Download Geoneutrinos and the energy budget of the Earth

Journal of Geodynamics 54 (2012) 43–54
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Journal of Geodynamics
journal homepage: http://www.elsevier.com/locate/jog
Review
Geoneutrinos and the energy budget of the Earth
Jean-Claude Mareschal a,∗ , Claude Jaupart b , Catherine Phaneuf a , Claire Perry a
a
b
GEOTOP, University of Quebec at Montreal, POB 8888, sta. Downtown, Montreal, Canada H3C3P8
Institut de Physique du Globe de Paris, 1, rue Jussieu – 75238 Paris Cedex 05, France
a r t i c l e
i n f o
Article history:
Received 4 July 2011
Received in revised form 19 October 2011
Accepted 20 October 2011
Available online xxx
Keywords:
Heat flow
Heat generation
Energy budget
Bulk silicate Earth
Urey number
Core cooling
Mantle cooling
a b s t r a c t
The total energy loss of the Earth is well constrained by heat flux measurements on land, the plate cooling
model for the oceans, and the buoyancy flux of hotspots. It amounts to 46 ± 2 TW. The main sources that
balance the total energy loss are the radioactivity of the Earth’s crust and mantle, the secular cooling of
the Earth’s mantle, and the energy loss from the core. Only the crustal radioactivity is well constrained.
The uncertainty on each of the other components is larger than the uncertainty of the total heat loss. The
mantle energy budget cannot be balanced by adding the best estimates of mantle radioactivity, secular
cooling of the mantle, and heat flux from the core. Neutrino observatories in deep underground mines
can detect antineutrinos emitted by the radioactivity of U and Th. Provided that the crustal contribution
to the geoneutrino flux can be very precisely calculated, it will be possible to put robust constraints on
mantle radioactivity and its contribution to the Earth’s energy budget. Equally strong constraints could
be obtained from a deep ocean observatory without the need of crustal correction. In the future, it may
become possible to obtain directional information on the geoneutrino flux and to resolve radial variations
in concentration of heat producing elements in the mantle.
© 2011 Elsevier Ltd. All rights reserved.
Contents
1.
2.
3.
4.
5.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The total heat loss of the Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.
Continental heat flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.
Oceanic heat flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1.
Young sea floor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2.
Old sea floor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3.
Bathymetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4.
Age distribution of the sea floor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.5.
Hot spots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The main sources of energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.
Heat producing elements in bulk silicate Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1.
Crustal heat production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2.
Mantle heat production: Urey number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.
Heat flow from the core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.
Secular cooling of the mantle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Determining U and Th with geoneutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.
Neutrino detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.
Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.
Mantle heat producing elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.
Crustal contribution to geoneutrino flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.
Directional information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Preliminary results and future studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
∗ Corresponding author. Tel.: +1 515 987 3000x6864; fax: +1 514 987 3635.
E-mail address: [email protected] (J.-C. Mareschal).
0264-3707/$ – see front matter © 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jog.2011.10.005
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J.-C. Mareschal et al. / Journal of Geodynamics 54 (2012) 43–54
1. Introduction
400
Heat flux (mW m
−2
)
350
Balancing the energy budget of the Earth has proved to be a
very difficult exercise. The total energy loss of the Earth can be calculated from heat flux measurements on land and from the cooling
plate model on the sea floor. This loss has to be balanced against
all the heat sources and the secular cooling of the Earth. The main
energy source is the decay of radioactive elements in the Earth’s
crust and mantle. The latter one is not directly measured. All the
other sources of energy are small: when added together, they represent less than the uncertainty on the energy budget. It is useful
to consider separately the radioactivity of the crust which is well
constrained by heat flux measurements combined with numerous
determinations of heat production in rock samples from that of
the mantle which must be inferred from different models. Another
reason for separating the crustal and mantle contributions is that
crustal radioactivity does not provide energy to maintain convection in the mantle. As far as the secular cooling is concerned it is
useful to separately consider the cooling of the core from that of
the mantle. Both can be estimated independently.
The total energy loss of the Earth is well constrained but, except
for the crustal heat production, there has been no direct observation to date that allows us to evaluate the different components
that enter in the Earth energy budget. It had been suggested for
some time that the radioactivity of the Earth’s deep interior could be
directly determined from the observation of neutrinos (Eder, 1966;
Marx, 1969; Avilez et al., 1981; Krauss et al., 1984; Kobayashi and
Fukao, 1991). With the recent development of neutrino detectors,
this so far tantalizing objective seems within reach (Raghavan et al.,
1998; Rothschild et al., 1998), and several observatories have now
reported detecting geoneutrinos Kamland collaboration (Araki,
T. and 86 collaborators), 2005; Enomoto et al., 2007; Borexino
collaboration group (Bellini and 89 collaborators), 2010; Kamland
collaboration (Gando, A. and 65 collaborators), 2011.
300
250
200
150
100
50
0
0
20
40
60
80
100
120
140
160
180
Age (My)
Fig. 1. Observed and predicted oceanic heat flux as a function of sea floor age. The
dotted line is the predicted heat flux for the half space cooling model. The average
observed heat flux (±one standard deviation) within different age groups is shown
by continuous (thin) lines.
Data from Stein and Stein (1994).
integrate the product of heat flux times the areal age distribution
for continental crust. It gives a value for the continental heat loss of
about 14 TW, almost identical to that obtained by the area weighted
average (Pollack et al., 1993).
2.2. Oceanic heat flow
The sea floor spreading hypothesis implies that the oceanic
lithosphere is hot when it forms at the mid-oceanic ridges and cools
as it moves away from the spreading centers. Half-space or plate
cooling models can be used to calculate the energy loss through the
sea floor. These models differ slightly in their boundary conditions
but their predictions are almost identical for young sea floor ages.
For a half-space cooling model, the temperature T varies with depth
z and distance x to the spreading center as:
z
2
v
z 2. The total heat loss of the Earth
T (x, z) = Tm erf
We shall briefly recall how the total energy loss of the Earth
has been determined. The heat loss has been calculated by many
authors (e.g., Sclater et al., 1980; Pollack et al., 1993; Jaupart et al.,
2007) and we shall follow their approach.
with Tm the temperature at the spreading center, v the half spreading rate, = x/v the age of the sea floor. The surface heat flux can
be calculated directly as:
2.1. Continental heat flow
To estimate the continental heat flux, we have used a data base
containing more than 18,000 heat flux measurements from the
continents and their margins. This number includes many additions to the data in the compilation by Pollack et al. (1993). The
measurements are very unevenly distributed geographically with
the majority of the data coming from Eurasia and North America. Two large continents, Antarctica and Greenland, remain largely
unsampled. The raw average of all continental heat flux values is
85.2 mW m−2 . This value is biased because the data set includes
many data collected for geothermal exploration in anomalously
hot regions. The bias is made evident when data from the USA
and the rest of the world are analyzed separately: the raw average is 112.4 mW m−2 for the USA vs. 80.7 mW m−2 for the rest of
the world. One way to remove the bias is by area-weighting: i.e.,
estimating the average over sufficiently large windows (1◦ × 1◦ ),
and then taking the average of all the windows. It yields an average heat flux for all the continents of ≈66 mW m−2 . Multiplying by
the continental surface area of 210 × 106 km2 gives 13.9 TW for the
total energy loss through the continents (Jaupart et al., 2007). An
alternative method to calculate continental heat loss is to bin the
data by “age”, determine the average heat flux for each age group,
x
Tm
Q () = √
= CQ −1/2
= Tm erf
√
2 (1)
(2)
where CQ depends on the temperature of the magma ascending at
the sea floor, and on the thermal properties (thermal diffusivity and
conductivity) of the cooling lithosphere.
In order to compare the oceanic heat flux measurements with
the model, data have been binned by age. Fig. 1 shows that the
observed heat flux is systematically less than predicted for sea
floor ages <60 My, and that heat flux is approximately constant and
higher than predicted for ages >80 My.
2.2.1. Young sea floor
Only heat that is conducted through the sea floor can be measured. At mid-oceanic ridges, most of the heat is transported by
the circulation of hydrothermal fluids through large open fractures
in the shallow crust. This convective component of the heat flux
accounts for the difference between the observations and the predictions of the cooling model. At depth, fractures are sealed by
the confining pressure and the plate cools by conduction only. In
regions of the sea floor that are well sealed by sediments, the heat
flux observations fit the cooling model and can be used to determine
the constant CQ . With the additional constraint that q( → ∞) → 0
(Harris and Chapman, 2004), the value of CQ ranges between 470
and 510 mW m−2 My1/2 .
J.-C. Mareschal et al. / Journal of Geodynamics 54 (2012) 43–54
−2500
45
4
3.5
−3500
3
−4000
dA/dt (km y−1)
−4500
−5000
2.5
2
Bathymetry (m)
−3000
−5500
−6000
0
20
40
60
80
100
120
140
160
180
Age (My)
2
1.5
1
Fig. 2. Worldwide average sea floor bathymetry as a function of age (solid triangle),
and predicted bathymetry for a cooling half space (dotted line).
0.5
Bathymetry data from Crosby and McKenzie (2009).
0
2.2.2. Old sea floor
For ages greater than 80 My, the heat flux levels off and is higher
than calculated for a half space cooling model. The common interpretation is that cooling of the mantle triggers the onset of small
scale convection which maintains a constant temperature at fixed
depth below the sea floor. Experiments designated to measure the
heat flux on sea floor older than 100 My have shown that it is almost
constant and equal to 48 mW m−2 .
2.2.3. Bathymetry
One consequence of the cooling of the sea floor is that the
average density of a rock column increases because of thermal
contraction:
m = −˛m T
where ˛ is the thermal expansion coefficient, m is mantle density, and T is the temperature difference at time . The change in
bathymetry can be calculated from the isostatic balance condition:
1
h =
(m − w )
d
0
˛
=
Cp (m − w )
−˛m
m (z, )dz =
(m − w )
d
T (z, )dz
0
[q(0, ) − q(d, )] d
0
where Cp is the specific heat of the lithospheric rocks and w density
of sea water. For a half space, d→ ∞ and q(d, ) → 0, we have:
h =
˛
Cp (m − w )
q()d
0
It gives:
h = h0 +
2˛
CQ 1/2 = h0 + CH 1/2
Cp (m − w )
The bathymetry of the sea floor fits the half-space cooling model
very well for ages less than 80 My. For older ages, the bathymetry
becomes flat, confirming that heat supplied at the base balances the
heat loss at the surface of the plate (Fig. 2). The constant CH is related
to CQ and, with standard values for the physical properties of the
mantle (˛ = 3.1 × 10−5 K−1 , Cp = 1170 J kg−1 K−1 , m = 3330 kg m−3 ,
and w = 1000 kg m−3 ), we obtain CH /CQ = 704 m3 W−1 My−1 . Measurements of the depth to the basement on old sea floor have been
used to determine a value of 345 m My−1/2 for CH which translates
as 480 mW m−2 My1/2 for CQ (Carlson and Johnson, 1994). This is
within the range obtained from the heat flux data set.
2.2.4. Age distribution of the sea floor
In order to determine the total oceanic heat loss, we integrate
the heat flux times the areal distribution of sea floor ages. The distribution of sea floor ages has been very well determined from studies
0
50
100
150
200
Age (My)
Fig. 3. Age distribution of the sea floor, not including the marginal basins: distribution from isochrons (solid line); best fit to the distribution (dotted line).
Data from Cogné and Humler (2004).
of the marine magnetic anomalies (Müller et al., 2008). There are
few ages higher than 180 My and the areal distribution appears to
decrease linearly with age , such that the areal distribution can
approximated by:
CA
1 − (3)
180
where is age in My (Fig. 3). In order to account for the
total area covered by the oceans including the marginal basins
(300 × 106 km2 ) the accretion rate CA = 3.4 km2 y−1 .
Integrating separately sea floor younger and older than 80 My
gives:
80
CQ −1/2 CA
Q80− =
0
180
Q80+ = q80
CA
1 − 180
1 − 80
180
d = 24.3 TW
d = 4.4 TW
(4)
Qoceans = 29 ± 1 TW
The error of the estimate of the present heat loss through the sea
floor is small, but the value obtained gives only a snapshot of the
mantle cooling. The sea floor spreading and subduction rates vary
on a time scale of several 100 My and are modulated by the Wilson cycles. The cumulative heat loss as a function of age depends
strongly on the spreading rate and on the sea floor age distribution.
For the triangular and the rectangular age distributions, the total
heat loss is calculated as:
√
4 2
1/2
Q =
SCQ CA for a triangular distribution
3
1/2
= 2CQ CA
for a rectangular distribution
(5)
where S is the total sea floor area; CQ and CA have been defined
above. A more general formulation can be found in the study by
1/2
Labrosse and Jaupart (2007). The total heat loss increases as CA
but, for the same spreading rate, it is slightly higher for the rectangular than for the triangular age distribution. With half the present
accretion rate and a triangular age distribution, the oceanic heat
loss could be as low as 20 TW. It could reach 35 TW with a spreading
rate that is 50% higher than present (Fig. 4).
Detailed studies of sea floor ages and past spreading rate have
shown that sea floor spreading rates could have decreased by as
much as 50% during the past 120 My (Müller et al., 2008). This
implies that the rate of heat loss through the sea floor was higher
46
J.-C. Mareschal et al. / Journal of Geodynamics 54 (2012) 43–54
Table 1
Estimates of the continental and oceanic heat flux and global heat loss.
35
present
slow
fast
Total heat loss (TW)
30
Continental
(mW m−2 )
Williams and von
Herzen (1974)
Davies (1980)
Sclater et al. (1980)
Pollack et al. (1993)
Jaupart et al. (2007)a
25
20
15
Total (TW)
61
93
43
55
57
65
65
95
99
101
94
41
42
44
46
a
The average oceanic heat flux does not include the contribution of hotspots. The
total heat loss estimate includes 3 TW from oceanic hotspots.
10
5
0
Oceanic
(mW m−2 )
0
50
100
150
200
Age (My)
Fig. 4. Cumulative total heat loss of the sea floor for three different distributions
of the sea floor age: the present triangular distribution, triangular distribution with
twice the present spreading rate and oldest sea floor 90 My, rectangular distribution
with oldest sea floor 180 My and spreading rate half of present. The total oceanic
area is 300 × 106 km2 , and CQ = 490 mW m−2 My−1/2 ; for ages >80 My, heat flux is
48 mW m−2 .
in the recent past than now (e.g., Loyd et al., 2007). This trend
could be part of a cyclic behavior on the time scale of the Wilson
cycle (250–400 My). If it is confirmed, it implies that the present
rate of heat loss is less than the long term average (Becker et al.,
2009), without considering other factors of secular variations such
as continental growth and changes in the total sea floor surface.
2.2.5. Hot spots
Hotspots bring additional heat to the oceanic plates. This heat is
not accounted for by the plate cooling model and should be added
to the oceanic heat loss. The extra heat flux is barely detectable, but
the heat that has been put in the plate can be estimated from the
volume of the swell of the sea floor: it amounts to 2–4 TW (Davies,
1988; Sleep, 1990). This is an upper bound because the oceanic
plate may be recycled in the mantle before the additional heat
reaches the surface. Whether the present low rate of heat transport by plumes from the core to the Earth surface is representative
of the long term average remains an open question.
Adding the heat from the hotspots to the continental and oceanic
heat flow gives the total energy loss at the Earth’s surface: 46 TW.
This value is not much different from the first estimates by Williams
and von Herzen (1974) (see Table 1). As discussed above, this value
may be different from the long term average because of secular
and/or cyclic variations in sea floor spreading and subduction rates
(see also Labrosse and Jaupart, 2007; Loyd et al., 2007).
3. The main sources of energy
The difference between the total heat loss of the Earth and the
energy production inside the Earth must be balanced by internal
cooling. Most of energy produced in the Earth comes from the decay
of radioactive elements. In the core, energy is also released as latent
heat by the freezing of the inner core and by its gravitational settling. The decrease in gravitational potential energy due to thermal
contraction of the Earth is not negligible, but it is stored as strain
energy and does not contribute to the budget (Birch, 1952).
3.1. Heat producing elements in bulk silicate Earth
Following Urey (1955), many researchers have used the chondritic meteorites as the starting material for the Earth and to
estimate the concentration in heat producing elements (HPE).
Although it had first been suggested that the total heat production in a “chondritic” Earth would be ≈28 TW, Wasserburg et al.
(1964) pointed out that Earth was depleted in K relative to the
meteorites, and that with the same abundance in U and Th, but
only 1/4 of the K, the total heat production would only be 20 TW.
Several different methods have been used to determine the composition and the abundance of radio-elements in the Earth mantle.
These have yielded slightly different estimates of the heat generation in bulk silicate earth (BSE), which includes the crust and mantle
(Table 2). The estimates by McDonough and Sun (1995), Hart and
Table 2
Radio-element concentration and heat production in meteorites, bulk silicate Earth, and mantle.
U (ppm)
Carbonaceous chondrites
0.02
0.015
Ordinary chondrites
CI chondrites
0.0080
Palme et al. (2003)
0.0070
McDonough and Sun (1995)
Bulk silicate Earth
From CI chondrites
0.020
Javoy (1999)
From EH chondrites
0.014
Javoy (1999)
From chondrites and lherzolites trends
0.021
Hart and Zindler (1986)
From elemental ratios and refractory lithophile elements abundances
0.020 ± 20%
McDonough and Sun (1995)
0.022 ± 15%
Palme et al. (2003)
0.017 ± 0.003
Lyubetskaya and Korenaga (2007)
Depleted MORB source
0.0032
Workman and Hart (2005)
Average MORB mantle source
0.013
Su (2000)
Th (ppm)
K (ppm)
A* (pW kg−1 )
0.07
0.046
400
900
5.2
5.8
0.030
0.029
544
550
3.5
3.4
0.069
270
4.6
0.042
385
3.7
0.079
264
4.9
0.079 ± 15%
0.083 ± 15%
0.063 ± 0.011
240 ± 20%
261 ± 15%
190 ± 40
4.8 ± 0.8
5.1 ± 0.8
3.9 ± 0.7
0.0079
25
0.59
0.040
160
2.8
J.-C. Mareschal et al. / Journal of Geodynamics 54 (2012) 43–54
Table 3
Some estimates of bulk continental crust heat production A, of the crustal component of heat flux for a 41 km thick crust Qc , and of the total heat production of the
continental crust.
A (␮W m−3 )
Qc (mW m−2 )
TW
Reference
0.74–0.86
30–35
6.4–7.4
0.83
0.92
0.58
1.31
1.25
0.93
0.70
0.55–0.68
0.94
34
38
24
54
51
38
29
23–29
39
7.1
8.0
5.0
11.3
11.1
8.0
6.1
4.8–6.1
8.2
0.84–1.15
0.70
0.79–0.99
34–47
29
32–40
7.1–9.8
6.1
6.8–8.2
Allègre et al. (1988), O’Nions
et al. (1979)
Furukawa and Shinjoe (1997)
Weaver and Tarney (1984)
Taylor and McLennan (1995)
Shaw et al. (1986)
Wedepohl (1995)
Rudnick and Fountain (1995)
McLennan and Taylor (1996)
Gupta et al. (1991)
Nicolaysen et al. (1981), Jones
(1988)
Gao et al. (1998)
Jaupart et al. (1998)
Jaupart et al. (2003)
Zindler (1986), and Palme et al. (2003) all yield ≈5 pW/kg, i.e., a total
of 20 TW for the heat production of BSE, but several authors have
argued for lower values of the mantle heat production. Javoy (1999)
has argued that the starting material for the Earth mantle should be
the enstatitic meteorites which give a lower heat production for the
present mantle than a chondritic composition. Boyet and Carlson
(2006) have used 146 Sm/142 Nd isotopes systematics to infer that
the abundances in U, Th, and K of the mantle were about 70% those
calculated for a chondritic mantle. More recently, Lyubetskaya and
Korenaga (2007) used an inversion method and obtained a heat
generation value of ≈4 pW/kg, i.e., a total of ≈16TW for BSE, also
lower than the commonly accepted values.
3.1.1. Crustal heat production
Different sampling methods have been used to estimate the
average heat production of the continental crust which give values between 0.6 and 1.3 ␮W m−3 (Table 3). This wide range can be
narrowed down because values higher than 1 ␮W m−3 are unlikely
since they imply that the total crustal heat production is higher that
the surface heat flux in stable continental provinces. It is probably
best to estimate the bulk crustal heat production directly from the
surface heat flux which integrate over the entire crust and is insensitive to local heterogeneities (Jaupart et al., 2003). The crustal heat
production can be determined in exposed crustal section, where
the entire crustal column is exposed. In stable provinces where the
crust is in thermal steady state, the bulk crustal heat production
can thus be determined by subtracting the mantle component from
the surface heat flux. The best estimates for the mantle heat flux
are 15 ± 3 mW m−2 (e.g., Jaupart and Mareschal, 1999; Roy and Rao,
2000). Such values are consistent with estimates of the mantle heat
flux obtained from geo-thermobarometry studies on mantle xenoliths (e.g., Rudnick and Nyblade, 1999; Kukkonen and Peltonen,
1999; Russell et al., 2001) There is a trend of decreasing heat production with crustal age (Table 4), but one cannot predict the heat
Table 4
Estimates of bulk continental crust heat production from heat flow data from Jaupart
et al. (2003).
Age group
Aa (␮W m−3 )
QC b (mW m−2 )
% Areac
Archean
Proterozoic
Phanerozoic
Total continents
0.56–0.73
0.73–0.90
0.95–1.21
0.79-0.99
23–30
30–37
39–50
32–40
9
56
35
Range of heat production in ␮W m−3 .
Range of the crustal heat flux component in mW m−2 .
c
Fraction of total continental surface, from Model 2 in Rudnick and Fountain
(1995).
a
b
47
production and surface heat flux on the basis of crustal age since
there are wide variations within each age group, particularly in the
Proterozoic. Integrating over the entire volume of the continental
crust yield a total heat production of ≈7.5 ± 1 TW. Crustal heat production is the only component in the energy budget which is well
constrained and estimated with a small uncertainty.
3.1.2. Mantle heat production: Urey number
The heat production of the mantle, obtained by removing from
BSE the radio-elements stored in the crust, is estimated at 9–14 TW,
depending on the model used for calculating BSE composition and
accounting for the much small uncertainty on the crustal heat production. Values higher than the upper limit of this range have been
proposed and are still used (e.g., Davies, 1999; Stacey and Davis,
2008).
Because the heat production in the crust does not provide energy
to drive mantle convection, it is useful to subtract it from the total
energy loss and focus on the mantle heat loss, which is 39 TW. The
ratio of the total heat production that is available to drive mantle
convection to the total heat loss is referred to as the Urey ratio. For
13 TW mantle heat generation, the Urey ratio is 0.33 but it could be
as low as 0.23 for the BSE radio-element abundance proposed by
Lyubetskaya and Korenaga (2007). The values for mantle heat production used by Stacey and Davis (2008) imply a Urey ratio larger
than 0.5, and the upper limit of Davies (1999) is 0.78. The present
Urey ratio is a key parameter for parameterized convection models
of the Earth where scaling laws are used to determine the rate of
heat loss. It has been shown that low (i.e., <0.7) values of the Urey
ratio lead to the “Archean thermal catastrophe” where the temperatures during the Archean (>2.5 Gy) would be hot and imply
massive melting of the mantle (e.g., Christensen, 1985; Korenaga,
2006) unless the present scaling laws are modified.
3.2. Heat flow from the core
Some authors have assumed that the heat flux from the core
is equal to the heat flux transported by the hotspots. There is no
reason that it should be so. The heat carried away by hotspots originating at the core mantle boundary must be less than the core’s
output (Labrosse, 2002; Mittelstaedt and Tackley, 2006). Hotspots
thus give a lower bound on the core heat flow of about 4 TW (Davies,
1993). A different bound can be obtained by calculating the minimum heat flux that would be conducted along an adiabat in the
core. Because the core is thought to have a very high thermal conductivity, the heat flux conducted along the adiabat is 40 mW m−2 ,
i.e., implying a total energy loss of 5 TW (higher than the heat
carried by hotspots). How much energy is required to power the
geodynamo has been much debated. Present estimates vary within
a wide range (5–14 TW) with a preferred value of 9 TW (Buffett,
2002; Nimmo, 2007).
This energy comes from the secular cooling of the core, the latent
heat released by the freezing of the inner core, and by the gravitational settling of the inner core. Some authors have proposed that
energy is also provided by heat producing elements in the core.
Potassium has been the preferred candidate (Goettel, 1976; Lee
et al., 2004), but the presence of U in the core has also been suggested (Herndon, 1996). 720 ppm of K in the core would entirely
account for the K deficit of BSE relative to the chondritic meteorites. With 720 ppm K, the core would generate an additional 8 TW
of energy. This remains a highly controversial question but most
geochemists are skeptical that any K has been stored in the core
(McDonough, 2003).
Energy flowing from the core into the mantle at a rate as high
as 10 TW implies that the inner core is a relatively young feature
unless there is radiogenic heat production. Results obtained by different authors show that without radiogenic heat, the inner core
48
J.-C. Mareschal et al. / Journal of Geodynamics 54 (2012) 43–54
Total heat loss 46 ± 2 TW
Liquidus temperature (°C)
1600
Heat production
Crust
7 TW
(6−7 TW)
1500
1400
1300
Heat production
Mantle
13 TW
(9−16 TW)
1200
0
1
2
3
Mantle cooling
17 TW
(8−18 TW)
4
Age (Gy)
Core heat loss
9 TW
(4−14 TW)
Fig. 5. Liquidus temperatures of basalts from ophiolites and greenstone belts with
MORB characteristics as a function of age.
Adapted from Abbott et al. (1994).
age would be between 0.4 and 1.9 Ga (Buffett, 2002; Labrosse, 2003;
Nimmo, 2007). With a high rate of energy flow from the core, the
presence of an inner core is not required to maintain the magnetic
field, but a young inner core is in contradiction with some geochemical estimates that put its age at 3.5 Gy (Brandon et al., 2003). The
presence of HPEs in the core would resolve this contradiction: with
300 ppm K in the core and a time-averaged heat flux of 8.5 TW, the
age of the inner core would approximately be the same as that of
the Earth. Without K, the inner core can be as old as the Earth only
if the core heat flow is less that 3 TW.
Fig. 6. Breakdown of the present mantle energy by Jaupart et al. (2007), with the
best estimates of the core heat flow and of the abundance of radio-elements in BSE
and the mantle cooling rate adjusted to balance the budget.
deficit. They balance the budget by adjusting the total heat production of the mantle (Table 5). For Stacey and Davis (2008), the total
heat generation of BSE would thus be 28 TW; for Davies (1999), the
heat production of the mantle could be as high as 28 TW, most of it
in the lower mantle, and the total for BSE could be thus higher than
that of a chondritic Earth not depleted in K.
4. Determining U and Th with geoneutrinos
3.3. Secular cooling of the mantle
Mantle temperatures can be calculated from the composition
of the Mid oceanic ridge basalts (MORB). Petrological studies on
Archean (3.5–2.5 Gy old) MORB like rocks suggest a modest cooling
rate of 50 K/Gy (Fig. 5, see also, Abbott et al., 1994). Cooling of the
mantle at a rate of 1 K/Gy yields ≈0.13–0.15 TW, depending on the
average thermal capacity of the mantle. If the present cooling rate
is not significantly different from this long term average, we obtain
that the mantle cooling contributes ≈7 TW.
If we simply add up our best estimates of the energy inputs
to the mantle energy budget, we obtain 7 + 13 + 9 = 29 TW and we
are 10 TW short of the present mantle energy loss of 39 TW. The
budget balancing would be even more difficult if we were to assume
that heat flow from the core is lower than 9 TW, or that the total
heat generation of BSE is less than 20 TW. The long term deficit
might even be higher than suggested if the present rate of sea floor
spreading is lower than the long term average.
In order to balance the budget, Jaupart and Mareschal (2011)
have considered that the present mantle heat production and core
heat flux are the least poorly constrained components. They have
balanced the budget by adjusting the present cooling rate of the
mantle to ≈120 K/Gy (Fig. 6 and Table 5). This value is inconsistent
with the long term estimate from komatiites. There are two ways
out of this conundrum: (1) the present rate of heat loss is mostly
determined by the age distribution of the sea floor may be higher
than the long term average, and/or (2) the present mantle cooling
rate is higher than the long term average. Alternative approaches
to balance the energy budget have been used by Davies (1999) and
by Stacey and Davis (2008). Although there are differences in the
details of their analysis, both authors assume that the mantle cooling rate is well constrained (<10 TW) and that the core heat flow
is low, i.e., it is the same as the total heat transported by hot spots
(4–5 TW). This does not allow for K in the core to make up for the
The total heat production in the Earth is an important and so
far poorly constrained component of the energy budget. Models
also differ in the radial distribution of the heat producing elements
in the mantle with the suggestion by some authors that the lower
mantle is very enriched in radioactive elements.
4.1. Neutrino detectors
Until recently, there was little hope to directly measure the
mantle heat production and its radial variation. The situation has
evolved after the development of underground neutrino observatories equipped with large liquid scintillation detectors that react
Table 5
Various estimates of the breakdown of the global budget in TW. Stacey and Davis
(2008) have added heat production in the continental crust to that of bulk silicate
earth. They also assume that gravitational potential energy released by thermal contraction produces heat rather than strain energy. Both Stacey and Davis (2008) and
Davies (1999) assume that hot-spots carry all the heat from the core.
Total heat loss
Crustal heat production
Mantle heat production
Crust mantle differentiation
Gravitational (thermal
contraction)
Tidal dissipation
Core heat loss
Mantle cooling
a
Stacey and
Davis
(2008)
Davies
(1999)
Jaupart et al.
(2007) range
(preferred value)
44
8
20
0.6
3.1
41
5
12–28b
0.3
46
6–8 (7)
11–15 (13)
0.3
0.1
5
9a
0.1
6–14 (8)
9–23 (18)c
3.5
8.0
Mantle cooling is fixed.
Lower mantle heat production is variable and adjusted to balance the other
terms in the budget.
c
Mantle cooling is adjusted to balance the budget.
b
J.-C. Mareschal et al. / Journal of Geodynamics 54 (2012) 43–54
49
to the anti-neutrinos produced by the decay of U and Th. It appears
that it will be possible to determine the amount of U and Th in
the Earth, and their distribution in different reservoirs (see all the
contributions in Dye, 2006).
The liquid scintillators detect inverse beta decay events due to
electron antineutrinos:
range of distances traveled by geoneutrinos is much larger than the
oscillation distance, it is adequate to use the average survival probability value of 0.56 ± 0.02 (Enomoto et al., 2007). This is not true
for reactors antineutrinos because they travel a fixed distance and
the survival probability must be calculated for each of the reactors.
e + p → n + e+
4.3. Mantle heat producing elements
(6)
The positron e+ promptly annihilates emitting two ␥ rays and
the free neutron is captured on protons with a mean time of 210 ␮s,
emitting a 2.2 MeV ␥ ray. It is the coincidence of the delayed event
that positively identifies the antineutrino inverse ␤ decay.
The cross section of the reaction depends on the anti-neutrino
energy squared:
e p→e+ n = 9.3 × E2 × 10−44 cm2
(E )
d˚(E )
dE dE (8)
Averaging the cross section over the entire energy spectrum gives
(Fiorentini et al., 2007):
238 U = 0.404 × 10−44 cm−2
232 Th = 0.127 × 10−44 cm−2
The cross section of the reaction () is very small: for a target of
1032 protons and one year exposure, the flux required to observe
one geoneutrino event is 1032 × 3.15 × 107 / ; which gives a
minimum flux of 7.67 × 104 cm−2 s−1 for 238 U antineutrinos and
2.48 × 105 cm−2 s−1 for 232 Th antineutrinos (Enomoto et al., 2007).
Detector exposure is measured by the total number of protons
in the detector times the exposure time. The practical unit for measuring detector exposure to geoneutrinos is 1032 protons-year (the
mass of a 1032 protons detector is 1.2 kT of liquid scintillator). The
terrestrial neutrino unit (TNU) refers to the total number of events
recorded per unit detector exposure.
In addition to the geoneutrinos from decay of radio-elements
in the Earth, antineutrinos are also produced in nuclear reactors
all over the world. The reactor signal from nearby reactors must
be calculated from detailed information on their power and fuel
composition.
4.2. Oscillations
One of the fundamental discoveries of recent studies in underground observatories is that neutrinos, that are a superposition of
different “flavors” e , , and , undergo oscillations from one flavor to another (as discussed and summarized by Gonzalez-Garcia
and Nir, 2003). The “survival” probability of an electron antineutrino varies with distance traveled from the source as follows:
Pe →e ≈ 1 − sin2 (212 )sin2
1.27m221
Lr
Ee
(9)
where 12 and m221 are the oscillation parameters. Lr is distance
(in m) and Ee is the antineutrino energy in MeV. The oscillations
parameters have been determined at the KamLAND neutrino observatory in Japan from measurements on reactors antineutrinos and
solar data to constrain the mixing angle as tan 2 ( 12 ) = 0.47 and
m221 = 7.58 × 10−5 eV 2 (Abe et al., 2008). For a 3 MeV antineutrino, the characteristic oscillation distance is ≈100 km. Because the
2
˚=
(7)
where E is in MeV, with a threshold energy of ≈1.8 MeV. The
maximum energy of 235 U and 40 K antineutrinos is below the detection threshold, and only antineutrinos from 238 U and 232 Th can be
detected. The total number of events detected is proportional to
the total number of target protons in the detector, Np , times the
exposure time, , times the total cross section of the reaction:
Np × The flux of neutrinos from the mantle depends on the total mass
of radio-elements and on their radial distributions if we assume a
spherically symmetric Earth with radius a. For a detector located at
the surface of the earth, the neutrino flux is obtained as:
=
a
2
1
Ni (u) log
0
a
d cos −1
0
1
d
0
Ni (r)r 2 dr
4(a2 − 2ar cos + r 2 )
1 + u
1−u
udu
(10)
with u = r/a and Ni (r) is the volumetric activity for radio-elements
at distance r from the Earth center. The angle between
the source and the detector’s direction is theta; because of the symmetry, is defined arbitrarily in the plane perpendicular to the
direction of the detector. For a uniform activity Ni0 between r/a = 0
and r/a = b, the flux is:
232 Th or 238 U
˚=
a
N
2 i0
b2 − 1
× log
2
1 + b
1−b
+b
(11)
The gravity field at the surface of or outside a spherically symmetric Earth depends only on the total mass of the Earth regardless
of the radial variation in density. Eq. (10) shows that the neutrino
flux depends on the radial distribution of the sources and that is
more affected by the shallow than by the deep sources. For example,
the geoneutrino flux is about 5% higher for radio-elements concentrated in the mantle than for a uniform distribution in the mantle
and core. Likewise, for the same total mass of radioactive elements,
the flux is ≈10% lower if the upper mantle is depleted by a factor
of 3 relative to the lower mantle.
For the BSE model of McDonough and Sun (1995), the total
neutrino activity from 238 U is 5.9 × 1024 s−1 and that of 232 Th is
5.1 × 1024 s−1 . For a uniform distribution throughout the entire
Earth the resulting flux at the surface ˚U = 1.2 × 106 cm−2 s−1 and
˚Th = 1.0 × 106 cm−2 s−1 for U and Th, yielding 15.1 and 4.0 TNU’s
(or 0.56 that number if oscillations are considered). Assuming that
the crustal enrichment in radio-element relative to the mantle is 60
that and radio-elements are distributed uniformly within the crust
and the mantle results in a 90% increase in flux and in the number
of neutrino events, with 29 and 7.6 TNU for U and Th respectively.
In that case, the difference between the latter model and a model
including a crust over a layered mantle is small.
Considering a model with a depleted mantle and no crust for
a crude estimate of the neutrino flux in oceans, we obtain fluxes
˚U = 0.72 × 106 cm−2 s−1 and ˚Th = 0.6 × 106 cm−2 s−1 , yielding 9
and 2.4 TNU for U and Th respectively.
4.4. Crustal contribution to geoneutrino flux
Estimating the abundance of U and Th in the mantle from
the geoneutrino observations is particularly difficult because the
largest part of the geoneutrino flux in continents comes from the
crust nearby the observatory and only 10–20% come from the mantle (e.g., Raghavan et al., 1998; Fiorentini et al., 2005; Enomoto et al.,
2007), depending on the local crustal composition and thickness.
The effect of the crustal component of the geoneutrino flux was
demonstrated by the study of Fiorentini et al. (2005) who showed
50
J.-C. Mareschal et al. / Journal of Geodynamics 54 (2012) 43–54
Fig. 7. Map of surface heat flux in continents. In stable continental regions, the main component of the heat flux is the crustal radioactivity. Oceanic areas have been greyed
out because the higher surface heat flux is due to the cooling of oceanic and bears no relation to radioactivity. In thermal steady-state, the geoneutrino flux is expected to
decrease over low heat flux regions and to increase over high heat flux regions.
Hzm
˚ =
2
1
log
2
1+
R2
2
zm
R
+
tan−1
zm
z m
R
(12)
where is the constant ratio of neutrino activity to heat production (see for instance Table 6). For a horizontally stratified crust,
we can simply add the contributions of several cylinders with different thicknesses. The effect of the stratification is significant near
the observatory and increases the neutrino flux if crustal heat production decreases downward (Fig. 8). For distances larger than two
crustal thickness, the geoneutrino flux no longer depends on the
vertical distribution but only on the integrated crustal radioactivity.
The point of such calculations is to illustrate the close relationship between the total crustal radioactivity that can determined
from heat flux and the neutrino flux at the observatory. Eq. (12)
is useful to estimate the near field geoneutrino flux, but it is not
bounded for R→ ∞ and the integration for the far field must be
performed on a spherical shell (Fig. 9).
When very detailed information on the crustal composition is
available and shows local enrichments in radio-elements, the oscillation parameters can be included in the calculation of the near
field contribution to the flux. A small increase in the neutrino flux
can indeed be observed in the very near field when oscillations
are included. For the sake of the example, we have calculated the
effect of an enriched vertical cylinder with twice the concentration
of radioactive elements as in the average crust. The oscillations are
calculated for an energy of 3 MeV and the oscillation parameters of
Abe et al. (2008). The effect is small but not entirely negligible and
results in the flux being about 9% higher than that estimated with
5
4
Φ/γ(QQm)
that the number of geoneutrino events to be expected in continental observatories varies between 30 and 65 /(1032 target protons
× year), with the highest event rates in regions where the crust is
thick. In this global study, the crustal geoneutrino flux was estimated from the model CRUST2.0 (Mooney et al., 1998) combined
with world averaged estimates of radio-element abundance in the
upper, middle and lower crust. Because the surface heat flux in
stable continental regions also depends on the radioactivity of the
crust, one expects a strong correlation of the predicted geoneutrino
flux with the measured surface heat flux (Fig. 7). Such a correlation
with surface heat flux is not observed on the predicted geoneutrino
flux map of Fiorentini et al. (2005) because it is based on a very
poorly constrained seismic crustal model which does not account
properly for variations in crustal composition.
In order to estimate the crustal neutrino flux ˚, we shall first
consider the geoneutrino flux at the origin of the coordinate system.
We first suppose that the crust is homogeneous. The contribution
of a homogeneous cylindrical layer with heat production H, thickness zm and radius R to the geoneutrino flux at the center can be
calculated:
3
undifferentiated
DI = 2.5
difference
2
1
0
0
5
10
15
20
r/zm
Fig. 8. Integrated neutrino flux for 2 different vertical distributions of radioactivity
in a layer of thickness zm . The observation site is located on the surface at the axis of
the cylinder. The total heat production (Q − Qm ) is the same for both models, but one
model has uniform vertical distribution of radio-elements, while the other has an
enriched upper crust of thickness 0.3 × zm . The differentiation index DI is the ratio
of surface to average heat production.
J.-C. Mareschal et al. / Journal of Geodynamics 54 (2012) 43–54
51
Table 6
Mantle and crust composition, heat production, and geoneutrino activity. The energy of K neutrinos is below the detection threshold.
Mantle (4 × 1024 kg)
Heat production (W/kg)
e activity (s−1 kg−1 )
Javoy (1999)
Composition (ppm)
Total mass (kg)
Heat production (TW)
e activity (s−1 )
McDonough and Sun (1995)
Composition (ppm)
Total mass (kg)
Heat production (TW)
e activity (s−1 )
Palme et al. (2003)
Composition (ppm)
Total mass (kg)
Heat production (TW)
e activity (s−1 )
Lyubetskaya and Korenaga (2007)
Composition (ppm)
Total mass (kg)
Heat production (TW)
e activity (s−1 )
Continental crust (2.3 × 1022 kg)
Rudnick and Gao (2003)
Composition (ppm)
Total mass (kg)
Heat production (TW)
e activity (s−1 )
Jaupart et al. (2003)
Composition (ppm)
Total mass (kg)
Heat production (TW)
e activity (s−1 )
U
Th
K
9.52 × 10−5
7.38 × 107
2.56 × 10−5
1.61 × 107
3.48 × 10−9
2.25 × 104
0.014
5.6 × 1016
5.3
4.1 × 1024
0.042
16.8 × 1016
4.3
2.7 × 1024
385
15.4 × 1020
5.4
(34.7 × 1024 )
0.020 ± 20%
8 × 1016
7.6
5.9 × 1024
0.079 ± 15%
31.6 × 1016
8.1
5.1 × 1024
240 ± 20%
9.6 × 1020
3.3
(21.6 × 1024 )
0.022 ± 15%
8.8 × 1016
8.4
6.5 × 1024
0.083 ± 15%
33.2 × 1016
8.5
5.3 × 1024
261 ± 15%
10.4 × 1020
3.6
(23.4 × 1024 )
0.017 ± 0.003
6.8 × 1016
6.5
5.0 × 1024
0.063 ± 0.011
25.2 × 1016
6.5
4.1 × 1024
190 ± 40
7.6 × 1020
2.6
(17.1 × 1024 )
1.3
3.0 × 1016
2.9
2.2 × 1024
5.6
12.9 × 1016
3.3
2.1 × 1024
1.5 × 104
3.45 × 1020
1.2
(7.8 × 1024 )
1.2–1.4
2.8–3.2 × 1016
2.7–3.0
2.1–2.4 × 1024
4.8–5.6
11.2–12.9 × 1016
2.8–3.3
1.8–2.1 × 1024
1.4–1.7 × 104
3.4–3.8 × 1020
1.1–1.4
(7.2–8.8 × 1024 )
the average survival probability 0.56 (Fig. 10). This example uses
a high value for the local enrichment to illustrate that it may be
necessary to account for the survival probability near the Sudbury
neutrino observatory where the crustal heat production is ≈30%
higher than the average Canadian shield (Perry et al., 2009).
4.5. Directional information
15
19
20.5
15.6
7.4
6.9–7.6
incoming neutrinos. Determining the direction of the incoming
neutrino with an accuracy of 5% has been considered a feasible
objective (Suzuki, 2006; Fields and Hochmuth, 2006; Hochmuth,
2006; Tonazzo, 2007). With this directional information, it will be
possible to perform a depth sounding of the Earth and to determine the vertical distribution of the radioactive elements U and
Th in the crust and mantle. One expects the flux of crustal neutrinos to be highest near the horizontal direction and the flux of
mantle neutrinos to be spread a wide range of dips with a maximum at intermediate inclinations (Fig. 11). The existence of two
1
1
0.8
0.8
0.6
0.6
Φ
Φ/Φ
tot
Neutrino detectors do not yet have the capability of measuring both the energy and the momentum, i.e., the direction, of the
Total
0.4
0.4
homogeneous
differentiated
0.2
0
0
0
0
5
10
no oscillation
oscillation
0.56 survival probability
0.2
15
3
100
200
300
400
radial distance (km)
distance (10 km)
Fig. 9. Cumulative neutrino flux for a thin spherical shell at the surface of a sphere.
The thickness of the shell (0.006 times the sphere radius) is analog to that of the
continental crust. The calculation with two different vertical distributions of HPEs
in the crust shows that the difference does not increase outside the near field region.
Fig. 10. Effect of crustal heterogeneities on the neutrino flux in the near field with
oscillations. The calculation is for a homogeneous crust except in the region within
30 km of the observatory where the radioactivity is double that of the average crust.
In this situation, an average correction for neutrino oscillation underestimates the
geoneutrino flux by 9%.
52
J.-C. Mareschal et al. / Journal of Geodynamics 54 (2012) 43–54
0.1
crust
mantle
0.08
Φ
0.06
5. Preliminary results and future studies
0.04
0.02
0
0
20
40
60
80
100
dip (o)
Fig. 11. Neutrino flux from the crust (a thin spherical shell with radius
0.994 < r/a < 1) and the mantle (0.5 < r/a < 0.994) as a function of the inclination. The
flux of crustal geoneutrinos exhibits a sharp maximum at near horizontal inclination. The flux of mantle geoneutrinos shows a distribution spread over a much wider
range of dip angles, with a maximum near 50◦ .
distinct mantle reservoirs, a depleted upper mantle and a primitive lower mantle, could also be ascertained from the variation of
the neutrino flux with inclination (Fig. 12). If it can be measured,
the variation of the geoneutrino flux with inclination will provide
a means to determine any enrichment in radioactive elements of
the lower mantle relative to the upper one. Because the flux from
crustal sources overwhelms the geoneutrino signal in continents,
resolving the difference between a homogeneous and a layered
mantle requires not only very large detector exposures but also
accounting for the crustal flux with extreme, perhaps unpractical,
precision. On the sea floor where the crustal flux is low and uniform,
directional measurements with very large detector exposure could
resolve the presence of a reservoir in the lower mantle enriched
in radioactive elements relative to the upper mantle. Such enrichment, which has been hypothesized from geochemical models, is a
key element for understanding mantle dynamics and evolution. It
0.025
0.02
Φ/Φ0
could be demonstrated following the deployment on the sea-floor
of a directional geoneutrino detector with very large total exposure.
Sea-floor geoneutrino detectors with directional information could
also test for the presence of an extremely large lower mantle reservoir of radio-elements (up to 27 TW) such as suggested by Davies
(1999), again a key information for models of mantle convection.
uniform
layered
0.015
0.01
0.005
0
0
20
40
60
80
o
dip ( )
Fig. 12. Variations of the mantle neutrino flux with inclination for two different
radial distributions of U and Th in the mantle. flux per unit dip angle is relative
to the total integrated flux ˚0 , and both radial distributions are compared to the
total integrated flux ˚0 for the uniform distribution a uniform distribution. The
differences between the two distributions are marked with the flux spread over
a much wider range of inclinations for the homogeneous than the two reservoirs
mantle. Note that the mantle flux is low (relative to the effective cross-section) and
that it is one order lower than the crustal flux. It translates in low event yield per
unit angle.
Two research groups, at the KamLAND neutrino observatory in
Japan and at the Gran Sasso observatory in Italy, have now reported
on their geoneutrino observations.
Recently, the Borexino group reported on their observations at
the Gran-Sasso observatory in Italy. The noise from nuclear reactors
is one tenth that at Kamioka and very detailed geological studies have been conducted to properly account for the complicated
crustal structure (Coltorti et al., 2011). The preliminary report has
identified 9.9 events for a 252.6T y exposure of the detector; this is
equivalent to a rate of 3.9 events/(100T y) Borexino collaboration
group (Bellini and 89 collaborators), 2010. The small geoneutrino
flux observed at Borexino is sufficient to rule out the existence of
a “nuclear reactor” in the Earth’s core that had been proposed by
Herndon (1996). Despite the small size of the detector (1.7 × 1031
target protons), these observations have led to a, perhaps not unexpected, but conclusive report.
The team at the Kamioka Liquid Scintillator Antineutrino Detector (KamLAND) was the first to report on geoneutrino observations.
With a total exposure target of 7.09 × 1031 protons year, this first
report concerned 28 (+16/−15) geoneutrino events, which corresponds to a flux 6.34(+ 3.6/− 3.4) × 108 cm−2 s−1 Araki, T. and
86 518 collaborators), 2005; Enomoto et al., 2007. These numbers are consistent with the BSE model: the central value for
the total heat generation of U and Th is 16 TW with a very large
uncertainty due the crustal contribution. These results at Kamioka
are particularly remarkable considering that the site is probably
the worst possible for geoneutrino observations, with very strong
noise from nuclear reactors and a very complicated crustal structure. In their most recent report, the KamLAND group analyzed
the geoneutrino events recorded during nine years (2135 days)
of operation and concluded that uranium and thorium contribute
20 ± 9 TW to the Earth heat flux (Kamland collaboration (Gando, A.
and 65 collaborators), 2011. Adding the heat generated by potassium yields a total heat production of 24 TW for the BSE, compared
with a range of 14–20 TW for the geochemical estimates discusses
above. This number still comes with a large error bar because of the
uncertainty on the crustal contribution which dominates the local
geoneutrino flux. For determining mantle composition in heat producing elements, the crustal contribution to the geoneutrino flux
must be very accurately accounted for. As shown in this article,
estimates based on “global” models are inadequate, and precise
measurements of the variations in heat flux and crustal radioactivity near the observatory will be needed (Perry et al., 2009; Dye,
2010).
Several other experiments are already underway or planned to
obtain data on the geoneutrino flux from large exposure target in
different observatories in deep mines around the world (Sudbury,
Ontario, Canada, Homestake, South Dakota, USA) (Chen, 2006).
Sudbury is located within the Canadian Shield deep inside the continent. The geology of the structure and the regional framework are
very well documented (see all the papers collected by Ludden and
Hynes, 2000), and, despite local variations in radioactivity, the site
is one of most favorable available for geoneutrino studies on land.
The construction of a large mobile detector on the sea-floor is being
considered and its deployment, costly as it maybe, is definitely feasible and would open another window on the mantle (Dye et al.,
2006; Dye, 2010).
J.-C. Mareschal et al. / Journal of Geodynamics 54 (2012) 43–54
With very large detector exposures at several land observatories
and reliable models of crustal heat production, it will be possible
to resolve the crustal and mantle components of the neutrino flux.
Although the capability of measuring direction is not available
yet, it is an important goal because it will permit resolution of
radial variations in mantle composition with very large detector
exposures on land and on the sea floor.
Acknowledgements
The authors are grateful to Steve Dye who commented on a
draft of the manuscript and to two anonymous reviewers for their
constructive comments. They thank Francis Lucazeau at IPGP who
provided an updated data base of heat flux measurements. This
work was supported by NSERC (Canada) through a discovery grant
to JCM.
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