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interior make chemical segregation essentially
irreversible. The outer parts of Earth contain
most of the heat-producing elements and supply
much of the secular-cooling part of the present
heat flow.
The major outstanding problems in the
Earth's thermal budget and thermal history
involve the role of hydrothermal circulation near
the top, and the role of radiative transfer of heat
near the bottom of the mantle. Convection mod-
eling has not yet covered the parameter range
that seems most pertinent from physical consid-
erations and geophysical data. The largest fail-
ings in this regard are the neglect of pressure
effects on material properties, and the use of
parameterized convection. What is needed is a
thermodynamically self-consistent approach that
includes the temperature, pressure and volume --
dependence of physical properties, realistic ini-
tial and boundary conditions, and the ability to
handle melting. Modeling has focused on models
that are do-able, and which are perceived by
modelers to represent constraints from other
fields. These include whole-mantle convection or
layered convection models with mass transfer
between layers, the persistence of large isolated
mantle
The perceived mismatch between heat sources
and surface heat flow and the assumption of a
homogenous upper mantle and undepleted lower
mantle have led to a series of complex propos-
als regarding mantle overturns and depths of
recycling. Continents affect the form of man-
tle heat loss; continents drift so as to be over
cold downwellings or near trenches. The stabil-
ity of cratonic roots and the temperatures of
komatiites do not constrain the thermal evolu-
tion of ocean basins or the rate of mantle con-
vection. Higher mantle temperatures may have
led to more vigorous convection (the Tozer effect)
but increased melting also removes volatiles and
increases the viscosity and strength of the upper
mantle-plate system. The Hadean and Archean
mantle may have been capped by a thick buoyant
unsubductable layer and may have been drier and
higher viscosity than the current mantle. There
appears to be no mismatch between observed
heat flow and plausible sources of heating.
Current radioactive heating is just part of the
equation. There are many open questions and
opportunities for new approaches and ideas are
enormous. The uncertainties are large and we
must not make the same mistake as Lord Kelvin,
who was confident in his estimate of the age of
the Earth.
reservoirs,
and
the
need
for
vigorous
chaotic stirring.
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