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Mantle Lithosphere Heat Flow
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In-situ Estimates of Lithospheric Mantle Heat Flow: New Measurements of Mantle
Xenolith Thermal Conductivities and a New Technique to Calculate Heat Flow with
Temperature-Dependent Thermal Conductivity
by
Paul Morgan1, 2 and Suzanne Y. O'Reilly2
To Be Submitted for Consideration for Publication in
Journal of Geophysical Research
September 2005
1
* Department of Geology, Box 4099, Northern Arizona University, Flagstaff, AZ 86011-4099,
USA. tel: (928) 523 7175; fax: (928) 523 9220; e-mail: [email protected]
2
National Center for Geochemistry and Metallogeny of Continents (GEMOC), and Department
of Earth and Planetary Sciences, Macquarie University, NSW 2109, Australia.
* Correspondence address
Mantle Lithosphere Heat Flow
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In-situ Estimates of Lithospheric Mantle Heat Flow: New Measurements of Mantle
Xenolith Thermal Conductivities and a New Technique to Calculate Heat Flow with
Temperature-Dependent Thermal Conductivity
Abstract
Uncertainties in the thermal parameters of continental crust prevent surface heat flow
values from being extrapolated down into the continental mantle lithosphere. Calculation of in
situ mantle lithosphere heat flow values from mantle xenolith data is complicated by
uncertainties in the applicability experimental data that indicate a strong dependence of mantle
thermal conductivity on temperature and the lack of direct methods fro calculating heat flow with
temperature-dependent thermal conductivity. New experimental data measuring thermal
conductivity on multi-grain mantle xenolith samples as a function of temperature confirm results
from single crystal measurements that radiative heat transfer increases mantle thermal
conductivity significantly above 400 to 500°C. A new formulation of Fourier’s Law has been
developed that allows heat flow and heat production to be determined directly from a plot in
which temperature-dependent thermal conductivity is combined with temperature-depth data
pairs. The value of this technique is demonstrated using synthetic data and by comparison of the
technique with published curve-fittingtechniques in parametric space for data from the Jerico
Pipe in the Slave Province, Canada.
Introduction
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Surface heat flow from continental lithosphere is, in general, a mixture of three
components: 1) heat generated within the lithosphere, primarily the upper, crust by decay of
unstable isotopes with long half lives (232Th, 235, 238U, and 40K); 2) heat advected to (or from) the
surface by vertical material fluxes associated with large-scale tectonic motions; and 3) and heat
conducted into the base of the lithosphere from the underlying asthenosphere. Heat flow in the
uppermost crust may then be redistributed by near-surface processes including thermal
convection by groundwater movements, erosion, and sedimentation, or redirected by thermal
refraction or surface temperature changes (Morgan, 2000). A number of authors, including
Vitorello and Pollack (1980), Morgan (1984, 1985), Morgan and Sass (1984), and Pollack et al
(1993) have presented data demonstrating that the tectonic component of heat flow becomes
insignificant with the increasing age of the last significant tectonic or magmatic event in the
region of the heat flow (the "tectonothermal age" of the heat flow), somewhat similar to the
decay of oceanic heat flow with age of oceanic crust (Sclater et al., 1980, 1981; Stein and Stein,
1992). However, unlike "old" (>70 Ma) oceanic crust (Stein and Stein, 1992, 1994), continental
cratons are not characterized by uniform, low heat flow, but by a significant range of values that
exceeds experimental uncertainties (Morgan, 1984, 1985, 2000; Morgan and Sass, 1984). Much
of this range may easily be explained in terms of variations crustal radiogenic heat production.
The key to at least partial separation of the crustal radiogenic and deep conductive
components of surface heat flow lies in the significance of a linear relation between surface heat
flow and surface heat production of the rocks in which the heat flow was measured. This relation
was first discovered to apply to large silicic plutons (Birch et al., 1968; Lachenbruch, 1968; Roy
et al., 1968, 1972) and is of the form:
Mantle Lithosphere Heat Flow
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qs = qr + bAs
(1)
where qs is surface heat flow, As is surface heat production, and qr and b are the parameters of the
relation generally referred to as the reduced heat flow and the depth parameter, respectively.
Heat flow-heat production data have been collected from a number of continental provinces
around the world (e.g., Vitorello and Pollack, 1980; Morgan, 1984, Pollack et al., 1993), and
although the data suggest a strong convergence in reduced heat flow for provinces with
tectonothermal ages of Phanerozoic or older (>235 Ma), qr = 27 + 4 mW m-2, there is still debate
concerning the significance of the linear heat flow-heat production relation especially as to
whether qr has a physical significance in terms of heat flow at any particular level in the crust,
Moho, or uppermost mantle. When it is given a direct physical significance, it is most commonly
assigned to be the crustal heat flow minus the upper crustal radiogenic contribution (e.g., Allis,
1979; Morgan, 1984; Jaupart et al., 1998). In this contribution we propose to overstep this
obstacle in extrapolation of heat flow downward from the surface by using data derived from
mantle xenolith samples to make in situ estimates of heat flow in the continental mantle
lithosphere.
Under stable tectonic conditions at depth, the lithosphere is generally considered to be the
conductive lid on the thermal engine of the Earth, and heat conduction is usually determined by
the product of two components according to Fourier’s Law, the thermal gradient, and the thermal
conductivity through which that gradient is determined. We have used mantle xenolith samples
to provide estimates of both of these components. We have also used xenolith samples to made
direct high-temperature thermal conductivity measurements on mutigrain mantle samples for
comparison with previously published laboratory and theoretical studies of single crystal olivine
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and other model mantle thermal conductivity studies. We have developed a data reduction
technique for calculating heat flow in a medium with variable thermal conductivity so that so
temperature-depth (pressure) data derived from geothermometry and geobarometry studies of
mantle xenolith samples can be combined directly with the thermal conductivity data to calculate
heat flow. These data and calculations allow us to make the first fully constrained in situ
estimates of heat flow in the mantle lithosphere.
Temperature/Depth Information from Geothermometry and Geobarometry
Mantle xenolith samples are used to calculate mantle temperatures-depth data points by
determining the depth (pressure) and temperature of origin of each sample using
chemical/mineral geobarometers and geothermometers, respectively. Geobarometers operate on
the principal that the solubility of some elements in specific minerals is strongly pressuredependent, but essentially independent of temperature, whereas other minerals can act as pressure
independent reservoirs for these elements. The concentration of an element is measured in a
mineral in which the element solubility has been calibrated as a function of pressure, and where
the mineral grain is in contact with a reservoir mineral for the element. Geothermometers
operate on a similar principal except minerals are chosen in which the solubility of an element is
strongly temperature-dependent, but essentially independent of temperature. Mineral
assemblages are more commonly found suitable for geothermometers in mantle xenoliths than
for geobarometers. Geobarometers yield pressure information which is converted to depth
assuming that pressure results from the overburden, i.e.:
Mantle Lithosphere Heat Flow
P ( d )   ( z ) gz z
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d
0
(2)
where P(d) is the pressure at depth d, ρ(z) is the density at depth z, and g is acceleration due to
gravity. References for individual geothermometers and geobarometers used in the calculation of
temperature and depth data used in this study are given with the presentation and discussion of
data below.
Mantle Lithosphere Thermal Conductivity
During the past three decades or so, great advances have been made in the use of thermal
models to understand the evolution of both continental and oceanic lithosphere (e.g., see reviews
in Sclater et al., 1980; Pollack, 1982; Morgan, 1984; and appropriate chapters in Haenel et al.,
1988). In all conductive heat flow problems, the thermal gradient is inversely proportional to
thermal conductivity. Thus, uncertainties in thermal conductivity directly result in uncertainties
in temperatures calculated at depth. Thermal conductivity has long been known to be dependent
on both composition and temperature (Birch and Clark, 1940). For rocks with relatively low
thermal conductivity at surface temperatures (< 2 W m−1 K−1), the temperature dependence of
thermal conductivity generally appears to be minor, although thermal conductivity of different
rock types is very significant for individual heat flow determinations (e.g., Sass and Morgan,
1988). For rocks with a room temperature thermal conductivities above 3 W m−1 K−1, however,
particularly rocks high in olivine content, a significant decrease in thermal conductivity with
increasing temperature is indicated by several experimental studies as temperature rise to 400 to
500°C, above which temperatures conductivities increase as radiative heat transport appears to
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become significant (e.g., Schatz and Simmons, 1972, and see data compiled in Roy et al., 1981).
Rocks that are likely to contribute significantly to the bulk thermal conductivity of the
crust typically have thermal conductivities in the range 2.0 to 2.5 W m−1 K−1 (e.g., Decker and
Smithson, 1975, Morgan and Gosnold, 1989), for which the temperature dependence of thermal
conductivity is possibly of importance, but this dependence is almost always ignored in thermal
models. Mantle rocks are generally assumed to have thermal conductivities ≥ 3 W m−1 K−1, and
although published experimental studies indicate strong temperature dependence of thermal
conductivity in the temperature range 0 to 900 °C, these effects are commonly also ignored, or
applied inconsistently. For example, for a widely quoted set of geotherms, Pollack and Chapman
(1977) used a temperature-dependent thermal conductivity model to compute geotherms in the
continental mantle, but a constant conductivity (diffusivity) cooling model to compute oceanic
mantle geotherms. Sclater et al. (1980), Morgan (1984), Morgan and Sass (1984), and many
others have used a constant thermal conductivity based upon an average of a temperaturedependent conductivity model (e.g., see Morgan, 1984, Figure 9). Why has there been no
consistent use of a temperature-dependent thermal conductivity model for mantle rcks?
Although the probable effects of radiative heat transport on mantle temperatures have
been discussed (Clark, 1957), and a number of studies have demonstrated the significance of
radiative heat transport at lithospheric temperatures in olivine and other minerals likely to be
importance in the upper mantle (e.g., Fujisawa et al., 1968; Fukao et al., 1968; Kanamori et al.,
1968; Schatz and Simmons, 1972; MacPherson and Schloessin, 1982; and others, see Roy et al.,
1981), these studies have not demonstrated the efficiency of radiative heat transport in multigrain rocks. The reduction in the efficiency of radiative heat transport in multi-grain rocks as a
Mantle Lithosphere Heat Flow
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result of photon scattering at grain boundaries is essentially unknown, and is commonly assumed
to cancel the effects of radiative heat transport (e.g., Clauser, 1988). However, in our preliminary
experiments described below, we have demonstrated that radiative heat transport is clearly
significant in multi-grain peridotitic mantle xenolith samples.
Techniques
Thermal conductivity has been measured using a modification of the steady-state dividedbar apparatus using an electrical resistance heater, the basic configuration for which is shown in
Figure 1. In order to keep this apparatus as simple as possible, the same heater was used to raise
the temperature of the sample to the ambient measurement temperature and to provide the
bidirectional heat flow through the stack of standards and the sample from which the thermal
conductivity was determined. The system was used as a thermal comparitor, using fused silica as
a calibration standard (Ratcliffe, 1959; Powell et al., 1966) and deducing the thermal
conductivities of samples from the relative temperature drops across the calibration standards and
the samples and from the relative geometries of the standards and samples. The repeatability of
the system in re-measuring the thermal conductivity of the fused silica standard from which it
was calibrated is shown in Figure 2. A recurring problem with this system was associated with
an increase in the uniaxial pressure of the stack caused by thermal expansion of the stack as it
was heated which caused fracturing of the standards. The effect of this fracturing on the results
from the system is clearly illustrated in Figure 2 by the low thermal conductivity determined for
the fused silica standard above 700oC at which temperature fracturing occurred during this run.
This fracturing was obviously an experimental inconvenience, but was clearly evident from a
Mantle Lithosphere Heat Flow
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sudden drop in the hydraulic pressure in the pump confining the stack, and did not appear to
invalidate the data collected before fracturing occurred.
== Figures 1 and 2 about here ==
This system was tested extensively with various experimental modifications and was
found to produce reproducible results under a variety of different confining pressures and stack
configurations. As many of the experimental runs above 500oC resulted in fractured standards in
the stack, we are only confident in the results from these runs as semi-quantitative. However,
within individual runs before standards were fractured, or between runs with similar stack
configurations, the results are considered to be significant. A sample of New England (Australia)
granite was also measured as a sample for which radiative heat transport was not expected to
have a major effect on the high temperature thermal conductivity to confirm that trends observed
in the mantle xenolith thermal conductivities were not an artifact of the experimental technique.
Distinctly different temperature-dependent behavior of thermal conductivity was demonstrated
for the granite sample and four different peridotitic mantle xenolith samples, the results for
which are summarized in Figure 3. The granite sample showed only a small temperature
component of thermal conductivity, decreasing from approximately 1.8 W m−1 K−1 at room
temperature to about 1.6 W m−1 K−1 at 400oC, above which temperature the thermal conductivity
gently increased. With the mantle xenolith samples, a decrease in the thermal conductivities of
20 to 40% was observed as the samples were heated from room temperature to about 400oC.
Above 400oC the conductivities were observed to increase again, returning to their room
Mantle Lithosphere Heat Flow
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temperature values at 700 to 800oC. Data are shown in Figure 3 for two different mantle xenolith
samples (see figure caption for descriptions) with different uniaxial confining pressures of
approximately 50 MPa (0.5 kbar) and approximately 150 MPa (1.5 kbar). Similar trends are seen
in the thermal conductivities of both samples as a function of temperature. By comparison with
the single crystal olivine thermal conductivity study of Schatz and Simmons (1972), these results
clearly demonstrate the significance of radiative heat transport in actual mantle samples, and thus
the project has succeeded in its primary goal. Our preliminary results indicate that radiative heat
transport is significant in mantle xenolith samples above temperatures of about 400oC, and these
results are in close agreement with the single-crystal results of Schatz and Simmons (1972).
Pending further multi-grain xenolith studies therefore, we base temperature-dependent
lithospheric mantle thermal conductivities on the approximations suggested by Schatz and
Simmons (1972).
== Figure 3 about here ==
The Problem of Analyzing Geotherms and Calculating Heat Flow in a Medium with
Temperature-Dependent Thermal Conductivity
Terrestrial heat flow values are most commonly calculated as the product of the
geothermal gradient and the thermal conductivity of the rocks through which the gradient was
measured. Linear sections of the geotherm are generally sought so that calculation of the thermal
gradient and its error may be made using an assumption of simple Gaussian statistics. If the
Mantle Lithosphere Heat Flow
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thermal conductivity changes in discrete intervals, short sections of linear thermal gradient may
be combined using a transformation of depth to thermal resistance to allow the heat flow to be
calculated over larger depth ranges in a single calculation (Bullard, 1939). Curved geotherms
usually result from vertical convective heat transfer by water, and these sections of the geotherm
are typically rejected in heat flow determinations. However, a curved geotherm may also result
from a continuously varying thermal conductivity. Such is the case in the mantle lithosphere.
Data presented above indicate that the thermal conductivity of the mantle lithosphere is
strongly temperature dependent (Figure 4; Schatz and Simmons, 1972; Morgan, 1993; Morgan
and Hoisch, 1994; Morgan and O’Reilly, 1994). A synthetic geotherm for the mantle lithosphere
and a steady-state mantle heat flow of 15 mW m-2 using this temperature-dependent thermal
conductivity is shown in Figure 5. A linear fit to this geotherm yields a gradient of 5.0604 oC
km-1, with a goodness of fit parameter R2 = 0.9967 (a high precision is given as these are
synthetic data). The mean thermal conductivity taken in 1 km increments from which this
geotherm was calculated is 3.0494 W m-1 K-1. The heat flow recalculated from the linear
geotherm and mean conductivity is 15.43 mW m-2, 3% higher than the heat flow from which the
geotherm was calculated. This error is introduced primarily from the linear approximation to the
nonlinear geotherm.
== Figures 4 and 5 about here ==
Rudnick and Nyblade (1999) and Russell et al. (2001) have attempted to overcome the
problem of making a linear approximation to a nonlinear geotherm by fitting calculated nonlinear
Mantle Lithosphere Heat Flow
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geotherms to the data. There is an additional parameter that adds curvature to the geotherm,
however, radiogenic heat production. The calculated non-linear geotherm method has been
extended to include radiogenic heat production by finding a best-fit in parametric space by
Russell et al. (2001). As shown below, however, if the temperature-dependent thermal
conductivity can be expressed in a form that can be integrated with respect to temperature, then
Fourier’s Law can be reformulated to incorporate temperature-dependent thermal conductivity as
a plotting parameter yielding heat flow and heat production without curve fitting.
New Heat-Flow Data Plot For Temperature-Dependent Thermal Conductivities
A new technique is proposed in which a transformation is made in the temperature data
using the temperature-dependent conductivity values allowing direct determination of heat flow
and heat production. If K(T) is temperature-dependent thermal conductivity, one-dimensional
steady-state heat flow, q, may be written as:
q  K (T )
T
z
(3)
where ∂T/∂z is the geothermal gradient. By convention in geothermal studies, q is measured
positive vertically upward, and ∂T/∂z is measured positive vertically downward. As discussed
above, is ∂T/∂z nonlinear when K(T) is a function of temperature. The equation may be reduced
to a linear plot by plotting ∂T/∂z versus ∂z yielding q as the slope of the plot.
When using mantle xenolith depth (pressure) and temperature data to estimate mantle
heat flow, the data are in the form of discrete depth-temperature pairs. Using a continuous
Mantle Lithosphere Heat Flow
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function for the thermal conductivity dependence on temperature, such as the polynomial fit to
the experimental data shown in Figure 4, conductivity can be determined for each individual
temperature, but there is no immediately obvious manner in which the conductivity should be
chosen for temperature intervals, ∂T, as the conductivity function is nonlinear, nor which pairs of
data should be chosen for these temperature intervals. This problem may be surmounted by
calculating all of the temperature intervals with respect to a single temperature reference data
point, such as absolute zero, T0. K(T)∂T for other xenoliths with temperatures Tn and depth zn
are then given by:
K ( Tn ) T   K ( T ) dT .
Tn
(4)
T0
For the fit shown in Figure 4:
K ( T )  c 0  c1 Tk  c 2 Tk 2  c 3 TK 3
(5)
where c 0 = +7.40, c 1 = -1.27 x 10-2, c 2 = +1.04 x 10-5, c 3 = -2.43 x 10-9, and T K is
absolute temperature. Thus:
K Tn T   c 0  c1 TK  c 2 TK 2  c 3 TK 3 dT
Tn
T0
T

n
TK 2
TK 3
TK 4
 c 0 T K  c 1
 c2
 c3
 c4 
2
3
4

 T0
(6)
where c 4 is the constant of integration. If T0 is taken as 0 (zero), the integral becomes:
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Tn 2
Tn 3
Tn 4
K Tn T  c 0 Tn  c 1
 c2
 c3
2
3
4
(7)
The results of applying this transformation to the synthetic data shown in Figure 6 are plotted in
Figure 7. The original heat flow of 15 mW m-2 is recovered from the slope of this plot.
== Figure 6 and 7 about here ==
Application of K(T)∂T versus Depth Plots to Mantle Xenolith Data
Application of the new plot heat flow determination technique for direct determination of
heat flow for cases of temperature-dependent thermal conductivity is shown for a variety of
mantle xenolith data sets in Figures 8.
== Figures 8 about here ==
Addition of Heat Production to the Problem
Radiogenic heat production in the mantle lithosphere is probably low, less than 0.05
μW m-3, but even this low value could be significant over a thickness of 100 km or more in the
mantle lithosphere. Attempts to determine mantle lithosphere heat production from xenolith data
have been included in the parametric fit techniques used by Russell and Kopylova (1999),
Rudnick and Nyblade (1999) and Russell et al. (2001). Using the reformulation of the heat flow
equation, heat flow and a constant heat production can be recovered from the K(T)∂T versus
Mantle Lithosphere Heat Flow
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depth plot.
The simplest distribution of heat production that can be assumed is that it is constant
throughout the mantle lithosphere, and this changes the heat conduction equation to:
q M  K (T )
T
 Az
z
(8)
where qM is the heat flow from the upper surface of the layer, which in the case of the mantle
lithosphere is the Moho, and A is the uniform heat production per unit volume in the layer. A
synthetic geotherm with temperature-dependent thermal conductivity and a uniform heat
production of 0.01 μW m-3 is shown in Figure 9.
== Figure 9 about here ==
Separating the variables in Equation 8 and integrating:
 (q
M
 A z ) dz 
 K ( T ) dT
(9)
When working with xenolith data and plotting ∫K(T)dT versus z, the limits of integration are
defined by the manner in which these parameters are calculated or defined. As defined above,
∫K(T)dT has an arbitrary origin, which has been taken as T0 = 0 (zero in Kelvin)) for
computational convenience. Depth, z, usually has its origin z = 0 at the surface, not at the
Mantle Lithosphere Heat Flow
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hypothetical depth where the temperature is absolute zero. These different origins do not have
significance if only slopes of the plot are used, but they must be considered in the interpretation
of the slopes.
Integrating the left-hand side of equation 9 yields:
Az2
qMz 
C
2
(10)
where C is the constant of integration. The right-hand side of equation 9 is the previously
calculated integral for the case without heat production. From equation 10, therefore, The form
of a plot of ∫K(T)dT versus depth with constant heat production should yield a 2nd order curve.
The synthetic data from Figure 9 are replotted in the form ∫K(T)dT versus depth in Figure 10. A
second order polynomial fit to these data recovers the parameters used to calculate the original
geotherm, a heat flow of 15 mW m-2 for qs and heat production of 0.01 μW m-3.
== Figure10 about here ==
The Importance of the Depth Origin for Calculations of Mantle Heat Flow and Heat
Production
The reason that the depth axis in Figures 9 and 10 are shifted to start at 0 km is that we
are interested in recovering the heat flow at the top of the layer with temperature-dependent
thermal conductivity and heat production, and this study has focused upon parameters typical of
Mantle Lithosphere Heat Flow
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the mantle lithosphere. The heat flow, q, in equation 3 and integration relation in Equation 4 is
the heat flow at z = 0: therefore the top of this layer for the synthetic geotherm has been set to
zero depth. For xenolith data sets in which zero depth corresponds to the ground surface, not the
top of the mantle lithosphere, the calculated heat flow will be a value extrapolated to the ground
surface with the implication that mantle lithosphere properties extend to the surface. The mantle
heat production is not affected by the depth datum. There are two methods by which the heat
flow may be corrected to the top of the mantle lithosphere: 1) adjust all depths so that they have
a datum of z = 0 at the top of the mantle lithosphere; or 2) correct the heat flow by subtracting
the heat production added by extrapolating the geotherm to the ground surface. This additional
heat flow is given by the product of the depth to the top of the mantle lithosphere and the mantle
lithosphere heat production.
In cases where the depth to the top of the mantle lithosphere is not known, a reasonable
approximation (guess) will not cause a significant error. Assuming a reasonably high estimate
for upper mantle heat production of 0.02 μW m-3, an uncertainty in the depth to the top of the
mantle lithosphere of ±10 km will introduce an uncertainty in heat flow at the top of the mantle
of ±0.2 mW m-2, which will almost certainly be less that the standard error of fitting a curve to an
array of xenolith-derived data and uncertainties in the thermal conductivity function.
Acknowledgements
Sue, Please insert GEMOC statement. I will add Fulbright, NASA and NSF
acknowledgements.
Mantle Lithosphere Heat Flow
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Mantle Lithosphere Heat Flow
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calculations, Eos, Trans. Am. Geophys. Un., 75(44), 648, 1994.
Morgan, P., and O'Reilly, S. Y., Thermal conductivity of planetary lithospheres: New estimates
from measurements on mantle xenolith samples, Lunar and Planet. Sci. XXV, 931-932,
1994.
Morgan, P., and O’Reilly, S. Y., Constraints on upper mantle heat flow from xenolith
thermobarometry and conductivity determinations, Eos, Trans. Am. Geophys. Un., 79
(45), p. F838, 1998.
Morgan, P. and Sass, J. H.,Thermal regime of continental lithosphere, J. Geodynamics, 1, 137-
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151, 1984.
O'Reilly, S. Y., and Griffin, W. L., Mantle metasomatism beneath western Victoria, Australia: I.
Metasomatic processes in Cr-diopside lherzolites, Geochim. Cosmochim. Acta, 52, 433447, 1988.
Pollack, H. N., The heat flow from the continents, Ann. Rev. Earth Planet. Sci., 10, 459-481,
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thickness of the lithosphere, Tectonophysics, 38, 279-296, 1977.
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Figure Captions
Figure 1. Schematic experimental configuration for high-temperature mantle xenolith thermal
conductivity determinations (not to scale).
The cross-section of the stack was square
with a side length of 30 mm, and typically the standards and sample were 10 mm thick.
(The xenolith samples were typically friable and more easy to saw than core). The heater
was a 22-gauge nichrome wire wound on a pyrophylite frame, supplied by a 0-50 V, 0-8
A regulated DC power supply. 0.015 inch (0.4 mm) diameter chrome-alumel
thermocouples in copper blocks were used for temperature sensors (T Point), with their
emf's measured by an 8-channel 16-bit analogue to digital converter, the output from
which was recorded directly by a desktop computer. The standards were fused silica.
The heat sinks were copper attached to external air-cooled finned aluminum heat sinks.
Pyrophyllite spacers were used between the end temperature sensors (T1 and T6) in order
to reduce the temperature drop across the measurement section of the stack. The stack
was mounted in a hydraulic press and typically operated under an axial pressure of about
50 MPa (0.5 kbar). The stack was thermally insulated with fiberglass with the exception
of the external air-cooled heat sinks. See Beck (1988) for examples of calibration and
data reduction techniques.
Figure 2. Plot of thermal conductivity as a function of temperature for remeasurements of the
fused silica calibration standard sample. The points show the remeasured thermal
conductivities; the dashed line shows the fused silica conductivity curve used for
calibration (calibration data taken from Powell et al., 1966). The low measured
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conductivity above 700oC was measured after a drop in hydraulic pressure in the
confining pressure pump indicated fracturing of one or more standards in the stack during
this run. This fracturing was an experimental inconvenience, but was clearly evident
from a sudden drop in the hydraulic pressure in the pump confining the stack, and did not
appear to invalidate the data collected before fracturing occurred.
Figure 3. Preliminary high-temperature thermal conductivity data for two mantle xenolith
samples and a check sample of granite. Solid square symbols show data collected at an
axial pressure of about 50 MPa (0.5 kbar) on a spinel lherzolite xenolith sample from a
Quaternary maar, Lake Bullenmerri, western Victoria, Australia. This sample was friable
and was impregnated with epoxy resin to facilitate cutting. It has not been characterized
chemically, but is expected to be very similar to other spinel lherzolite xenoliths from the
same locality reported by O'Reilly and Griffin (1988) and Griffin et al. (1988). These
data were collected during both the heating and cooling cycles of two heating runs to a
mean sample temperature of approximately 530oC, and no consistent hysteresis in the
results was observed. Solid circle symbols show data collected at an axial pressure of
about 150 MPa (1.5 kbar) on a less-friable, unimpregnated sample of a spinel lherzolite
xenolith from the same locality and designated as SGN1 by O'Reilly and Griffin (1988),
Griffin et al. (1988), and Chen et al. (1991) who give detailed chemical analyses of this
xenolith. The predominant mineral in this xenolith is olivine with a composition of Fo92.
The dashed line shows the predicted olivine conductivity of Schatz and Simmons (1972).
Open square symbols show data collected on an unimpregnated sample of I-type granite
from the Lachlan Fold Belt, New South Wales, Australia, and the chemical characteristics
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of this granite have been reported and discussed by Sawka and Chappell (1986) and
others. Similar temperature dependent behavior of thermal conductivity for silica-rich
samples has been observed in the temperature range 0 to 800oC by U. Seipold
(GeoForschungsZentrum Potsdam, Germany) using a transient heating technique (J. H.
Sass, personal communication, 1993).
Figure 4. Thermal conductivity of olivine as a function of absolute temperature (from Schatz and
Simmons, 1972). Similar results were obtained in the range 400-1200 K for multi-grain
mantle xenolith samples by Morgan (1993) and Morgan and O’Reilly (1994). The fit is a
third order polynomial fit.
Figure 5. Synthetic geotherm calculated for the mantle lithosphere for a steady mantle heat flow
of 15 mW m-2 and the temperature-dependent thermal conductivity shown in Figure 1. A
linear fit to this geotherm and the parameters of this fit are also shown. The thermal
conductivity as a function of depth for this temperature distribution is shown in Figure 6.
Figure 6. Temperature-dependent thermal conductivity as a function of depth for the geotherm
shown in Figure 5.
Figure 7. Plot of

Tn
T1
K ( T ) T versus depth for synthetic mantle heat flow data shown in Figure
2. The slope of this plot is heat flow, q. A least squares fit to this plot gives a slope of 15
mW m-2, which was the heat flow used to calculate to the data, and the goodness of fit, R2
= 1.
Figure 8. Mantle xenolith data from the Slave Craton, Canada (data from Russell et al., 2001).
Heat flow for all data is 16 mW m-2.
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Figure 9. Mantle xenolith data from the Kaapvaal craton, South Africa. Heat flow for all data is 15.5
mW m-2.
Figure 10. Mantle xenolith data from Daldyn, Siberia. (Data from Griffin et al., 1996). Heat
flow for all data is 12.8 mW m-2.
Figure 11. Synthetic geotherm calculated assuming a surface heat flow of 15 mW m-2, a
temperature-dependant thermal conductivity, and internal heat production of 0.01 μW m3
. Temperatures are started at 400˚C to bring the geotherm into the temperature range
where the temperature variations in thermal conductivity are most significant. The reason
for starting the depth axis at 0 km is explained in the text.
Figure 12. Plot of

Tn
T1
K ( T ) T versus depth for synthetic mantle heat flow data shown in
Figure 9. A least-squares second-order polynomial fit to this plot gives values
corresponding to the integral relation 2 of 15 mW m-2 for qs and 0.01 μW m-3 for A,
which were the parameters used to calculate to the data, and a goodness of fit, R2 = 1.
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Figure 1
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Figure 2
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Figure 3
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Figure 4
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Figure 5
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Figure 6
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Figure 7
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Figure 8
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Figure 9
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Figure 10
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Figure 11
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Figure 12
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