown and Solar

(1998a,b) and Solar et al. (1998) documented mig-

matites in subhorizonal shear zones in metasedimen-

tary rocks of the Central Maine Belt (CMB), New

England, that were thrust upon Proterozoic Bronson

Hill basement during the Devonian. The CMB is a

high-T, low-P metamorphic belt, analogous to the

Proterozoic terrane in the Black Hills. These authors

proposed that melts were extracted from the migma-

titic source region and then migrated along the shear

zone system to higher levels in the crust due to

pressure gradients generated by buoyancy and tec-

tonic stresses. Leucogranites and pegmatites that

occur in the CMB are isotopically heterogeneous

like the granites and pegmatites in the Black Hills

(Tomascak et al., 1996; Pressley and Brown, 1999),

reflecting extraction and migration of small melt

batches from the source region. Similarly, the iso-

topically heterogeneous High Himalaya leucogranites

occur within metasedimentary sequences that lie in

the hanging wall of the Main Central Thrust (Deniel

et al., 1987; Guillot and Le Fort, 1995). Zhu and Shi

(1990) and Harrison et al. (1997, 1998) proposed

that the granites were generated because of shear

heating along the thrust fault. The occurrence of

leucogranites and their sources in shear zone systems

suggests a causal relationship between thrusting and

melt production, although others have argued essen-

tially the opposite, that melts within the crust pro-

mote movement of major faults and exhumation of

orogens (e.g., Hollister, 1993).

Because of the similar geologic conditions at the

level of granite emplacement in the CMB and the

Black Hills, we propose that the HPG was generated

in shear zones along imbricate thrusts at the interface

between the Wyoming province and overthrusted

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

imbricated Archean and Proterozoic interface would

have lead to intrusion of isotopically heterogeneous

leucogranitic dikes that reflect the range of composi-

tions of the exposed potential source rocks. Further-

more, as shown in Fig. 7b, melting in shallower parts

of the shear zone would more likely lead only to

muscovite-dehydration melting giving rise to the B-

rich granite suite, while melting in the hotter deeper

part of the shear zone system would have also

involved biotite, thus leading to the Ti-rich HPG suite.

We suggest that melts generated in the shear zone

system migrated along a listric faults to the current

level of erosion. The NNW-striking faults in the Black

Hills may be an expression of the upper structural

level of the fault system.

A potential consequence of melt generation by

shear heating is that shear stress in the shear zone

may drop once melt forms. Conversely, as an active

part of the shear zone weakens, shear stress may be

amplified in other parts of the shear zone system, in a

manner similar to stress amplification due to viscous

relaxation within the ductile crust (Kusznir and Bott,

1977). Furthermore, after melts are extracted, shear

stress in the source region may again increase. On the

other hand, in many convergent orogens, including

the Black Hills and the CMB, granite generation

occurred at the waning stages of deformation in

orogenic cycles. This may indicate that once melt

forms, strain is accumulated in the partially molten

zones reducing deformation elsewhere (Brown and

Solar, 1998b). However, at the level of granite

emplacement in upper parts of a listric system closer

to the brittle–ductile transition, the crystallized gran-

ites may not be deformed as strain there is likely to be

lower.


Leucogranites such as the HPG and the Maine

granites have often been interpreted as post-tectonic,

largely because of general lack of deformation in the

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

and Bartlett, 1998). In addition, granite emplacement

at high levels in the crust has been advocated as cause

of high-T, low-P metamorphism (e.g., Moench and

Zartman, 1976; Lux et al., 1986; De Yoreo et al.,

1991). Our thermotectonic model shows, however,

that granites can appear syn-collisional or post-colli-

sional depending on the depth of the crust where

metamorphic and crystallization ages are obtained

and on the metamorphic minerals that are dated. Near

the source region, dates for peak metamorphism,

migmatites, and arrested granite plutons, as recorded

for example by monazite, may be similar. However,

age of early garnet growth may be older than anatexis

associated with peak metamorphism. In contrast, in

shallower parts of the crust where metamorphic rocks

may have already cooled down from peak thermal

conditions prior to granite generation at a greater

depth because of unroofing, even regional metamor-

phic ages recorded by a mineral that grew during peak

thermal conditions are likely to be older than crystal-

lization age of granites. Thus, the granites may appear

post-tectonic, when in fact they are not.

7. Conclusions

We propose that shear heating during thrusting of

Proterozoic metasedimentary rocks over the Archean

Wyoming province during the Trans-Hudson orogeny

contributed significantly to generation of the HPG. By

using published values for shear strength of schists

and reasonable convergence rates, we have shown that

sufficient heat can be generated in ductile shear zones

in middle portions of thickened crusts to cause partial

melting. Our model reproduces well the timing of

regional deformation and metamorphism prior to

granite intrusion in the Black Hills. In contrast to

other thermal models for crustal melting that require

unusually high concentrations of radioactive elements

or very high rates of decompression-melting, our

model is consistent with the observed concentration

of heat-producing isotopes in the Black Hills and the

common association of migmatites and leucogranites

with shear zones in convergent orogens. Our model

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.


also resolves the issue of the occurrence of apparently

post-tectonic granites in convergent orogens, as these

may simply reflect temporal differences in ages of

peak metamorphism at different levels of the crust

because of syncollisional unroofing.

Acknowledgements

Constructive comments of Donna Whitney and an

anonymous reviewer lead to significant improvement

of the paper. The study was supported by NSF grants

EAR-9417979 to Nabelek and EAR-9506460 to Liu.

References

Baird, D.J., Nelson, K.D., Knapp, J.H., Walters, J.J., Brown, L.D.,

1996. Crustal structure and evolution of the Trans-Hudson oro-

gen: results from seismic reflection profiling. Tectonics 15,

416–426.

Bird, P., 1991. Lateral extrusion of lower crust from under high top-

ography in the isostatic limit. Journal of Geophysical Research

96, 10275–10286.

Brown, M., 1994. The generation, segregation, ascent and emplace-

ment of granite magma: the migmatite-to-crustally-derived gran-

ite connection in thickened orogens. Earth Science Reviews 36,

83–130.

Brown, M., Solar, G.S., 1998a. Granite ascent and emplacement

during contractional deformation in convergent orogens. Journal

of Structural Geology 20, 1365–1393.

Brown, M., Solar, G.S., 1998b. Shear-zone systems and melts: feed-

back relations and self-organization in orogenic belts. Journal of

Structural Geology 20, 211–227.

Byerlee, J.D., 1978. Friction of rocks. Pure and Applied Geophysics

116, 615–626.

Chamberlain, C.P., Sonder, L.J., 1990. Heat-producing elements and

the thermal and baric patterns of metamorphic belts. Science

250, 763–769.

Dahl, P.S., Frei, R., 1998. Step-leach Pb–Pb dating of inclusion-

bearing garnet and staurolite, with implications for Early Proter-

ozoic tectonism in the Black Hills collisional orogen, South

Dakota, United States. Geology 26, 111–114.

Dahl, P.S., Frei, R., Dorais, M.J., 1998. When did the Wyoming

Province collide with Laurentia?: new clues from step-leach

Pb–Pb dating of garnet independent of its inclusions. Geolog-

ical Society of America Abstracts with Programs 30, 109.

Dahl, P.S., Holm, D.K., Gardner, E.T., Hubacher, F.A., Foland,

K.A., 1999. New constraints on the timing of Early Proter-

ozoic tectonism in the Black Hills (South Dakota), with im-

plications for docking of the Wyoming province with

Laurentia. Geological Society of America Bulletin 111,

1335–1349.

Deniel, C., Vidal, P., Fernandez, A., Fort, L.P., Peucat, J.J., 1987.

Isotopic study of the Manaslu granite (Himalaya, Nepal): infer-

ences on the age and source of Himalayan leucogranites. Con-

tributions to Mineralogy and Petrology 96, 78–92.

De Yoreo, J.J., Lux, D.R., Guidotti, C.V., 1991. Thermal modeling

in low-pressure/high-temperature metamorphic belts. Tectono-

physics 188, 209–238.

Duke, E.F., Shearer, C.K., Redden, J.A., Papike, J.J., 1990. Proter-

ozoic granite–pegmatite magmatism, Black Hills, South Dakota:

structure and geochemical zonation. In: Lewry, J.F., Stauffer,

M.R. (Eds.), The Early Proterozoic Trans-Hudson Orogen of

North America. Geological Association of Canada Special Paper,

vol. 37, pp. 253–269.

England, P.C., Molnar, P., 1993. The interpretation of inverted meta-

morphic isograds using simple physical calculations. Tectonics

12, 145–157.

England, P.C., Thompson, A.B., 1984. Pressure– temperature– time

paths of regional metamorphism I. Heat transfer during the evo-

lution of regions of thickened crust. Journal of Petrology 25,

894–928.

Grunder, A.L., 1995. Material and thermal roles of basalt in crustal

magmatism: case study from eastern Nevada. Geology 23,

952–956.

Guillot, S., Le Fort, P., 1995. Geochemical constraints on the

bimodal origin of High Himalayan leucogranites. Lithos 35,

221–234.

Harris, N.B.W., Inger, S., 1992. Trace element modeling of pelite-

derived granites. Contributions to Mineralogy and Petrology

110, 46–56.

Harris, N.B.W., Massey, J., 1994. Decompression and anatexis of

Himalayan metapelites. Tectonics 13, 1537–1546.

Harrison, T.M., Lovera, O.M., Grove, M., 1997. New insights into

the origin of two contrasting Himalayan belts. Geology 25,

899–902.

Harrison, T.M., Grove, M., Lovera, O.M., Catlos, E.J., 1998. A

model for the origin of Himalayan anatexis and inverted meta-

morphism. Journal of Geophysical Research 103, 27017–27032.

Helms, T.S., Labotka, T.C., 1991. Petrogenesis of Early Proterozoic

pelitic schists of the southern Black Hills, South Dakota: con-

straints on regional low-pressure metamorphism. Geological

Society of America Bulletin 103, 1324–1334.

Hochstein, M.P., Reneauer-Lieb, K., 1998. Heat generation asso-

ciated with collision of two plates: the Himalayan geothermal

belt. Journal of Volcanology and Geothermal Research 83,

75–92.

Hoffman, P.F., 1990. Subdivision of the Churchill province and

extent of the Trans-Hudson orogen. In: Lewry, J.F., Stauffer,

M.R. (Eds.), The Early Proterozoic Trans-Hudson Orogen of

North America. Geological Association of Canada Special Pa-

per, vol. 37, pp. 15–39.

Holdaway, M.J., 1971. Stability of andalusite and the aluminum

silicate phase diagram. American Journal of Science 271, 97–

131.

Hollister, L.S., 1993. The role of melt in the uplift and exhumation

of orogenic belts. Chemical Geology 108, 31–48.

Holm, D.K., Dahl, P.S., Lux, D.R., 1997. 40Ar/39Ar evidence for

Middle Proterozoic (1300–1500 Ma) slow cooling of the south-


ern Black Hills, South Dakota, midcontinent, North America:

implications for Early Proterozoic P–T evolution and posttec-

tonic magmatism. Tectonics 16, 609–622.

Huerta, A.D., Royden, L.H., Hodges, K.V., 1998. The thermal struc-

ture of collisional orogens as a response to accretion, erosion,

and radiogenic heat production. Journal of Geophysical Re-

search 103, 15287–15302.

Jamieson, R.A., Beaumont, C., Fullsack, P., Lee, B., 1998. Barro-

vian regional metamorphism: where’s the heat? In: Treloar, P.J.,

O’Brien, P.J. (Eds.), What Drives Metamorphism and Metamor-

phic Reactions? Geological Society of London Special Publica-

tion, pp. 23–51.

Kirby, S.H., Kronenberg, A.K., 1987. Rheology of the lithosphere:

selected topics. Reviews of Geophysics 25, 1219–1244.

Krogstad, E.J., Walker, R.J., 1994. High closure temperatures of the

U–Pb system in large apatites from the Tim Mountain pegma-

tite, Black Hills, South Dakota, USA. Geochimica et Cosmochi-

mica Acta 58, 3845–3853.

Krogstad, E.J., Walker, R.J., 1996. Evidence of heterogeneous crus-

tal sources: the Harney Peak Granite, South Dakota, U.S.A.

Transactions of the Royal Society of Edinburgh: Earth Sciences

87, 331–337.

Krogstad, E.J., Walker, R.J., Nabelek, P.I., Russ-Nabelek, C., 1993.

Lead isotopic evidence for mixed sources of Proterozoic gran-

ites and pegmatites, Black Hills, South Dakota, USA. Geochi-

mica et Cosmochimica Acta 57, 4677–4685.

Kusznir, N.J., Bott, M.H.P., 1977. Stress concentration in the upper

lithosphere caused by underlying visco-elastic creep. Tectono-

physics 43, 247–256.

Lachenbruch, A.H., 1970. Crustal temperature and heat produc-

tion—implications of the linear heat-flow relation. Journal of

Geophysical Research 75, 3291–3300.

Le Breton, N., Thompson, A.B., 1988. Fluid-absent (dehydra-

tion) melting of biotite in metapelites in the early stages of

crustal anatexis. Contributions to Mineralogy and Petrology

99, 226–237.

Le Fort, P., 1975. Himalayas, the collided orogen. Present knowl-

edge of the continental arc. American Journal of Science 275A,

1–44.

Le Fort, P., Cuney, M., Deniel, C., France-Lanord, C., Sheppard,

S.M.F., Upreti, B.N., Vidal, P., 1987. Crustal generation of the

Himalayan leucogranites. Tectonophysics 134, 39–57.

Liu, M., Furlong, K.P., 1993. Crustal shortening and Eocene exten-

sion in the southeastern Canadian Cordillera: some thermal and

rheological considerations. Tectonics 12, 776–786.

Lux, D.R., DeYoreo, J.J., Guidotti, C.V., Decker, E.R., 1986. Role

of plutonism in low-pressure metamorphic belt formation.

Nature 323, 794–797.

Mancktelow, N.S., Grasemann, B., 1997. Time-dependent effects

of heat advection and topography on cooling histories during

erosion. Tectonophysics 270, 167–195.

Moench, R.H., Zartman, R.E., 1976. Chronology and styles of mul-

tiple deformation, plutonism, and polymetamorphism in the

Merrimack Synclinorium of western Maine. Geological Society

of America Memoir 146, 203–238.

Nabelek, P.I., Bartlett, C.D., 1998. Petrologic and geochemical

links between the post-collisional Proterozoic Harney Peak

leucogranite, South Dakota, USA, and its source rocks. Lithos

45, 71–85.

Nabelek, P.I., Glascock, M.D., 1995. REE-depleted leucogranites,

Black Hills, South Dakota: a consequence of disequilibrium

melting of monazite-bearing schists. Journal of Petrology 36,

1055–1071.

Nabelek, P.I., Liu, M., 1999. Petrogeneis of leucogranites in the

Black Hills, South Dakota, as the consequence of shear heating

during thrusting. Geology 27, 523–526.

Nabelek, P.I., Ternes, K., 1997. Fluid inclusions in the Harney Peak

Granite, Black Hills, South Dakota, USA: implications for sol-

ubility and evolution of magmatic volatiles and crystallization of

leucogranite magmas. Geochimica et Cosmochimica Acta 61,

1447–1465.

Nabelek, P.I., Russ-Nabelek, C., Denison, J.R., 1992a. The gener-

ation and crystallization conditions of the Proterozoic Harney

Peak leucogranite, Black Hills, South Dakota, USA: petrologic

and geochemical constraints. Contributions to Mineralogy and

Petrology 110, 173–191.

Nabelek, P.I., Russ-Nabelek, C., Haeussler, G.T., 1992b. Stable

isotope evidence for the petrogenesis and fluid evolution in

the Proterozoic Harney Peak leucogranite, Black Hills,

South Dakota. Geochimica et Cosmochimica Acta 56,

403–417.

Norton, J.J., Redden, J.A., 1990. Relations of zoned pegmatites to

other pegmatites, granite, and metamorphic rocks in the south-

ern Black Hills, South Dakota. American Mineralogist 75,

631–655.

Patino-Douce, A.E., Harris, N., 1998. Experimental constraints on

Himalayan anatexis. Journal of Petrology 39, 689–710.

Peacock, S.M., 1989. Thermal modeling of metamorphic pressure–

temperature– time paths: a forward approach, in metamorphic

pressure – temperature – time paths. In: Spear, F.S., Peacock,

S.M. (Eds.), Short course in Geology Series, vol. 7. AGU,

Washington, DC, pp. 57–102.

Pressley, R.A., Brown, M., 1999. The Phillips Pluton, Maine, USA:

evidence of heterogeneous crustal sources, and implications for

granite ascent and emplacement mechanisms in convergent

orogens. Lithos 46, 335–366.

Redden, J.A., Peterman, Z.E., Zartman, R.E., DeWitt, E., 1990.

U–Th–Pb zircon and monazite ages and preliminary interpre-

tation of the tectonic development of Precambrian rocks in the

Black Hills. In: Lewry, J.F., Stauffer, M.R. (Eds.), The Early

Proterozoic Trans-Hudson Orogen. Geological Association of

Canada Special Paper, vol. 37, pp. 229–251.

Royden, L.H., 1993. The steady state thermal structure of eroding

orogenic belts and accretionary prisms. Journal of Geophysical

Research 98, 4487–4507.

Ruppel, C., Hodges, K.V., 1994. Pressure– temperature– time paths

from two-dimensional thermal models: prograde, retrograde,

and inverted metamorphism. Tectonics 13, 17–44.

Rutter, E.H., Brodie, K.H., 1988. The role of tectonic grain size

reduction in the rheological stratification of the lithosphere.

Geologische Rundschau 77, 295–308.

Scaillet, B., France-Lanord, C., Fort, L.P., 1990. Badrinath–Gang-

otri plutons (Garhwal, India): petrological and geochemical

evidence for fractionation processes in high Himalayan leuco-


granite. Journal of Volcanology and Geothermal Research 44,

163–188.

Shea, W.T., Kronenberg, A.K., 1992. Rheology and deformation of

an isotropic mica schist. Journal of Geophysical Research 97,

15201–15237.

Solar, G.S., Pressley, R.A., Brown, M., Tucker, R.D., 1998. Granite

ascent in convergent orogenic belts: testing a model. Geology

26, 711–714.

Spear, F.S., 1993. Metamorphic Phase Equilibria and Pressure–

Temperature–Time Paths. Mineralogical Society of America,

Washington, DC, 799 pp.

Spear, F.S., Cheney, J.T., 1989. A petrogenetic grid for pelitic

schists in the system SiO2–Al2O3–FeO–MgO–K2O–H2O.

Contributions to Mineralogy and Petrology 101, 149–164.

Stebbins, J.F., Carmichael, I.S.E., Weill, D.E., 1983. The high tem-

perature liquid and glass heat contents and heats of fusion of

diopside, albite, sanidine, and nepheline. American Mineralogist

68, 717–730.

Stuwe, K., 1998. Heat generation of Cretaceous metamorphism in

the Eastern Alps—a discussion. Tectonophysics 287, 251–269.

Terry, M.P., Friberg, L., 1990. Pressure– temperature – time path

related to the thermotectonic evolution of an Early Proterozoic

metamorphic terrane, Black Hills, South Dakota. Geology 18,

786–789.

Thompson, A.B., Connolly, J.A.D., 1995. Melting of the continental

crust: some thermal and geological constraints on anatexis in

continental collision zones and other tectonic settings. Journal of

Geophysical Research 100, 15565–15579.

Toksoz, N., Bird, P., 1977. Modelling of temperatures in continental

convergence zones. Tectonophysics 41, 181–193.

Tomascak, P.B., Krogstad, E.J., Walker, R.J., 1996. Nature of the

crust in Maine, USA: evidence from the Sebago batholith. Con-

tributions to Mineralogy and Petrology 125, 45–59.

Treloar, P.J., 1997. Thermal controls on early-Tertiary, short-lived,

rapid regional metamorphism in the NW Himalaya, Pakistan.

Tectonophysics 273, 77–104.

Vance, D., Harris, N., 1999. Timing of prograde metamorphism in

the Zanskar Himalaya. Geology 27, 395–398.

Yuen, D.A., Fleitout, L., Schubert, G., Froidevaus, C., 1978. Shear

deformation along major transform faults and subduction slabs.

Journal of the Royal Astronomical Society 54, 93–120.

Zen, E., 1995. Crustal magma generation and low-pressure high-

temperature regional metamorphism in an extensional envi-

ronment; possible application to the Lachlan Belt, Australia.

American Journal of Science 295, 851–874.

Zhao, W., Morgan, W.J.P., 1987. Injection of Indian crust into

Tibetan lower crust; a two-dimensional finite element model

study. Tectonics 6, 489–504.

Zhu, Y., Shi, Y., 1990. Shear heating and partial melting of granite:

thermal structure of overthrusted terrains in the Greater Hima-

laya. Chinese Journal of Geophysics 33, 341–351.


Documents

Thermo-rheological, shear heating model for …web.missouri.edu/~lium/Research/Papers/Nabelek01tectono.pdfThermo-rheological, shear heating model for leucogranite generation, metamorphism,