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.
P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388374
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
P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 375
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
P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388376
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.
P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 377
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
P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388378
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.
P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 379
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.
P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388380
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.
P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 381
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).
:
:
P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388382
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.
P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 383
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.
P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388384
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.
P.I. Nabelek et al. / Tectonophysics 342 (2001) 371–388 385
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.
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