TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-12-491-2018Crustal heat production and estimate of terrestrial heat flow in central
East Antarctica, with implications for thermal input to the East Antarctic
ice sheetGoodgeJohn W.Department of Earth and Environmental Sciences, University of
Minnesota, Duluth, MN 55812, USAJohn Goodge (jgoodge@d.umn.edu)8February20181224915045July201714August201710November20175January2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://tc.copernicus.org/articles/12/491/2018/tc-12-491-2018.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/12/491/2018/tc-12-491-2018.pdf
Terrestrial heat flow is a critical first-order factor governing the thermal
condition and, therefore, mechanical stability of Antarctic ice sheets, yet
heat flow across Antarctica is poorly known. Previous estimates of
terrestrial heat flow in East Antarctica come from inversion of seismic and
magnetic geophysical data, by modeling temperature profiles in ice boreholes,
and by calculation from heat production values reported for exposed bedrock.
Although accurate estimates of surface heat flow are important as an input
parameter for ice-sheet growth and stability models, there are no direct
measurements of terrestrial heat flow in East Antarctica coupled to either
subglacial sediment or bedrock. As has been done with bedrock exposed along
coastal margins and in rare inland outcrops, valuable estimates of heat flow
in central East Antarctica can be extrapolated from heat production
determined by the geochemical composition of glacial rock clasts eroded from
the continental interior. In this study, U, Th, and K concentrations in a
suite of Proterozoic (1.2–2.0 Ga) granitoids sourced within the Byrd and
Nimrod glacial drainages of central East Antarctica indicate average upper
crustal heat production (Ho) of about
2.6±1.9µWm-3. Assuming typical mantle and lower
crustal heat flux for stable continental shields, and a length scale for the
distribution of heat production in the upper crust, the heat production
values determined for individual samples yield estimates of surface heat flow
(qo) ranging from 33 to 84 mW m-2 and an average of
48.0±13.6 mW m-2. Estimates of heat production obtained for
this suite of glacially sourced granitoids therefore indicate that
the interior of the East Antarctic
ice sheet is underlain in part by Proterozoic continental lithosphere
with an average surface heat flow, providing constraints on both geodynamic
history and ice-sheet stability. The ages and geothermal characteristics of
the granites indicate that crust in central East Antarctica resembles that in
the Proterozoic Arunta and Tennant Creek inliers of Australia but is
dissimilar to other areas like the Central Australian Heat Flow Province that
are characterized by anomalously high heat flow. Age variation within the sample suite indicates that
central East Antarctic lithosphere is heterogeneous, yet the average heat
production and heat flow of four age subgroups cluster around the group mean,
indicating minor variation in the thermal contribution to the overlying ice
sheet from upper crustal heat production. Despite these minor differences,
ice-sheet models may favor a geologically realistic input of crustal heat
flow represented by the distribution of ages and geothermal
characteristics found in these glacial clasts.
Introduction
Heat production and heat flow are fundamental characteristics
of continental crust (Rudnick and Fountain, 1995). Together they provide
important constraints on the thermal and petrogenetic history of cratonic
lithosphere, and heat flow is an indicator of modern geodynamic environments.
The Antarctic lithosphere is uniquely important because it underlies Earth's
largest ice caps, including numerous subglacial lakes, and it is critical in
governing the thermal state and mechanical stability of overlying ice
(Pollard et al., 2005; Jamieson and Sugden, 2008; Van Liefferinge and Pattyn,
2013; Schroeder et al., 2014). Terrestrial heat flow in Antarctica has a
strong influence on basal ice temperatures, amount of basal ice at its
pressure melting point, and the formation of liquid water, all of which
affect basal ice conditions, mechanical properties of glacial bed material,
degree of basal sliding, erosional effectiveness, and the distribution of
hydrologic networks and subglacial lakes (e.g., Siegert, 2000; Pollard et
al., 2005; Pollard and DeConto, 2009). Despite its importance in governing
ice-sheet mass balance – and therefore as an input parameter for ice-sheet
growth and stability models – only a few estimates of conductive heat flow
are available from measurements in subglacial sediment or from temperature
profiles in Antarctic ice (e.g., Begeman et al., 2017; Fischer et al., 2013).
This is particularly problematic for East Antarctica, where the ice cap
exceeds 4 km in thickness in many areas. In order to develop accurate models
of past ice-sheet behavior and forward models of ice-sheet stability, it is
therefore crucial to have good estimates of terrestrial heat flow from East
Antarctica.
Continent-wide models for terrestrial heat flow come from both seismological
and satellite magnetic data. To address a lack of direct heat flow
measurements in Antarctica, Shapiro and Ritzwoller (2004) modeled surface
heat flow by first correlating seismic velocity data from the crust and upper
mantle in regions of known heat flow, and then extrapolating these results to
a seismic model of Antarctic lithosphere. Over a broad region of East
Antarctica they estimated surface heat flow to be notably low, uniform, and
similar to other old cratons (mostly 35–60 mW m-2, with a mean
estimate for East Antarctica of 57 mW m-2). Similarly, An et
al. (2015) used a 3-D S-wave velocity model to construct temperature profiles
for Antarctic lithosphere, from which they derived an average surface heat
flux of 47 mW m-2 for the central Gamburtsev Subglacial Mountains
region in East Antarctica. Fox Maule et al. (2005) used satellite magnetic
data to model the depth to Curie temperature and then inverted the resulting
thermal profile to generate a distribution of heat flow (see also Purucker,
2012); this modeling likewise predicted heat flow in East Antarctica to be
similar to the results obtained from seismology, with an average heat flux of
50–60 mW m-2 in the central part of East Antarctica. In order to
evaluate areas that may preserve very old ice, generally requiring relatively
thick, slow-moving ice under cold conditions with low basal heat flux, Van
Liefferinge and Pattyn (2013) derived an average distribution of heat flow
from a simple mean of existing geophysical models (Fig. 1); this
continent-wide synopsis highlights a relatively uniform pattern of low heat
flow in East Antarctica (mostly < 55 mW m-2). Using a thermal model
that assumes basal ice temperatures above Antarctic subglacial lakes are
equal to the pressure-melting point, Siegert (2000) estimated geothermal heat
flow to vary between 37 and 65 mW m-2, although most estimates for
East Antarctica are < 60 mW m-2. In general terms, these different
models, despite coarse kernel size, are consistent with one another and
indicate heat flow in most of East Antarctica between about
35 and 60 mW m-2.
Terrestrial heat flow in Antarctica, from the mean geothermal heat
flux model of Van Liefferinge and Pattyn (2013), which averages heat flow
determined from multiple geophysical data sets. White box shows area of
Fig. 2, including glacial drainage sourcing bedrock igneous rock clasts
(white outline).
Map showing potential source areas for dated glacial igneous clasts,
superimposed on the Bedmap2 subglacial topography of East Antarctica
(Fretwell et al., 2013). Principal features are ice-sheet catchment areas
(marked by thin blue drainage divides), ice flow directions in the broad Byrd
Glacier drainage (arrows; Rignot et al., 2011), and areas of Precambrian
basement exposure (pink). Composite source area (outlined by heavy white
line) was determined from the ice flow fields that contribute ice to each of
the sample sites (white circles). Other sampled sites are shown by black
circles. Because transport distance is not known for any of the individual
clasts, possible bedrock sources could lie anywhere between the sample sites
and the top of the ice-shed overlapping the Gamburtsev Subglacial Mountains
(GSM). Sample sites: LWA is Lonewolf Nunataks, MSA is Mt. Sirius, TNA is
Turret Nunatak. Other abbreviations: ASB is Aurora Subglacial Basin, GM is
Grove Mountains, LT is Lambert trough, LV is Lake Vostok, MR is Miller Range,
PCM is Prince Charles Mountains, and WSB is Wilkes Subglacial Basin. Outlet
glaciers: Bd is Beardmore, By is Byrd, Ni is Nimrod, Sc is Scott, and Sh is
Shackleton.
In addition to models based on remote geophysical observations, there are
also some field-based estimates. Using a measured temperature profile in the
EPICA ice borehole at Dome C, Fischer et al. (2013) derived a geothermal heat
flux of about 54 mW m-2 by fitting a model of heat flow and basal ice
melting to the thermal profile. A geological approach was taken by Carson et
al. (2014), who derived heat flow using values for heat production estimated
from the abundances of radioactive elements in crustal rocks sampled from
outcrop near the Amery Ice Shelf (compiled by Carson and Pittard, 2012). From
a coastal transect across rock exposures at Prydz Bay, the resulting profile
indicates that heat flow in this area of Archean to Proterozoic igneous and
metamorphic crust is highly variable over a distance of about 200 km, ranging
from an average of 31 mW m-2 in the Vestfold Hills to 44 mW m-2
in the Rauer Islands and 55–70 mW m-2 in the area of southern Prydz
Bay. Locally, high heat-producing Cambrian granitoids indicate heat flow
values as high as ∼ 85 mW m-2. Their model results thus show
variable heat flow governed to first order by the age and type of crust
represented and punctuated by heat production spikes contributed from Th-rich
granitoids. Although much of the area underlying the Rauer Islands and
Vestfold Hills has low heat flow (< 50 mW m-2) typical of
Proterozoic and Archean crust, Carson et al. (2014) emphasized that some
early Paleozoic granites with anomalously high heat
production can cause local
elevation of heat flow (> 80 mW m-2), as observed in the Central
Australian Heat Flow Province (CAHFP; McLaren et al., 2003). Thus, spatially
coarse models of heat flow based on geophysical data across East Antarctica
indicate relatively typical continental values ranging from about 35 to
60 mW m-2, yet there are some indications of locally elevated heat
flow in areas underlain by high heat-producing granites.
Although there are no measurements of terrestrial heat flow obtained directly
from subglacial sediment or rock in East Antarctica, rock clasts eroded from
the continental interior and transported to the margin can provide insight
into the subglacial geology and, therefore, heat production. In this paper,
the concentrations of heat-producing elements in glacial igneous rock clasts
provide a unique opportunity to assess heat flow in the deep continental
interior. The major ice drainages in East Antarctica are marked by nearly
radial flow away from central ice divides and domes toward the continental
margin (Fig. 2), providing natural proxy samples of the continental interior
by bedrock erosion during glacial flow (Peucat et al., 2002; Goodge et
al., 2008, 2010, 2017). Unique among the major drainages, glacial ice in Byrd
Glacier and related smaller drainages moves nonradially from the main ice
divides because it is obstructed by the high-standing Transantarctic
Mountains (peak elevations > 4000 m). Ice flows through the mountains via
channelized outlet glaciers, but it also ablates in areas where it ramps up
against the mountain range (Whillans and Cassidy, 1983). Glacial moraines are
formed both along the margins of the outlet glaciers and where ice is
ablating, forming lag deposits adjacent to the mountains. As part of a study
of East Antarctic crustal history, glacial moraines were sampled at sites
between the Byrd and Beardmore glaciers (Fig. 2). Ice-velocity fields show
that material transported in the greater Byrd system may have been eroded
from a broad area of central East Antarctica, potentially from near the
upstream boundary along the major ice divide connecting Dome A and Dome C.
As proxies for subglacial geology, igneous clasts eroded from central East
Antarctica and collected from moraines adjacent to the central Transantarctic
Mountains were dated and analyzed geochemically for major and trace elements
– including the major heat-producing elements U, Th, and K – yielding values
of radiogenic heat production. Surface heat flow was then estimated by
assuming mantle and lower crustal heat-flux contributions and a length scale
for reduction in upper-crustal radiogenic heat production. The results
indicate that heat production among most of the samples in this group is
within the range expected for average continental crust and that terrestrial
heat flow for a large region of central East Antarctica is like that commonly
observed in Precambrian shield areas. Estimates from this analysis
corroborate previous geophysical models of heat flow in East Antarctica and
can be used as first-order constraints in ice-sheet and lithospheric thermal
models.
Glacial igneous clasts
Glacial igneous rock clasts were collected as part of a separate study to
obtain lithologic, petrologic, and isotopic information about the Precambrian
crust of East Antarctica (Goodge et al., 2017). About a dozen sites were
sampled where glacial moraines are exposed, extending > 1500 km along the
length of the Transantarctic Mountains from the Convoy Range in southern
Victoria Land to Strickland Nunatak near Reedy Glacier (Fig. 2). The original
purpose of the clast sampling was to obtain a representative set of samples
from the ice-covered East Antarctic craton in order to address questions of
crustal age, composition, and Precambrian history by investigating their age
and isotopic compositions. In the field, any rock clasts that represented
potential cratonic basement were collected within an allotted ground time,
thus providing an effectively randomized sample. Over 300 large individual
clasts were obtained. For the previous study, five sites yielded the most
useful samples; the other sites were dominated by clasts of Beacon Supergroup
sediment or Ferrar dolerite eroded from the Transantarctic Mountains. A major
effort was then undertaken to screen the crystalline clast samples by
reconnaissance in situ U-Pb geochronology in order to cull samples with Ross
orogen (∼ 500 Ma) or younger ages in order to focus solely on the Precambrian crustal history of the shield
interior. Analysis of the remaining suite of 22 samples included detailed
petrography, mineral analysis, geochemical analysis, mineral separation,
precise U-Pb geochronology, O-isotope analysis, and Hf-isotope analysis (see
Goodge et al., 2017).
In this contribution, results are presented from samples collected at three
sites for which geochemical data are available from dated Precambrian rock
clasts – Lonewolf Nunataks (LWA and LWB), Mt. Sirius (MSA), and Turret
Nunatak (TNA) (Fig. 2; Table 1). At Lonewolf Nunataks, elongate bands of
distributed moraine and ice-matrix debris follow narrow flow lines related to
ice movement along the southern margin of Byrd Glacier. This site, at the
southern margin of Byrd Glacier, was the single most productive site sampled,
presumably because the Byrd ice stream is among the fastest outlet glaciers
traversing the Transantarctic Mountains and capable of significant glacial
erosion. It is numerically oversampled compared to other sites (Table 1),
yet it contains the full range of clast ages obtained for the whole suite
(1.2–2.0 Ga) so is likely to be representative of the craton interior.
Sites at Turret Nunatak and Mt. Sirius are dominated by Gondwanide debris,
but they also yielded a small number of distinctive crystalline clasts.
Together, these sites comprise a suite of pre-Ross igneous samples with ages
ranging from about 1.2 to 2.0 Ga. The igneous clasts consist mainly of
intermediate to felsic igneous rocks that represent magmatic components of
the ice-covered East Antarctic craton. They are granitic to granodioritic in
composition and contain hornblende, biotite and/or muscovite; some samples
are two-mica granitoids of peraluminous composition. Detailed sample
descriptions are provided by Goodge et al. (2017), including petrographic
features, geochemical data, cathodoluminescence (CL) images of zircons, and
zircon isotopic data (U-Pb, O, and Lu-Hf).
Zircon U-Pb ages from this suite of glacially transported granitoid clasts
show that the crust in central East Antarctica was formed by a series of
magmatic events at ∼ 2.01, 1.88–1.85, ∼ 1.79, ∼ 1.57,
1.50–1.41, and 1.20–1.06 Ga (Goodge et al., 2008, 2010, 2012, 2017). The
dominant granitoid populations are ca. 1.85, 1.45 and 1.20–1.06 Ga. None of
these igneous ages are known from the limited outcrop in the region. Samples
of metamorphic rock clasts from the same moraines have similar Proterozoic
ages ranging from about 1.1 to 1.9 Ga (Goodge et al., 2010; Nissen et
al., 2013). When compared to nearby mountain outcrops, the types and ages
of these samples indicate that the crust of central East Antarctica comprises
plutonic and metamorphic rocks unlike those seen in the central
Transantarctic Mountains (Nimrod Complex ages of ca. 3.1, 2.5, and 1.7 Ga;
Goodge et al., 2001; Goodge and Fanning, 2016). Likewise, they are different
from igneous and metamorphic rocks exposed at the Adélie Land coast
(ages of ca. 2.4 and 1.7 Ga; Oliver and Fanning, 1997), although one
population is similar in age to ∼ 1.6 Ga glacial clasts sampled by
Peucat et al. (2002). As shown in Fig. 2, the glacially eroded igneous clasts
discussed here may also sample the Gamburtsev Subglacial Mountains, which is
thought to have nucleated growth of the East Antarctic Ice Sheet (DeConto and
Pollard, 2003; Bo et al., 2009; Rose et al., 2013).
Estimates of Ho and qo for igneous clast
samples, central East Antarctica.
a Samples collected at the following sites: LWA and LWB are Lonewolf
Nunataks (two sites), MSA is Mt. Sirius, and TNA is Turret Nunatak (see Goodge et
al., 2017).
b Heat production (Ho) was calculated from geochemical
analysis in two ways. Method 1 uses the relation Ho=10-2ρ
(9.67[U] + 2.63[Th] + 3.48[K]) using values after Rybach (1988) and
Hasterok and Chapman (2011). Method 2 uses the relation Ho=ρ (0.9928[U] H(U238) +0.0071[U] H(U235) + [Th]
H(Th) + 1.19 × 10-4[K] H(K40)), after Turcotte and Schubert
(2014). Both assume an average density (ρ) for granitic rocks of
2.7 g cm-3.
c Surface heat flow (qo) determined from qo=qm+qr+(Hohr)
(Turcotte and Schubert, 2014). Moho heat flux (qm) is assumed to be 14 mW m-2 for stable
continental shield areas (Mareschal and Jaupart, 2013; Jaupart et al., 2016),
lower crustal heat flow (qr) is assumed to be 15 mW m-2, and length
scale for reduction in heat production with depth (hr) is assumed to be
7.3 km.
d Artemieva et al. (2017).
It is important to note that only with high-quality age data for this igneous
clast suite is it possible to constrain potential heat production and heat
flow within the west-central interior of East Antarctica. In the absence of
age data, the origin of glacially transported clasts is largely unconstrained
and a large fraction of any such samples could be sourced from the Ross
orogen or from younger Beacon cover in the Transantarctic Mountains, neither
of which inform subglacial heat flow in the craton interior. Thus, simply
sampling moraines to obtain a large set of geochemical data without
geochronological control may yield misleading results. Although it would be
beneficial to have a larger sample set taken from a potentially wider
catchment area, this would require substantial logistical and analytical
resources beyond those employed by this initial reconnaissance study.
Analytical methods
Bulk-rock X-ray fluorescence (XRF) and inductively coupled plasma mass
spectrometry (ICPMS) analyses of major and trace element compositions were
completed in the GeoAnalytical Lab at Washington State University (Goodge et
al., 2017). Prior to analysis, fresh chips of each sample were handpicked
and a standard amount (approximately 28 g) was ground in a swing mill with
tungsten carbide surfaces for 2 min. For XRF analysis of major elements,
3.5 g of sample powder was weighed in a plastic mixing jar with 7 g of
spec pure dilithium tetraborate (Li2B4O7). The mixed powders
were emptied into graphite crucibles and loaded into a muffle furnace for
fusion at 1000 ∘C. After being removed from the oven to cool, each bead
was reground in the swing mill and the resulting glass powders were replaced
in the graphite crucibles and refused for 5 min, then cooled to form a glass
bead. Their lower flat surfaces were then ground on 600 silicon carbide grit
and finished briefly on a glass plate to remove any metal from the grinding
wheel. The concentrations of 29 elements in the unknown samples were measured
on a ThermoARL Advant'XP+ sequential X-ray fluorescence spectrometer by
comparing the X-ray intensity for each element with the intensity obtained
from USGS standard samples (PCC-1, BCR-1, BIR-1, DNC-1, W-2, AGV-1, GSP-1,
G-2, and STM-1), using the values recommended by Govindaraju (1994) and beads
of pure vein quartz used as blanks for all elements except Si. Twenty
standard beads are routinely run and used for recalibration approximately
once every 3 weeks or after the analysis of about 300 unknowns. The
intensities for all elements were corrected for line interference and
absorption effects due to all the other elements using the fundamental
parameter method.
For trace elements, powdered samples were mixed with 2 g of
Li2B4O7 flux, placed in a carbon crucible and fused at
1000 ∘C in a muffle furnace for 30 min. After cooling, the
resultant fusion bead was briefly ground in a carbon-steel ring mill and a
250 mg portion was weighed into a 30 mL, screw-top Teflon PFA vial for
dissolution in water, HNO3, H2O2, and HF and warmed on a hot
plate until a clear solution was obtained. Samples were then diluted to a
final weight of 60 g with de-ionized water. Solutions were analyzed for 27
elements on an Agilent model 4500 ICPMS and were diluted an additional
10× at the time of analysis using Agilent's Integrated Sample
Introduction System (ISIS). This yielded a final dilution factor of
1:4800 relative to the amount of sample fused. Instrumental drift was
corrected using Ru, In, and Re as internal standards and applying a linear
interpolation between In and Re to compensate for mass-dependent differences
in the rate and degree of instrumental drift. Isobaric interferences of
rare earth and other oxides were optimized with correction factors using
mixed-element solutions. Standardization was accomplished by analyzing
duplicates of three in-house rock standards interspersed within each batch of
18 unknowns.
Heat production and estimated heat flowSample geochemical characteristics
Major, trace and rare-earth element geochemical data show that the granitoid
samples are Si-rich with > 65 wt % SiO2, and many have SiO2
of 70–75 wt %. Trace-element abundances are enriched with light
rare-earth elements (LREEs) and depleted in heavy rare-earth elements (HREEs)
relative to chondrites, and they are enriched in large ion lithophile (LIL)
elements and slightly depleted in high field-strength (HFS) elements relative
to mid-ocean ridge basalt (MORB). Their trace and rare-earth element
signatures are quite similar to modern continental-margin magmatic arc
systems (e.g., Cascades, Andes) or evolved volcanic arcs, and they show very
similar patterns and abundances as magmas interacting with thick crust (e.g.,
Davidson et al., 1990, 1991; Wörner et al., 1994). Some of the samples
resemble Si-rich, peraluminous leucogranites found in regions of
overthickened continental crust (Frost et al., 2001). In broad terms, then,
the trace-element compositions indicate that the melts that produced these
igneous rocks interacted with thick, evolved continental crust, but that they
are dissimilar generally from intraplate granitoids.
Heat-producing elements
The concentrations of the heat-producing elements U, Th, and K in 18 granitoid
samples are listed in Table 1. The concentration of U is generally low,
ranging up to about 6 ppm (mean = 2.0). Thorium ranges widely, from 1 to
98 ppm (mean = 23.7), and K similarly varies from 0.5 to 8 wt %
K2O (mean = 4.34). Most of the samples have normal concentrations of
U, Th, and K that are quite similar to the ranges expected for Proterozoic and Archean
granites (Artemieva et al., 2017), and ratios of Th / U and K / U are
mostly in the range typical of Middle and Late Proterozoic granites
(Table 1). Most samples show a linear relationship between Th / U and
K / U (Fig. 3), indicating that the samples as a group show coherent
geochemical behavior and no evidence of significant mobilization of their
heat-producing elements.
(a) Plot of Th / U vs. K / U in glacial igneous
clasts, with detail in (b) that excludes sample 10MSA-2.3. Linear
regression in (b) was calculated for all samples minus sample
10MSA-2.3.
Three samples show some notable variations, however. Sample 10MSA-2.3 is a
red-colored biotite leucogranite with very low U and moderately high Th and
K, which results in highly elevated ratios of Th / U and K / U; these
high ratios are chiefly a result of the low U concentration in this sample.
It appears weathered on the surface but has a zircon
δ18O = 8.2 ‰ (Goodge et al., 2017), indicating a
crustal melt origin with no hydrothermal alteration in the source area.
Sample 10MSA-3.5 is a foliated Ms-Bt leucogranite with undetectable U and low
Th and K, resulting in an abnormally low concentration of heat-producing
elements. This sample has a zircon δ18O = 5.1 ‰,
indicating a mantle melt origin. Sample 10LWA-6.3 has undetectable U, high
Th, and average K, resulting in an anomalously high value of heat production as a
result of very high Th. This sample is a layered biotite granite with zircon
δ18O = 7.1 ‰, indicating a crustal melt origin with no
hydrothermal alteration in the source area.
Heat production
The geochemical compositions of igneous rocks can be used to determine
crustal heat production based on their concentrations of radioactive
elements. Heat production (Ho) was calculated for these clast
samples based on rock density and concentrations of the heat-producing
elements U, Th, and K by applying two different algorithms:
Ho=10-2ρ9.67[U]+2.63[Th]+3.48[K],Ho=ρ0.9928[U]H(238U)+0.0071[U]H(235U)+[Th]H(Th)+1.19×10-4[K]H(40K),
where Ho is surface heat production (µWm-3),
ρ is density (kg m-3), [U] is the concentration of U (ppm),
[Th] is the concentration of Th (ppm), [K] is the concentration of
K2O (wt %), H(238U) is the heat production from the isotope
238U (9.37×10-5 W kg-1), H(235U) is the heat
production from the isotope 235U (5.69×10-4 W kg-1),
H(Th) is the heat production from the isotope 232Th (2.69×10-5 W kg-1), and H(40K) is the heat production from the
isotope 40K (2.79×10-5 W kg-1). Method 1 was
calculated as in Eq. (1) from the formula of Rybach (1976, 1988) using
values from Hasterok and Chapman (2011). Method 2 uses the formulation of
Turcotte and Schubert (2014) as given in Eq. (2). Both methods are included
here for the purposes of comparison and so the values can be
compared with results from other areas that use either of the calculations.
Density (ρ) was assumed to be 2.7×103 kg m-3 in all
cases. Using Method 1, the igneous clast compositions yield estimates of heat
production ranging from 0.25 to 7.49 µWm-3, with an average
of about 2.6 µWm-3 and 1σ standard deviation of
1.9 µWm-3 (Table 1). Most of the variation observed in these
samples comes from variations in concentrations of U and Th. Method 2 gives
quite similar results. It is notable that the two samples with both the
highest and lowest calculated heat production (10MSA-3.5 and 10LWA-6.3) have
anomalous concentrations of U and/or Th, suggesting that these may represent
outliers that are not representative of crust in the glacial catchment area.
Estimates of heat production versus age are plotted in Fig. 4. Compared to an
average value of surface heat production in stable continental shield
regions of ∼ 2 µWm-3 (Jaupart et al., 2016), most of
the Antarctic clast samples are of similar magnitude, with 11 of 18 falling
between 1 and 4 µWm-3. Some of the values are higher than
those reported for other cratonic areas (e.g., Canadian Shield and Grenville
orogen; Mareschal and Jaupart, 2013; Jaupart et al., 2016) and most are
higher than the bulk upper crustal average of about
1.6 µWm-3 (Kemp and Hawkesworth, 2003; Jaupart et
al., 2016). As a group, the granite clast values overlap a range of
1–3 µWm-3 observed in granites globally (Artemieva et
al., 2017), and their mean of about 2.6 µWm-3 is quite
similar to the global average granitic heat production of
2.5 µWm-3 (Rybach, 1976; Haenel et al., 1988). The glacial
granite clasts overlap significantly with Proterozoic granites worldwide
(Artemieva et al., 2017), with an average heat production of
3.83±2.14µWm-3 (Fig. 4). Heat production from the
clasts is comparable to estimates obtained from Archean and Paleoproterozoic
bedrock exposed in the coastal region of southern Prydz Bay
(2.4–2.6 µWm-3; Carson and Pittard, 2012; Carson et
al., 2014). Four of the clasts give high values between 4.0 and
7.5 µWm-3, which are similar to global occurrences of crust
characterized by high heat production (Mareschal and Jaupart, 2013; Jaupart
et al., 2016) and exemplified by the Central Australian Heat Flow Province
(Neumann et al., 2000; Sandiford and McLaren, 2002; McLaren et
al., 2003). Nonetheless, all but two of the samples in this suite have heat
production less than the mean for the CAHFP (4.6 µWm-3).
Plot of surface heat production (Ho) vs. age for igneous
glacial clasts. Data are listed in Table 1. Range of heat production values in
Ross orogen granites from unpublished data. For comparison, values are shown
from East Antarctica (Carson and Pittard, 2012; Carson et al., 2014), the
Central Australian Heat Flow Province (CAHFP; McLaren et al., 2003), the
Canadian Shield (Mareschal and Jaupart, 2013; Jaupart et al., 2016), and
areas of high heat production in stable continental provinces (“hot crust”;
Mareschal and Jaupart, 2013; Jaupart et al., 2016). Average heat production
in Middle and Late Proterozoic granites of about 3.8 µWm-3
are from Artemieva et al. (2017). Bulk upper crustal average of about
1.6 µWm-3 from Kemp and Hawkesworth (2003).
The variability in heat production shown by the data presented here resembles
that observed in regions comprised of Precambrian shields or granitic
batholiths and likely represents real heterogeneities in the source region.
Although the precise distribution of heat-producing rocks in the source area
from which these clast samples were eroded is not known, this group may
collectively provide a qualitatively random sample that provides a means to
assess the average heat production for a broad region of the continental
interior. Compared to examples globally (Mareschal and Jaupart, 2013; Jaupart
et al., 2016; Artemieva et al., 2017), the Proterozoic igneous rocks in this
study indicate that heat production in central East Antarctica is like that
of typical continental shield areas and demonstrably different from the
anomalously warm region represented by the CAHFP. Geological and geophysical
correlations between cratonic rocks in southern Australia (Gawler craton) and
the Wilkes Land region of East Antarctica (e.g., Oliver and Fanning, 1997;
Aitken et al., 2014; Goodge and Finn, 2010; Boger, 2011; Goodge and Fanning,
2010, 2016), have been used as the basis for extrapolating high heat flow
values reported for the CAHFP into East Antarctica (Carson et al., 2014). To
date, no direct constraint on terrestrial heat flow has been provided for
this area of Wilkes Land, and how far south toward Dome C and the upper
Aurora and Wilkes subglacial basins this province may extend is not clear.
However, the data reported here indicate that areas of west-central East
Antarctica at least as far north as 80∘ S may best be characterized
as having only modest heat production.
Heat flow
Geothermal heat flow can be estimated from the empirical relation with
crustal heat production (Lachenbruch, 1968; Roy et al., 1968). In the absence
of direct terrestrial heat flow measurements, as is the case for Antarctica,
it is possible to calculate heat flow from heat production by assuming the
thickness of the upper crustal heat-producing layer (Sandiford and McLaren,
2002; Turcotte and Schubert, 2014). This thickness, hr, is the
length scale for a decrease in Ho with depth in the upper crust
(where most heat-producing elements are concentrated) and is determined from
the slope of the function linking heat flow and heat production (q–H).
Although Ho is thought to decrease exponentially with depth
(Lachenbruch, 1968), a first-order estimate of terrestrial heat flow can be
obtained from
qo=qm+qr+(Hohr),
where qo is the surface heat flow (mW m-2), qm
is the mantle heat flow, qr is the “reduced” heat flow
contributed by heat production in the middle and lower crust, and other terms
are as defined above. For stable Precambrian continental crust, average
values for qm are about 14 mW m-2 and qr is
about 15 mW m-2 (Sandiford and McLaren, 2002; Perry et al., 2006;
Lévy et al., 2010; Mareschal and Jaupart, 2013; Jaupert et al., 2016).
Based on similarities in age and thickness to the Canadian and Scandinavian
shields, a value of 7.3 km for hr is used here. Using the
relationship above and heat production results, the surface terrestrial heat
flow is estimated from the igneous clast population to range from about
31–84 mW m-2 (Table 1), with an average of
48.0±13.6 mW m-2 (1σ standard deviation; Fig. 5). The
average value may be regarded as an integrated estimate of heat flow across
the area of erosion within the catchment, but it is probably a maximum
because it is derived from values of heat production that are biased toward
crustal granites.
Histogram of heat flow values estimated from heat production in the
glacial clasts. Mean value (magenta) is 48.0 mW m-2 (n=18) with
a 1σ standard deviation of 13.6 mW m-2. Consideration of
uncertainties in calculation of heat flow indicates an overall uncertainty of
about ±21 mW m-2 (see text). Range of heat flow values modeled for East
Antarctica are shown for comparison
(light pink; Van Liefferinge and Pattyn, 2013). Global average values for
Archean cratons and Proterozoic lithosphere are shown by ruled bars (Nyblade
et al., 1999).
Uncertainties
Because estimates of heat flow are used in ice-sheet models, it is important
to consider uncertainties in the values used as input parameters. Here I
consider uncertainties in the estimates of heat production and heat flow
provided above.
Uncertainties in Ho
Laboratory precision on elemental analyses is very high (instrumental
precision within 0.2 % for K2O by XRF and within 2 % for U and
Th by ICPMS), density is assumed, and constants of heat production for
various elements are assumed. Therefore, individual uncertainties for
Ho were not calculated because they are expected to be very low
relative to other parameters involved in the calculation of heat flow.
Uncertainties in qo
Uncertainties in the linear relationship used to calculate surface heat flow
(qo) can be modeled using the following expression:
Δqo=Δqm+Δqr+H‾oΔhr+h‾rΔHo,
where Δqo is the sum of uncertainties represented by the
variables included in Eq. (3). Determining reasonable values for most of the
Δ terms is problematical because the corresponding terms in the
heat-flow equation are either based on model-derived values or are simply
poorly constrained by limited empirical data. Because geological and
seismological data indicate that East Antarctica is a stable craton, we can
use typical cratonic values for qm and qr as a basis
for evaluating uncertainty in these terms. For this analysis, Δqm is taken to be ±2.5 mW m-2 based on a compilation
of estimates worldwide for stable continental shield areas that range mostly
from 12 to 17 mW m-2 (Mareschal and Jaupart, 2013; Jaupart et
al., 2016). Uncertainty in the lower-crustal term, Δqr, is
taken to be 3.0 mW m-2, assumed as a general variance (±20 %)
around a representative value of 15 mW m-2 for lower-crustal heat
flow. A mean value of H‾o=2.6µWm-3
is used from the data reported here and the representative average value of
h‾r=7.3 km that was used to calculate heat flow is
assumed here. Uncertainty in heat production, ΔHo, is taken
as a 1σ standard deviation of the calculated values
(1.86 mW m-2), and uncertainty in the length scale, Δhr, is assumed to be 1500 m (±20 %), corresponding to the
magnitude of subglacial topographic relief along the transport direction
within the glacial source area catchment. Based on these inputs, we can
derive a general uncertainty for the surface heat flow term (Δqo) of about 23 mW m-2 (Fig. 5). This is a large value
compared to the nominal mean value of 48 mW m-2 obtained here, and it
reflects large natural variability in lithosphere properties as well as few
direct constraints on mantle heat flow, lower crustal heat flow, and the
vertical distribution of heat-producing elements in continental crust. Of
this estimated uncertainty, 24 % is contributed by the Δqm and Δqr terms, and 76 % is attributed to
the multiplying effects of the thickness and uncertainty of the upper-crustal
heat-producing layer (h‾r and Δhr).
Only 8 % is contributed by ΔHo itself. Together, the
large combined uncertainty is therefore contributed mainly by mantle heat
flow, lower crustal heat flow, and the vertical distribution of
heat-producing elements; conversely, estimates of upper crustal heat
production from the glacial clast samples are not an important source of
uncertainty. Nonetheless, the overall range in surface heat flow covered by
this uncertainty is consistent with the range of values reported for other
cratons, lending support to the idea that the recovered glacial clasts are
indeed representative of heat flow known from typical Archean and Proterozoic
shield areas. Despite the inherent large uncertainties, the first-order
results can help to inform future ice-sheet modeling.
Discussion
The glacial igneous clasts sampled for this study indicate that upper crustal
heat production for at least a part of central East Antarctica is in the
range of 0.3–7.5 µWm-3, with an average value of
2.6±1.9µWm-3 (n=18). Assuming typical values
of mantle heat flux, lower-crustal heat flux, and an upper-crustal length
factor appropriate for stable continental cratons, the derived heat
production corresponds to an average surface heat flux of 48 mW m-2.
This approach assumes typical cratonic values for mantle and lower-crustal
contributions, which it is reasonable given what is known about East
Antarctic lithosphere (e.g., An et al., 2015). The net upper crustal
contribution to surface heat flow is therefore about 19 mW m-2.
Although clasts eroded from the subglacial bedrock surface represent a close
approach to a random sampling of continental crust in East Antarctica, it is
certainly possible that other rocks buried more deeply beneath the glacial
interface in the upper or middle crust may harbor high heat-producing
elements. In such a case, the distribution of heat-producing elements with
depth may yield a greater total crustal contribution to heat flow. Given a
lack of specific constraints to the contrary, however, a conservative
approach is to assume a distribution of heat-producing elements based on
analysis and models from other similar cratons. Several lines of evidence
indicate that upper continental crust in most cratons is dominated by
granites (study of exposed basement, borehole data, seismology; Artemieva et
al., 2017), which are unique in having high concentrations of heat-producing
elements U, Th, and K (Jaupart and Mareschal, 2003). This can yield an order
of magnitude greater heat production compared to granulites, gabbros, and
amphibolites of the middle and lower crust (Artemieva et al., 2017). In
general, granites in the upper crust therefore provide the greatest
contribution to surface heat flow. If the Mesoproterozoic and
Paleoproterozoic granitic samples of this study are representative of upper
continental crust in cratonic East Antarctica, they likely provide a
significant crustal contribution to surface heat flow.
Despite a small sample size, the results here are considered to be
representative of crust in central East Antarctica. Firstly, it is important to
note that the collection process was as randomized as possible given the time
limitations at each site. All igneous clasts with potential age and
geochemical signature were sampled, providing a large composite sample set.
Secondly, the samples screened for detailed petrologic analysis have a wide age
distribution, are well characterized in terms of geochemistry and isotopic
composition, and comprise distinct petrogenetic groups (see Goodge et
al., 2017). That is, they are not cogenetic or derivative from one another
but rather representative of heterogeneous crust. Thirdly, none of the clast
ages are known from other areas of bedrock exposure in the Transantarctic
Mountains or along the greater Wilkes Land margin, such that they appear to
represent a heretofore unrecognized and unique cratonic igneous terrain. At a
minimum, the results obtained from this sample suite apply to the source area
indicated on Fig. 2. Extrapolation over a broader area is unconstrained but
may include some or all of the greater Byrd Glacier drainage network, perhaps
extending as far north as Dome C. Although the data provided in this study
are thought to be representative of crust in the interior of west-central
East Antarctica, it is not possible to resolve gradients in geothermal
properties within the sampled drainage area. For example, a comparison of
samples at sites MSA (n=3) and LWA (n=10) shows no discernable
pattern in age, heat production, or heat flow. Given the lack of a higher sampling
density, the small clast sample size, sample age variation, and heterogeneity
of bedrock geology underlying the Transantarctic Mountains make it difficult
to distinguish gradients in either heat production or heat flow across
individual drainages.
The total surface heat flux is quite similar to the average heat flux of
53 mW m-2 from 13 cratonic shield provinces globally (Jaupart et
al., 2016). Likewise, Nyblade and Pollack (1993) found average surface heat
flow values of 42 mW m-2 for Archean provinces and 47 mW m-2
for Paleoproterozoic provinces, which represent a general depletion of
heat-producing elements in continental crust with increasing age. The heat
flow results obtained here are also similar to earlier estimates for East
Antarctica determined by geophysical modeling and inversion of ice borehole
temperature profiles, which indicate a broad region with low to moderate
values of 50–60 mW m-2 (Shapiro and Ritzwoller, 2004; Fox Maule et
al., 2005). An et al. (2015) used a 3-D S-wave velocity model to construct
temperature profiles for Antarctic lithosphere, from which they derived an
average surface heat flux of 47 mW m-2 for the Gamburtsev province.
This is lower than the average of 57 mW m-2 proposed by Shapiro and
Ritzwoller (2004) or East Antarctica but quite comparable to the estimate
provided here.
Taken together, the heat production and surface heat flow values estimated
for the glacial igneous clasts discussed here appear to be representative of
typical Archean–Proterozoic cratonic lithosphere. As a group they are
distinctly different from the regional pattern shown by anomalously warm
Proterozoic crust in central Australia with average qo=80 mW m-2 (McLaren et al., 2003), which has been suggested to extend
across the Wilkes Land margin of Antarctica based on Gondwana supercontinent
reconstructions (Carson et al., 2014; Aitken et al., 2014). Despite general
age similarities among some of the clast population with parts of the Gawler
Craton, and basement age correlations that indicate continuity of Mawson-type
crust into the Wilkes sector of East Antarctica (Goodge and Fanning, 2016),
the proxy heat production determinations and heat flow estimates provided
here suggest that central portions of the East Antarctic ice sheet are
underlain by stable continental crust with quite normal thermal properties
represented by average values of heat production of about
2.5 µWm-3 and heat flow of about 50 mW m-2.
Estimates of terrestrial heat flow such as those provided here can also be
used to assess the effect of heat flow on ice-sheet mass balance. For
example, Pollard et al. (2005) evaluated the effect of varying heat flow
regimes on ice-sheet behavior by modeling changes in Antarctic ice volume,
ice-sheet surface elevation, and area of the base at its pressure-melting
point as a function of differing heat-flow regimes. Their models used three
different geothermal heat flow distributions: (a) a uniform heat flow of
37.7 mW m-2, representing typical values of Archean cratons;
(b) a uniform heat flow of 75.4 mW m-2 to mimic Proterozoic lithosphere
characterized by high crustal heat production; and (c) a spatially varying heat
flow based on the distributions of different crustal provinces extrapolated
from craton-margin geology and including values of 41 and 55 mW m-2
across most of East Antarctica. The values of heat production and heat flow
estimated for central East Antarctica in this study are most consistent with
their third approach: the average heat flow value of the Proterozoic
granitoid samples is higher than in the case of uniform Archean lithosphere,
yet lower than that assumed for Proterozoic lithosphere with high crustal
heat production. Because the modeling of Pollard et al. (2005) shows a large
effect of heat flow on the area of the ice-sheet base at its pressure-melting
point, inputting appropriate values of crustal heat flow is vitally important
for predicting, for example, the thermal and physical conditions of the basal
ice-sheet regime.
Pie charts summarizing distribution of heat flow estimates in this
study. (a) Distribution of
heat flow by quintiles between 30 and 80 mW m-2. Quintile averages are
shown with the highest quintile represented by one sample with calculated
heat flow of about 84 mW m-2. (b) Distribution of average
heat flow by age groups. Values are shown in Table 2.
Heat flow estimates in proportions based on quintile ranges and
age.
Binned by quintile Binned by age QuintileHeat flowNo.%AgeHeat flowNo.%(mW m-2)(Ma)(mW m-2)135.560.33120955.420.12243.550.28145541.870.41356.040.22177049.660.35463.320.11201347.520.12583.610.06
To provide a simple model for the distribution of heat flow across the
catchment area sampled in this study, mean heat flow values were calculated
in two ways (Table 2). Firstly, the set of 18 samples was divided into equal
quintiles representing ranges of 10 mW m-2 each. Average heat flow
values were calculated for each quintile, as was a percentage of the
measurements falling in that range (Fig. 6a). Each quintile thus represents a
proportionally based average heat flow value that could be used as an input
for ice sheet models. Assuming that the igneous and metamorphic crust beneath
the East Antarctic ice sheet is heterogeneous in age and composition, this
proportional distribution of heat flow values may better reflect the
complexities of crustal geothermal input as a function of subglacial area
compared to a simple average. Secondly, the samples were grouped by age and
average heat flow values calculated for each of four groups (Fig. 6b). This
approach provides a reasonable estimate of heat flow potentially contributed
by igneous crust that is proportionally represented by different age groups. Although
the sample values were divided arbitrarily into five groups using the first
method, this approach shows that about 61 % of the sample results are
< 50 mW m-2 (also indicated by the skewed distribution of values in
Fig. 5), indicating that the bulk of crust underlying the East Antarctic ice
sheet has a relatively low long-range average heat flow. The second approach,
perhaps more useful from a modeling perspective because it groups samples by
age, illustrates that for individual age groups the values are also quite
modest, ranging from about 42 to 55 mW m-2, and are similar to the total
group average. It is noteworthy that this range is nearly identical to the
heterogeneous heat-flow model adopted by Pollard et al. (2005), appearing to
validate the earlier study. Future ice-sheet stability modeling combined with
the estimates of low to intermediate subglacial heat flow found in this
study may thus help to further refine predictions of ice-sheet behavior.
Conclusions
Based on geochemical analysis of a suite of glacially eroded
granitic rock clasts, the average heat production from an inferred large
Proterozoic igneous crustal province in central East Antarctica is estimated
to be about 2.5 µWm-3, and the corresponding average surface
heat flow is about 48 mW m-2. These geothermal properties are quite
similar to average Archean and Proterozoic cratonic shields globally, despite
being biased here to granitic compositions. Although the source of the
granite clasts is not precisely known, they were likely derived from a region
extending into central East Antarctica from near the inlet to Byrd Glacier.
This region contrasts with other areas marked by high heat flow, such as the
Central Australia Heat Flow Province and some parts of East Antarctica near
Prydz Bay, indicating that crust in those areas likely does not extend into
central regions of the continental interior.
Heat flow as estimated in this study is valuable for several reasons.
Firstly, the values obtained here are similar to an estimate of heat flow
derived by modeling of a borehole temperature profile near Dome C
(54 mW m-2; Fischer et al., 2013), helping to validate the earlier
model finding. Likewise, they are consistent with the general range of values
indicated by inversion of geophysical data from cratonic East Antarctica
(e.g., Shapiro and Ritzwoller, 2004; Fox Maule et al., 2005; An et
al., 2015). The average value of heat flow determined in this study
(48 mW m-2) is quite similar to that obtained by An et al. (2015) from
inversion of recent high-quality S-wave data in central East Antarctica
(47 mW m-2). More specifically, the values obtained here show a
similar range to those indicated in the model derived from magnetic data (Fox
Maule et al., 2005); both studies indicate that lithologic and, therefore, geothermal
variations are real. Secondly, the new data provide a unique estimate of heat
production and terrestrial heat flow that can be used as an input to
ice-sheet stability models. In particular, they validate the general approach
by Pollard et al. (2005) in which basal heat flow is varied by area depending
on age and character of the subglacial geology. There is similar variability
within this sample group that probably reflects the lithologic heterogeneity
that is expected in continental shields. Thirdly, although the data presented
here provide a good approximation of both heat production and heat flow in an
otherwise inaccessible region of East Antarctica, the existing uncertainties
associated with extrapolating heat flow from heat production illustrate the
critical need for precise in situ measurements of terrestrial heat flow from
the subglacial environment. One attempt at this beneath the Whillans Ice
Stream in West Antarctica (Fisher et al., 2015) measured a heat flux of
285 mW m-2. This extraordinarily high value, even greater than that
observed on modern ocean ridges (typically ∼ 100–250 mW m-2
near the ridge axis and one-third of that for oceanic crust > 50 Ma;
Stein, 1995), likely is perturbed by advective heat transfer associated with
subglacial flow of water and is therefore not representative of terrestrial
heat flow in West Antarctica. A more recent measurement of 88 mW m-2
obtained in subglacial sediment near the grounding zone of the Whillans Ice
Stream provides a better constraint on geothermal heat flow in West
Antarctica and contrasts with estimates for cratonic East Antarctica (Begeman
et al., 2017). Despite the difficulty in obtaining reliable heat flow data
from the subglacial environment, it should be a high research priority and
can be addressed by drilling through the ice sheets at as many sites as
possible in order to assess crustal heterogeneity. Lastly, these estimates of
low to moderate crustal heat flow indicate that some large regions of the
interior East Antarctic ice sheet may be expected to be frozen at the bed,
which is of use to future drilling projects that plan to intersect the
glacial bed.
Samples referred to in this study are housed at the
University of Minnesota Duluth and available on request to the author.
Data supporting the conclusions are listed in Table 1.
The author declares that he has no conflict of interest.
Acknowledgements
Field and analytical portions of this project were supported by the National
Science Foundation (award 0944645). Jacqueline Halpin and Jean-Claude
Mareschal provided helpful feedback on the approach to estimating heat
production and heat flow, and Jeff Severinghaus kindly reviewed an earlier
draft manuscript. John Swenson generously provided insight into the treatment
of uncertainties.
Edited by: Olaf Eisen
Reviewed by: two anonymous referees
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