Download Earth`s energy budget

Earth’s Energy Equation, simplified
Qsurface ≈ Hradioactive + Hmantle secular cooling + Qcore
Qsurface ≈ 44 TW (surface heat flow measurements)
Hradioactive ≈ 20 TW (chondrite-based composition models)
Hsecular cooling ≈ 9-18 TW (50-100 K/Ga, based on petrologic
studies and rates of continental uplift)
Qcore ≈ 2-15 TW (geodynamo requirements, age of inner
core, conductive heat flow across
core/mantle boundary layer, heat transport
by plumes)
How much heat are we loosing?
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Modified from Pollack et al. (1993)
•Generally accepted
global value is
~44±1 TW (c.f.,
Pollack et al., 1993)
•Hofmeister and
Criss (2005) argue
for much lower
surface heat flow
(~31 TW).
•Difference reflects
debate over the
importance of
hydrothermal
circulation in
transporting heat
near mid-ocean
ridges
Was mantle heat flow higher or lower in the past?
Standard view: Higher mantle temperatures in the early Earth
result in lower mantle viscosity, more rapid convection, and
higher surface heat flow.
Alternate view: Higher mantle temperatures in the early Earth
result in deeper initiation of mantle melting and extraction of
water and other volatile species. This increases viscosity of the
melt-depleted region, resulting in thicker, stiffer tectosphere,
more sluggish plate tectonics, and lower surface heat flow.
How much radiogenic heat production?
Major element trends in chondrite meteorites and mantle xenoliths
0.16
0.12
melt depletion
Al/Si
Nebular processes
0.08
0.04
0.00
0.60
0.80
1.0
1.2
Mg/Si
1.4
1.6
Al2O3 and U concentration variations in chondrites
18
16
[U] (ppb.)
Approx. U content of Earth
(~20-21 ppb in PM)
14
12
10
Approx. Al 2 O 3 content of Earth
(~4.2 wt.% in PM)
8
1.5
2.0
2.5
Al2O3 (wt.%)
3.0
3.5
How much potassium?
Bulk Silicate Earth Concentration
(normalized to CI)
10
1
K
Volatile loss
Cu
0.1
Core
formation
0.5%
Pb
1%
2%
4%
0.01
Sulfide segregation
0.001
0.0001
1800
1600
1400
1200
1000
800
50% Condensation temperature
(McDonough & Sun, 1995; Allegre et al., 2001)
600
400
K/U in MORB (Jochum et al., 1983)
20000
K/U
15000
Average = 12,700
10000
5000
0
500
1000
K (ppm)
1500
2000
Is the chondritic model valid?
146Sm
=> 142Nd
T1/2 = 103 Ma
Possible explanations for the
difference in 142Nd/144Nd in
terrestrial and chondritic
samples include:
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1) Earth has non-chondritic
relative abundances of Sm
and Nd, possibly due to
early impact erosion of
proto-crust.
2) There is an enriched
“hidden” reservoir with low
142Nd/144Nd somewhere in
the mantle.
Could a giant impact
such as the moonforming impact have
ejected an early protocrust rich in
incompatible heatproducing elements?
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This scenario could
account for the 142Nd
depletion in terrestrial
samples relative to
chondrites but would
suggest significantly
less than 20 TW
present-day radiogenic
heat production in the
Earth.
Hmantle secular cooling ≈ Mmantle*Cp*dT/dt
How can we estimate rates of mantle cooling?
Rates of continental uplift (constant freeboard argument) (c.f.,
Galer & Metzger,1996)
FeO-MgO or REE fractionation trends in Archaean basalts or
komatiites (adiabatic melting models) (c.f., Mayborn & Lesher,
2004)
“Lock-in” ages of lithospheric mantle xenoliths (coupling between
lithospheric and asthenospheric cooling) (c.f., Bedini et al., 2004)
All of these methods suggest mantle secular cooling of ~50120 K/Ga, and most suggest 50-60 K/Ga since the archaean,
but all are highly model-dependant.
How do we measure
mantle cooling rates?
Mantle cooling causes
uplift of continental crust
as the underlying mantle
becomes denser.
Average metamorphic
pressures of exposed
Archean terranes suggest
mantle cooling rates of
~50-60 Ga since 3 Ga.
From Galer & Metzger, 1996
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Constraints on heat flow across the core/mantle boundary
Power requirements of the geodynamo: ???
Conduction along outer core adiabat: ~7 TW
(c.f., Anderson, 2002)
Conduction across CMB: ~7-14 TW
(c.f., Buffett, 2003)
Heat transport by mantle plumes: ~2-13 TW
(c.f., Davies, 1988; Zhong, 2006)
Qcond = A(dT/dZ)
Qcond, CMB = ~8-14 TW
T = ~1000-1800 K
 = 9.5 Wm-1K-1
h = 200 km
(dT/dZ)oc = ~0.94 K/km

46 Wm-1K-1
Qcond, oc = ~7 TW
c.f., Anderson, 2002;
Buffett, 2003
Thermal consequences of inner core crystallization
Egrav = 4.1x1028 J
Elatent = 7x1028 J
Ecooling = 18.2x1028 J
Etotal = 29.3x1028 J
(+/- 18x1028J)
(Labrosse et al., 2003)
For CMB heat flow of 6-15
TW, age of onset of inner
core crystallization is less
than ~1.5 Ga.
Largest sources of uncertainty are core Cp, slope of melting curve.
Segregation of crust, either early in Earth history or
continuously through plate subduction, could store large
amounts of U, Th, and K at base of mantle
CMB
Core-mantle heat flow decreases with increasing
CMB radiogenic heat production
200
H
= 0 TW
H
= 10 TW
H
= 25 TW
CMB
Height above CMB (km)
CMB
CMB
150
Q
100
core
Q
core
Q
core
-3.3 TW
3.4 TW
=
7.8 TW
50
0
-1000
=
=
-800
-600
-400
-200
o
 T ( C)
0
200
4500
D" heat production = 10 TW
(primordial layer)
D" heat production = 10 TW
constant accumulation
O
Outer core temperature ( C)
D" heat production = 0 TW
4000
3500
4000
3000
2000
Time b.p. (Ma)
1000
0
Heat production within the core?
Experimental and theoretical studies suggest potassium
could partition into the core under the right circumstances.
•Potassium can enter sulfide liquids at low pressure
•At high pressure (>25 GPa) potassium acts like a transition
metal, can enter metal phases directly
•Low-pressure segregation of sulfides or high-pressure
core/mantle equilibration could result in significant quantities
of potassium in the Earth’s core.
Were the conditions necessary for potassium to enter the
Earth’s core present during core formation?
Effect of sulfide fractionation during core formation
on Cu concentrations in the mantle
Primitive Mantle (normalized to CI)
10
Volatile loss
1
Cu
0.1
Core formation
Pb
2% S
0.01
10% S
0.001
0.0001
1800
1600
1400
1200
1000
800
50% Condensation temperature (K)
(McDonough & Sun, 1995; Allegre et al., 2001)
600
400
CI-normalized
Primitive Mantle Concentration
Alkali metal depletion trend-volatile loss or core segregation?
1
Li
(s-p at ~1 TPa)
Volatile depletion trend
Na
(~100 GPa)
(~25 GPa)
K
Ga
Rb
(~10 GPa)
0.1
1100
K
(1)
(2)
(~5 GPa)
Cs
1060
1020
980
50% Condensation temperature
s-d transition pressures from Young (1991) and other literature sources
Condensation temperatures from Allegre et al. (2001) after Wasson (1985)
940
Silicate Earth K/Rb fractionation from high-P core formation
500
D
Rb
= 20x D (Hillgren et al., 2005)
K
Silicate Earth K/Rb
450
Estimated BSE value
400
350
300
250
Chondritic value
200
0
20
40
[K]
60
core
(ppm)
80
100
Questions an anti-neutrino observatory could help answer:
1) What is the total radiogenic heat budget of the Earth?
What is the composition of the Earth?
2) Are heat-producing elements concentrated in the lower
mantle or at the core/mantle boundary?
3) Does the core contain heat-producing elements?
What is really needed:
1) Detection of neutrinos or anti-neutrinos produced from
decay of 40K
2) Directional detectors