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Earth and Planetary Science Letters 223 (2004) 65 – 77
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Variations of surface heat flow and lithospheric thermal structure
beneath the North American craton
J.C. Mareschal a,*, C. Jaupart b
a
GEOTOP-UQAM-McGill, P.O. Box 8888, Sta. ‘‘downtown’’, Montreal, H3C3P8, Canada
b
Institut de Physique du Globe, 4 pl. Jussieu, 75252 Paris, France
Received 31 October 2003; received in revised form 6 April 2004; accepted 7 April 2004
Abstract
Two end-member models have been proposed to explain the variations in surface heat flow in stable continents, calling
for changes of either crustal heat production or heat flow at the base of the lithosphere. The scale of the surface heat flow
variations controls how these variations affect the thermal structure and thickness of the lithosphere and provides
constraints on these models. Data in the Canadian Shield and the Appalachians are now extensive enough to address
problems of scale and relationship between average heat flow and heat production. We analyze the global data set as well
as data from five compositionally distinctive subprovinces. Within each province, on scales < 500 km, observed heat flow
variations are linked to changes of local crustal structure. For the five subprovinces, the average values of heat flow (Q̄)
and heat production (Ā) conform to the simple relationship Q̄ = Qo + HĀ, where H c 9 km and Qo c 33 mW m 2. This
shows that, on scales larger than the dimensions of these provinces (>500 km), variations in crustal heat production
dominate and hence that variations of mantle (Moho) heat flow must be small. The large heat flow step at the Grenville –
Appalachian boundary ( c 16 mW m 2) may be accounted for by a change in crustal heat generation only. In that case,
the lithosphere is c 40 km thinner in the Appalachians than in the Shield. At wavelengths of 500 km or more, mantle
(Moho) heat flow variations are constrained to be smaller than the detection limit of heat flow studies, or about F 2 mW
m 2, and may not be correlated with surface geology. Downward continued to the base of the lithosphere, the amplitude
of these variations depends on wavelength and must be smaller than F 7 mW m 2. Such variations imply that
temperature differences must be smaller than 400 K at 150 km depth. These bounds are consistent with seismic shear wave
velocity variations and geothermobarometry studies on mantle xenoliths.
D 2004 Elsevier B.V. All rights reserved.
Keywords: lithosphere; heat flow; heat production
1. Introduction
Interest in continental roots has recently soared as
it has become clear that they are chemically distinct
* Corresponding author.
E-mail addresses: [email protected]
(J.C. Mareschal), [email protected] (C. Jaupart).
0012-821X/$ - see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.epsl.2004.04.002
from oceanic mantle sampled at mid-ocean ridges and
that they affect mantle convection currents [1– 4]. The
thermal regime of the roots is one of the key elements
to understand their nature and evolution. Determining
the thermal conditions at the base of the continental
lithosphere is also important because they are used as
a constraint that models of mantle convection must
satisfy [5]. Relevant data on the thermal structure of
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J.C. Mareschal, C. Jaupart / Earth and Planetary Science Letters 223 (2004) 65–77
the roots have come from heat flow measurements [6]
and from geothermobarometry on mantle xenoliths
[7]. Knowledge of the distribution of seismic velocities in these roots has been steadily improving, but it
is difficult to discriminate between temperature and
composition effects [4,8].
In stable continents, for ages greater than about
500 Ma, thermal transients have decayed and surface
heat flow is the sum of crustal heat production and
of the heat supply at the base of the lithosphere.
Identifying these two components is an essential step
for calculating continental geotherms. Surface heat
flow varies by large amounts because of shallow
heat production contrasts. Thus, as long as sampling
of continental heat flow and heat production was
inadequate, it was necessary to define systematic
trends in the data to supplement insufficient coverage
in one area with measurements from other areas. Age
is an obvious control variable, and hence ‘‘characteristic’’ continental geotherms were calculated for
heat flow values corresponding to worldwide averages for specific age groups [9,10]. These geotherms
may not apply to any specific province because of
the large variations of bulk crustal heat generation
among provinces of the same age [11].
Within a single craton, such as the North American craton for example, there are significant variations of surface heat flow over a range of scales
[6,13]. Variability at short spatial scales bears no
consequence for the deep lithosphere. For a study of
lithospheric structure, one must determine an average
heat flow value over a scale which is sufficiently
large for a reliable downward continuation of the
temperature field: The thicker the lithosphere, the
larger-scale the horizontal averaging. Thus, the determination of lithospheric thickness and average
heat flow cannot be treated independently. Ignoring
this may lead to substantial errors, as shown by two
extreme examples. For a global study of mantle
convection, Pari and Peltier [5] used the worldwide
heat flow database and retained only degrees 1 –12
in the spherical harmonic expansion of heat flow. On
that scale ( c 3000 km), different provinces are
lumped together, and the geologically active Basin
and Range province is associated with a lower heat
flow than the Canadian Shield. On the other hand,
one-dimensional calculations on 1j 1j grid
( c 100 100 km) in the eastern European platform
yield some very short wavelength heat flow variations near the base of the lithosphere that are
implausible [12]. Since the Pollack and Chapman
studies [9,10], a large number of heat flow and heat
production data have been obtained in previously
poorly sampled regions, notably in Precambrian
Shield areas of Canada and India. Furthermore, it
is now clear that the Precambrian lithosphere is quite
thick (>200 km), and this must be considered when
averaging heat flow.
In this paper, we analyze data now available for
the Canadian Shield and the Appalachians, including
recent new heat flow and heat production measurements [14 – 19]. These data are extensive enough to
address problems of scale and relationship between
average heat flow and heat production. Two classes
of continental geotherms are derived from heat flow
data depending on the heat flow at the base of the
lithosphere, which is taken to be either constant or
proportional to the surface heat flow. We use simple
considerations on diffusive heat transport to show
that significant (>10%) variations in mantle (Moho)
heat flow are not consistent with the presence of a
thick lithosphere. We establish a new relationship
between heat flow and crustal heat production at the
province – subprovince scale ( c 500 km) in the
Canadian Shield and in the Appalachians. Variations
in crustal heat production and mantle composition
account for a good part of the observed seismic
velocity heterogeneities in the mantle part of the
lithosphere.
2. Two classes of geotherms for the continental
lithosphere
Fig. 1 illustrates the basic variables and parameters
of this problem. The average value of and variations
in surface heat flow data are Qs F Dqs. Subtracting the
contribution of crustal heat sources, one obtains the
‘‘mantle’’ heat flow and its variations, Qm F Dqm.
Finally, the supply of heat at the base of the lithosphere at depth z = L is called the ‘‘basal’’ heat flow
and is denoted as Qb F Dqb. The relationships between heat flow variations at these three levels are
scale-dependent. Here, the ‘‘lithosphere’’ is defined as
the mantle upper boundary layer where heat is transported by conduction only. There is no reason to
J.C. Mareschal, C. Jaupart / Earth and Planetary Science Letters 223 (2004) 65–77
Fig. 1. Diagram showing the three kinds of heat flow values
considered in this paper. Qs is the surface heat flow. Subtracting
from it the contribution of crustal heat sources yields the mantle heat
flow Qm. The supply of heat at the base of the lithosphere is Qb.
Each heat flow value is associated with horizontal variations of
magnitude Dqs, Dqm, Dqb. The relationships between these three
variations depends strongly on horizontal scale.
assume that it extends to the same depth everywhere
and that its base is perfectly flat. Thus, when the
lithosphere thickness varies spatially, calculations for
conductive heat transport are carried out down to the
smallest lithosphere thickness.
2.1. The local linear relationship
Early work on continental heat flow focused on a
linear relationship between the local values of heat
flow and heat production within a few geological
provinces [20]:
Q ¼ Qr þ AD
67
weak at best, as demonstrated by data from large
Precambrian provinces of India [21], Canada [14]
and South Africa [22,23]. Theory shows that, at small
wavelengths, horizontal heat transport smoothes out
deep differences in heat production rates. Thus, surface
heat flow is only sensitive to shallow heat production
contrasts and the depth scale D is related to the
horizontal correlation distance of heat production
[24 – 26]. In Appendix A, we also show that for
wavelengths larger than crustal thickness, the heat
flow and heat production power spectra become proportional, and therefore variations in integrated crustal
heat production are directly reflected in the surface
heat flow.
2.2. Two models for the mantle heat flow
Because of the high radioactivity of crustal rocks,
the ‘‘age dependence of heat flow’’ implies that there is
a relatively simple relation between age and bulk
crustal heat production. Pollack and Chapman [9,10]
addressed this question by noting a correlation between the reduced heat flow and the average heat flow
Q̄ in a few geological ‘‘provinces’’. They added
estimates of lower crustal heat production and
obtained a model in which the mantle heat flow is
nearly proportional to the surface heat flow. This
relationship is not valid at short spatial scales by
construction. It is supposed to hold for sufficiently
ð1Þ
where Q and A stand for the observed heat flow and the
local heat production of rocks of the crystalline basement, respectively. The slope D has dimension of
length and Qr is called the reduced heat flow. This
relationship documented small-scale ( c 10 –30 km)
variations of heat flow and heat production.
The accumulation of large data sets of heat flow and
heat production and theoretical considerations have led
to re-evaluate this relationship. It is now clear that the
crust is heterogeneous on all scales in both the horizontal and vertical directions. The correlation between
local values of surface heat flow and heat production
only holds over exposed plutons very enriched in
radioactive elements [20]. Over other rock types, it is
Fig. 2. Various relationships that have been proposed between
surface and mantle heat flow. Pollack and Chapman’s predicted
mantle heat flow was calculated following [37] with D = 10 km, Pari
and Peltier [5] used Qm = 0.35Qs and Jaupart and Mareschal [6] give
the range 11 – 15 mW m 2.
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J.C. Mareschal, C. Jaupart / Earth and Planetary Science Letters 223 (2004) 65–77
Fig. 3. Two models of lithospheric thickness variation with surface
heat flow. We use the intersection of the geotherm with the 1250 jC
adiabat as the base of the lithosphere.
large scales to allow 1-D models of vertical thermal
structure down to the base of the lithosphere, but the
validity of this implicit assumption has never been
examined. A different model was put forward by Pinet
et al. [13] from their analysis of heat flow and heat
production in the Abitibi and Grenville provinces of
the Canadian Shield. They proposed that surface heat
flow varies mostly because of crustal composition and
that mantle heat flow remains in the narrow range of
11– 15 mW m 2.
These studies suggest two convenient end-members for the basal heat flow, such that it is either
constant or proportional to the surface heat flow.
These two models are shown in Fig. 2. They lead to
markedly different predictions for lithosphere structure and thickness because temperatures in the mantle
lithosphere vary much more when the basal heat flow
varies than when crustal heat production varies. For
example, Fig. 3 shows how the depth to the 1250 jC
isentropic profile varies with surface heat flow accord-
Fig. 4. Heat flow map of the Canadian Shield. White dots are heat flow sites. Archean provinces: Superior (Sup), Hearne and Rae; Proterozoic
Provinces: Trans-Hudson Orogen (THO), Grenville (Gre); Paleozoic Province: Appalachians (App); Paleozoic Basins: Williston (Will), Hudson
Bay (H.B.). The Abitibi subprovince is outlined in south eastern part of Superior. Eastern limit of Thompson Belt is also shown.
J.C. Mareschal, C. Jaupart / Earth and Planetary Science Letters 223 (2004) 65–77
Table 1
Mean heat flow and heat production in different belts and provinces
of North America
hQia
rQb NQc hAia
(mW m 2)
(AW m 3)
Superior
(>2.5 Ga)
Superior
(excluding
Abitibi)
Abitibi
Trans-Hudson
Orogen
(1.8 Ga)
THO (juvenile
crust only)
THO
(Thompson
Belt)
Grenville
(1.1 Ga)
Appalachians
( < 0.5 Ga)
rAb
NAd
42 F 2
12
57
0.95 F 0.15 1
44
45 F 2.4
12
26
1.4 F 0.26
21
37 F 1
42 F 2
7
11
26
49
0.41 F 0.07 0.33 21
0.73 F 0.07 0.50 47
37 F 1.4
7
38
0.6 F 0.08
53 F 1.6
5
10
1.12 F 0.10 0.32 11
41 F 2
11
30
0.80e
57 F 1.5
13
79
2.6 F 0.27
1.2
0.48 36
1.9
50
a
Mean F one standard error.
Standard deviation on the distribution.
c
Number of sites.
d
Number of heat production values. Each value is based on
many samples.
e
Area-weighted average.
b
ing to both models. These two models differ in one
crucial aspect, the magnitude of basal heat flow
variations. The relationship between horizontal variations of basal heat flow, mantle heat flow and surface
heat flow is the main theme of this study.
2.3. Variations in heat flow and crustal heat
production in the Canadian Shield
There are now more than 300 reliable heat flow
values in the Canadian Shield (including 150 good heat
flow determinations in Lake Superior) with corresponding heat production values for most of the land
sites. (This data set is available upon request from http://
www.geotop.uqam.ca/geophysique/flux/index.htm).
There are different scales of variations in heat flow
and heat production. For this study, we shall not
consider the scale of the individual intrusions which
bears no consequence for the deep lithosphere. The
new heat flow map of the Shield (Fig. 4) shows that
heat flow contours cross province boundaries but are
related to subprovinces with relatively specific geolog-
69
ical and petrological characteristics. This is confirmed
by the statistics that show that, on the largest scale, the
mean heat flow does not vary significantly between
Provinces (Table 1). However, on the scale of individual belts or sub provinces, there is much variability.
This is best documented in the Trans-Hudson Orogen
(Table 2).
Data are too sparse and unevenly distributed to
properly estimate the power spectrum of surface heat
flow, but they are sufficient to assess the scales of
heat flow variability. To this aim, we have calculated
the average heat flow over increasingly larger areas in
the Precambrian (i.e., excluding the Appalachians
which forms a rather narrow belt at the edge of the
continent). We have paved the Shield with squares of
given side length and calculated the average heat flow
for each square. We have then determined how the
mean and standard deviation of these averages vary
with scale. The results are presented in Table 3. We
see that there is almost no difference between the
standard deviation of the individual heat flow values
and that of the 50 50 km averages (8.9 vs. 8.8 mW
m 2). The standard deviation decreases to 7.3 mW
m 2 for areas 250 250 km and to 4.3 for 500 500
km. The mean is almost constant, which shows that
sampling is adequate. The very slight decrease in the
mean may be explained by the increased weight of
isolated very low heat flow values (Voisey Bay on the
coast of Labrador and Nielsen Island in Hudson Bay).
In these remote areas, sampling remains insufficient.
This analysis confirms that, in the Archean and
Table 2
Mean heat flow and heat production in four different belts of the
Trans-Hudson Orogen
Northern
volcanic belt
Southern
volcanic belt
Central gneiss
domain
Thompson Belt
hQi
(mW m 2)
rQ
NQ
hAi
(AW m 3)
rA
34 F 2.3
7
9
0.81 F 0.15
0.45
9
42 F 1.8
8
23
0.45 F 0.07
0.32
22
37 F 3.0
6
4
1.02 F 0.31
0.63
4
52 F 1.2
4
9
0.98 F 0.07
0.19
8
NA
hQi is the mean heat flow F one standard error, rQ is the standard
deviation on the heat flow distribution, NQ is the number of sites,
hAi is the mean heat production F one standard error, rA is the
standard deviation on heat production and NA is the number of sites
for which heat production values are available. Each ‘‘site’’ value is
based on many samples.
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J.C. Mareschal, C. Jaupart / Earth and Planetary Science Letters 223 (2004) 65–77
Table 3
Variations of the mean and standard deviation of heat flow values
with length scale of averaging window
Scale
(km)
l( Q)
(mW m 2)
r( Q)
(mW m 2)
Na
–b
50
250
500
40.6
39.8
39.5
39.9
8.9
8.8
7.3
4.3
316c
126
36
15
a
Number of windows.
All data set with individual heat flow values.
c
Number of heat flow measurements in the Canadian Shield
data set.
b
Proterozoic, most heat flow variations are of short
wavelengths ( V 250 km).
3. Scale of heat flow variations and deep thermal
structure
We shall now examine the differences in the deep
thermal structure beneath the Precambrian provinces
which are compatible with the surface observations.
The magnitude of these differences depends on the
basal heat flow.
This ratio becomes >1 below zmax:
k
1 Qb
cosh
zmax ¼
2p
Dqs
ð3Þ
for the Canadian Shield, where surface heat flow
values of 22 mW m 2 have been measured, Qb must
be < 20 mW m 2. For surface heat flow variations
Dqs = 5 mW m 2 and with wavelength k = 500 km,
we have zmax c 160 km. According to this model,
therefore, the lithosphere thickness cannot exceed 160
km beneath the Shield, which is not consistent with
present estimates.
Additional constraints can be obtained by a study of
temperature variations at depth. Changes in heat flow at
the base of the lithosphere affect temperatures at depth
when their wavelength is much larger than lithospheric
thickness L. For a given wavenumber, k, variations of
temperature DTb(k) and heat flow Dqb(k) at the base of
the lithosphere are related by:
DTb ðkÞ ¼
sinhðkLÞ Dqb ðkÞL
kLcoshðkLÞ
K
ð4Þ
where K thermal conductivity. This can be rewritten as
a function of surface heat flow:
sinhðkLÞ Dqs ðkÞL
kL
K
3.1. Changes in basal heat flow
DTb ðkÞ ¼
In the Precambrian Shield of North America, there
are heat flow variations with an amplitude of about 5
mW m 2 over wavelengths c 500 km, i.e., with
peak-to-peak variations of 10 mW m 2. Without
knowledge of crustal heterogeneity, such variations
might be attributed to changes of basal heat flow
alone. We shall now show that this interpretation is
untenable. By downward continuation, the amplitude
of heat flow perturbations increases with depth. Clearly, one condition is that such perturbations must not
exceed the mean heat flow value; otherwise, there
would be areas where temperature decreases with
depth and heat is conducted downward into the convecting mantle. For given wavenumber k and wavelength k (such that k = 2p/k), the amplitude of the heat
flow perturbation relative to the basal heat flow Qb
increases with depth as:
This shows that lateral variations in basal heat flow lead
to large variations in basal temperature when kL>1. For
L = 160 km, k c 500 km and Dq s = 5 mW m 2 ,
DTb = 500 K. The overall temperature change at 160
km depth would thus be as large as 1000 K, which is not
realistic.
Alternatively, we may apply the same principles to
determine bounds on the mantle heat flow for a given
lithosphere thickness, for example, L = 200 km. We use
the fact that the basal heat flow cannot be larger than 20
mW m 2 and hence that its variations must smaller
than this value. For Dqb < 20 mW m 2 and Dqs = 5 mW
m 2, we have k>600 km. This shows that observed
heat flow variations, which occur on a characteristic
wavelength of only 500 km, cannot be attributed to
changes of basal heat flow alone. If they were so, the
implied temperature variations would be ridiculously
large. For k = 500 km and Dq s = 5 mW m 2 ,
DTb c 800 K (a peak-to-peak change of 1600 K!).
Note that this is a very conservative argument, as the
DqðzÞ Dqs
¼
coshkz
Qb
Qb
ð2Þ
ð5Þ
J.C. Mareschal, C. Jaupart / Earth and Planetary Science Letters 223 (2004) 65–77
upper bound of 20 mW m 2 for basal heat flow
variations cannot be achieved in practice.
3.2. Changes of crustal heat generation
One alternative interpretation is that heat flow
variations are due to changes of crustal heat production.
We have calculated the effect of variations in the
average crustal heat production on temperature at the
base of the lithosphere. For a variation of heat production DA(k) with wavenumber k uniformly distributed
with depth, and assuming that the heat flow at the base
is constant, the temperature at depth z in the lithospheric mantle varies as follows:
DT ðz; kÞ ¼
DAðkÞ coshðkzm Þ 1
cosh½kðz LÞ
;
k 2K
coshðkLÞ
71
Appalachian Belt, the surface heat flow is 16 mW m 2
higher than in the Shield. If this change is attributed to
a change of basal heat flow alone, the basal heat flow
and the lithosphere thickness must vary by more than
25 mW m 2 and 150 km, respectively, which is
clearly unrealistic. On the other hand, the heat flow
change at the Grenville – Appalachian boundary may
be accounted for by a change in crustal heat generation
[15]. In that case, temperatures in the shallow Appalachian mantle are c 150 K higher than in the Shield
and the Appalachian lithosphere is c 40 km thinner
than in the Shield. Both estimates must be regarded as
lower bounds because they do not include the possible
contribution of basal heat flow variations of long
wavelength (500 km) and small amplitude (i.e.,
Dqm c 2 mW m 2, Dqb c 7 mW m 2) which will
be discussed later.
ð6Þ
where zm is crustal thickness. In the long-wavelength
limit, this reduces to the 1-D calculation, which gives
the maximum temperature variation at the Moho:
DTmax ¼
z2m
DA
:
2K
4. The magnitude of basal heat flow variations
4.1. Long-wavelength trends in heat flow and heat
production
ð7Þ
In these equations, as shown in Appendix A, for a given
variation of surface heat flow DQs, the associated
variation of average crustal heat production, DA,
depends on wavelength. At small scales, it is larger
than the estimate based on a 1-D calculation, i.e.,
DA c z Qs/zm.
Fig. 6 shows the temperature perturbation from Eq.
(6), normalized to DTmax, for a ratio zm/L = 0.2. It
shows that, except for the very long wavelengths (k/
L c 5), crustal heat generation has little effect on
temperature at the base of the lithosphere. For instance, the high heat flow anomaly in the Thompson
Belt is narrow ( < 100 km) and does not affect mantle
temperatures. On a scale of c 500 km, heat flow
variations have a peak to peak amplitude of c 10
mW m 2 (across the Abitibi or from the THO to the
Superior), resulting in 80 K temperature differences at
the base of the crust.
3.3. The Appalachians
The same line of argument leads to more dramatic
results for the Appalachians. In the 500– 800-km-wide
The observations and physical arguments on heat
transport in thick lithosphere demonstrate that surface
heat flow variations record mostly changes of crustal
heat production and hence that changes of mantle heat
flow must be small. To proceed further, one must
evaluate how much can be accounted for by changes
of heat production alone. This can only be done by
studying the relationship between large-scale average
values of heat flow and heat production. This is now
possible with the large amount of data available in the
Canadian Shield and the Appalachians.
Heat flow data cannot resolve deep variations of
thermal structure at small scales. We shall argue later
that the uncertainty on heat flow data is about F 2 mW
m 2. This is due partly to measurement errors and
partly to insufficient knowledge on the relationship
between heat flow and heat production. Using again
Eq. (2) for L = 200 km and Dqs>2 mW m 2, the
condition that Dqb < 20 mW m 2 implies that k>300
km. Thus, the minimum scale for detecting changes of
basal heat flow is about 300 km. In North America,
well-defined provinces or subprovinces with different
geological structures have typical dimensions of about
500 km. We therefore use five of these with contrasting
72
J.C. Mareschal, C. Jaupart / Earth and Planetary Science Letters 223 (2004) 65–77
heat flow and heat production characteristics. In the
Archean Superior Province, the Abitibi subprovince is
distinguished from the rest of the Province because it
has large volumes of greenstones (altered basic flows
and intrusives). In the Proterozoic Trans-Hudson Orogen, we exclude the Thompson belt at the edge of the
Superior craton from the rest of the Orogen, because it
is a narrow (60 km) belt made of reworked Archean
sediments and metamorphic rocks. In contrast, the rest
of the Orogen is such that the upper crust is made of
juvenile rocks of true Proterozoic age. The Grenville
province includes a large volume of reworked Archean
crust and is a complex collage of small terranes [27].
The Appalachians contain enriched granites and metasediments in the upper crust. On the scale of these five
large provinces ( c 500 km), average values of heat
flow and surface heat production are statistically correlated (Fig. 5). The data are close to a relationship of
the form
Q̄ ¼ Qo þ H Ā
ð8Þ
where Q̄ and Ā are province wide averaged heat flow
and heat production. That this relationship takes the
same form as the ‘‘local’’ relationship (1) is fortuitous.
In northern America, the latter is only valid for relatively small-scale variations (typically 10 –50 km) of
heat flow and heat production over Appalachian plu-
tons and does not hold in the older provinces (Grenville, Trans-Hudson Orogen, Superior Province). The
new relationship (Eq. (8)) reflects variations of average
heat flow on a much larger scale (>500 km) and relies
on a very large data set.
The new relationship is clearly inconsistent with
the assumption that surface and mantle heat flows are
proportional to one another. Formally, it is not possible to rule out variations of mantle heat flow between
the five provinces, but the data require that such
variations get cancelled by opposite variations of
lower crustal heat production. It is hard to explain
how this may be achieved in practice, and the simplest
hypothesis is that the mantle heat flow is approximately the same beneath the five provinces. For the
Abitibi, Grenville and Appalachian provinces, independent geophysical and petrological constraints on
crustal structure show indeed that changes of crustal
heat production account for the observed heat flow
variations [13,14]. A search for all models consistent
with all the available data, including gravity data and
bounds on heat production rates for the various rock
types involved, leads to a range of 11 –15 mW m 2
for the mantle heat flow [28]. The same range is also
valid for the Trans-Hudson Orogen [17]. Variations of
the mantle heat flow may not be exactly zero but must
be smaller than departures from the best-fitting relationship (Fig. 5), or about 2 mW m 2. This estimate
is close to the intrinsic uncertainty of heat flow
measurements [6].
4.2. Crustal structure in the North American craton
Fig. 5. Mean heat flow and heat production in various provinces and
subprovinces of the Canadian Shield. Bars show the standard error on
the mean. The Thompson Belt is a small-scale feature ( c 60 km) and
was not included for determining the best fitting line to the data.
At a scale of 500 km, the average surface heat flow
is not sensitive to the vertical distribution of heat
production and only records the total amount of heat
generated (Appendix A). Relationship (8) indicates
that variations in the upper crust contribute to most (if
not all) heat flow variations between the five subprovinces. This does not imply that there are no
variations in heat production in the lower crust but
that they are smoothed out, which implies that they
occur on short wavelengths. For a mantle heat flow
estimate of 13 mW m 2 [6] and a crustal thickness of
39 km, the contribution of crustal material below the
surface layer of thickness H c 9 km is about 20 mW
m 2, corresponding to an average heat production of
0.67 AW m 3. This is close to the average value for
J.C. Mareschal, C. Jaupart / Earth and Planetary Science Letters 223 (2004) 65–77
Archean crust [11]. On a large scale, therefore, continental crust in these provinces can be schematically
described as a variable upper layer over a uniform
background made of average Archean crustal material.
Within a single geological province, there may be
long-wavelength heat flow variations. For example,
there is a systematic East – West increase of heat flow
across the Archean Abitibi province on a scale of about
800 km. This heat flow variation is not reflected in
surface heat production and is due to changes in mid to
lower crustal heat production within the Abitibi [13].
Relationship (8) shows that, on average, the difference
between the Abitibi and the rest of the Superior is
explained by a layer of greenstones of thickness H c 9
km in the Abitibi upper crust. (Heat flow provides an
estimate of the thickness of the greenstones, which has
long been an issue.)
The Thompson Belt, which is also shown in Fig. 5
is a relatively small-scale feature (it is a c 60-kmwide belt separating the THO and the Superior Province) and does not affect temperatures at great lithospheric depths. It does not fit the relationship because
the whole crust must be more radiogenic to account
for the large difference in heat flow with the surrounding provinces (i.e., the slope of the line between the
THO and the Thompson Belt is 45 km) [18].
73
mW m 2 implies that Dqb < 7 mW m 2. For an
average thermal conductivity of 3 W m 1 K 1, such
a variation in basal heat flow would imply DTb < 200
K, i.e., temperature differences at 150 km depth which
may be as large as 400 K. At very large scale (>1200
km), horizontal diffusion can be neglected and hence
we have Dqb < 2 mW m 2 and DTb < 100 K. The
range of mantle heat flow compatible with our data in
the Canadian Shield and the Appalachians, 11 –15
mW m 2 [13,17] is wide enough to permit such
variations.
5. Discussion
From the above considerations, horizontal differences in temperature within the lithosphere of the
Canadian Shield, which includes provinces of Archean and Proterozoic age, may exceed 200 K
depending on horizontal scale. For example, variations of basal heat flow at a scale of 500 km could
be as large as F 7 mW m 2, implying basal
temperature differences of up to 400 K. We now
briefly evaluate these results in the light of recent
seismological studies of lithospheric structure in the
Canadian Shield and constraints from geothermobarometry on mantle xenoliths.
4.3. Maximum basal heat flow variations
Relationship (8) shows that only small variations
of mantle heat flow are allowed within the Shield and
between the Shield and the Appalachians. Uncertainties in heat production and heat flow data allow for as
much as c 4 mW m 2 changes of the non-radiogenic heat flow component (i.e., Dqm = 2 mW m 2)
[6,28]. This is the magnitude of departures from the
best-fitting relationship in Fig. 5. All indications are
that, in Canada, corrections for the last glaciation are
small [29] and that they should not add to the
uncertainty on mantle heat flow.
By definition, such ‘‘hidden’’ heat flow variations
may or may not be correlated with the surface
geology. There is a limit on wavelength, as discussed
above. For illustration purposes, we take L = 150 km,
corresponding to the smallest estimate of lithosphere
thickness in this part of the north American continent.
For k < 300 km, there is no useful constraint on
variations of basal heat flow. For k>500 km, Dqs < 2
5.1. Seismic velocities in the Precambrian lithospheric mantle
Seismic studies have shown different scales of
velocity variations in the Precambrian lithospheric
mantle of North America. P wave velocity can vary
locally by >2% between 150 and 250 km depth on a
scale of 100 –200 km in association with hot-spot
tracks and kimberlite fields [30,31]. Such small-scale
features cannot affect surface heat flow. At the scale
of c 500 km, which is compatible with our heat flow
averages, inversion of surface wave data suggests
lateral variations in shear wave velocity between 80
and 150 km depth [32,4]. At 150 km, Vs varies
between about 4.65 and 4.85 km s 1 at the latitudes
of the heat flow survey [32].
Both composition and temperature affect seismic
wave velocity [4,33]. One difficulty is to properly
account for anelastic effects [34,35]. The average
compositional difference between Archean and Prote-
74
J.C. Mareschal, C. Jaupart / Earth and Planetary Science Letters 223 (2004) 65–77
rozoic lithospheric mantle can account for about 1% of
Vs variations [4]. At 150 km depth, the 4% Vs variations
indicated by the surface wave data can be accounted for
by temperature differences between 100 and 200 K
depending on the magnitude of anelastic effects [4].
This is consistent with the heat flow constraints. At a
depth of 150 km, given their characteristic wavelength
of c 500 km, the seismically determined temperature
differences cannot be due to variations of crustal heat
production only (Fig. 6) and require small variations of
basal heat flow ( c 2 mW m 2).
5.2. Mantle heat flow variations
Our analysis shows that mantle heat flux variations
are small and that heat flow data allow poor resolution
on lateral changes of heat flux at the base of the
lithosphere. This is due partly to the fact that the basal
heat flux is small, implying that even a small absolute
uncertainty represents a significant fraction of the
large-scale average. The analysis, however, leads to
the important observation that changes of basal heat
flux may not be correlated with surface geology.
Using measurements of phase and group velocities
of fundamental mode surface waves and a ‘‘diffraction
tomography’’ method, Shapiro et al. [32] have determined the ensemble of shear velocity models which
satisfy the data down to a depth of 400 km with a
horizontal resolution of about 500 km. They used heat
flow data with two end models of crustal heat production to obtain the range of Moho temperature and
mantle heat flow consistent with the surface observations. Shear velocity values are converted to temperature using the method and parameters of [4] and only
models that fall within the permissible range are
retained. The best-fitting temperature gradients in the
mantle part of the lithosphere are calculated and converted to heat flux using an average conductivity value
of 3 W m 1 K 1. The standard deviation of heat flow
values increases with increasing heat flow and reaches
a maximum of 2.5 mW m 2. One problem with the
procedure is that no allowance is made for horizontal
diffusion, implying in particular that there can be no
difference between mantle and basal heat flows.
Shapiro et al. [32] find that mantle heat flow
variations are not well correlated with the distribution
of geological provinces and can be as large as 5 mW
m 2 within a single province, such as the Superior
for example. The average heat flow values vary
significantly across the Canadian Shield and the
Appalachians, ranging from 11 mW m 2 in the center
of the Shield to 24 mW m 2 beneath part of the
Appalachians. These results are sensitive to the starting assumption of a constant temperature gradient in
the mantle part of the lithosphere. Nevertheless, they
are consistent with the constraints from heat flow
data: at the wavelength of 500 km of relevance here,
our analysis shows that the range of basal heat flow
values may be as large as 14 mW m 2 (i.e., Dqb c 7
mW m 2).
5.3. Geothermobarometry from mantle xenoliths
Fig. 6. Mantle temperature perturbations due to horizontal variation
in crustal heat production with wavelength k/L. The temperature is
normalized to the one dimensional temperature change beneath the
crust (DAzm2/2K).
The resolution of surface heat flow data decreases
with depth in the lithosphere. Xenoliths studies complement the heat flow and are useful to reduce the
uncertainties on the thermal state of the deep lithosphere. In the Canadian Shield, temperatures deduced
from mineral assemblages in mantle xenoliths are
systematically lower in the Slave than in the Superior
Province [7]. Temperature gradients are comparable,
which is consistent with weak variations of heat
supply at the base of the lithosphere. Only two heat
flow values are available in the Slave province, which
prevents a quantitative analysis. We note, however,
that, on average, the temperature difference between
the Superior and Slave xenoliths is 100 K, which is
J.C. Mareschal, C. Jaupart / Earth and Planetary Science Letters 223 (2004) 65–77
consistent with the variations documented elsewhere
in the Shield.
6. Conclusions
Two end models for the basal heat flow ( Qb
proportional to surface heat flow, Qb constant) yield
distinctly different geotherms. Variations in lithospheric thickness are less when basal heat flow stays
within a small range than when it is proportional to
surface heat flow.
The spatial scale of the variations cannot be ignored. Our analysis shows that, for reliable models of
deep lithospheric structure, heat flow averages must
be made on a scale of at least 500 km. Variations of
local crustal heat production occur on smaller scales
and must be properly accounted for, which requires a
large number of heat flow and heat production data.
Such dense data coverage is available in very few
areas. In the Canadian Shield, large surface heat flow
variations appear at the scale of the subprovince
( < 500 km). Variations in mantle heat flow can not
account for these variations if the lithosphere is thick
( c 250 km).
Changes in crustal heat production are sufficient to
account for most of the variability in surface heat
flow, with mantle heat flow ranging 11 –15 mW m 2.
The magnitude of deep temperature variations is
poorly constrained by heat flow data and strongly
depends on horizontal scale. At 150 km depth, temperature may vary by as much as 400 K.
Acknowledgements
John Sass and an anonymous reviewer provided
critical reviews and comments which improved the
manuscript. This research was supported by NSERC
(Canada) and INSU (CNRS) (France). [VC]
Appendix A . Scale of heat flow and heat
generation variations
The scale of the crustal component of heat flow
variations is related to that of heat production. The
theory shows that surface heat flow is a much smoother
75
field than heat production. This is easily demonstrated
by considering the power spectra of both fields. For
heat sources restricted to the crust, the Fourier spectra
of heat flow and heat production are related by [36]:
Z zm
!
!
Qð kÞ ¼
Að k; zÞexpðkzÞdz
ðA1Þ
0
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
!
where k ¼ ðkx ; ky Þ and k ¼ kx2 þ ky2 :
For uniform vertical distribution of heat sources in
the crust, we find the relation for the power spectra of
heat production PA and heat flow PQ:
!
PA ð kÞ
!
PQ ð kÞ ¼
ð1 expðkzm ÞÞ2
k2
ðA2Þ
which for kzm < 1 (k/zm>2p) yields PQ(k)~PA(k)zm2.
This implies that the change in crustal composition in
the Abitibi subprovince is well recorded in the heat
flow data.
The assumption that heat source variations are
coherent over the entire crustal column is unrealistic
but maybe useful to model variations in heat production at the scale of a subprovince. At a smaller scale,
we must also consider the vertical variations in heat
production. Studies of variations of heat production
with depth in the KTB borehole suggest that the 3-D
power spectrum of heat sources follows a power law
[11]:
PA ðkx ; ky ; kz Þ ¼ Cðkx2 þ ky2 þ kz2 Þb=2
with b c 3.7 [11]. Using
Z l
1
!
!
Að k; zÞ ¼
Að k; kz Þexpðikz zÞdkz
2p l
ðA3Þ
ðA4Þ
we find:
Z l !
1
Að k ; kz Þ
!
Qð kÞ ¼
ð1 expðkzm Þ
2p l k þ ikz
expðikz zm ÞÞdkz :
ðA5Þ
Straightforward but tedious calculations show that for
k/zm>1:
!
!
PQ ð kÞ~PA ð k; 0Þz2m ;
ðA6Þ
which generalizes the results above when the heat
sources vary with depth. At very long wavelengths,
76
J.C. Mareschal, C. Jaupart / Earth and Planetary Science Letters 223 (2004) 65–77
the surface heat flow variations do not depend on how
the heat sources are distributed vertically but only on
the vertically averaged of heat production. For short
wavelengths, the power spectrum of heat flow depends
on the power spectrum of the heat sources. For a power
law spectrum of heat sources, the distribution of heat
flow is smoother than heat production [11].
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