Heat - The Solid Earth - page 306

Figure 7.17. Since
temperatures in the
mantle are approximately
adiabatic, the temperature
of rising mantle material
follows the adiabat. The
rising mantle material is
initially too cool to melt.
At point M, where the
mantle adiabat and the
melting curve intersect,
melting starts. The
melting rock then follows
the melting curve until the
melt separates from the
residue S. The melt then
rises to the surface as a
liquid along a liquid
adiabat.

Temperature

liquid
adiabat

S

M

SOLID LIQUID

the lower mantle the temperature gradient is also likely to be adiabatic and may
be adiabatic down to the boundary layer at the base of the mantle. However, some
calculations of the temperature for the basal 500-1000 km of the lower mantle
give a gradient significantly greater than that of the adiabat. Calculated values
for the mantle temperature close to the core-mantle boundary consequently vary
widely, ranging from 2500 K to 4000 K (Fig. 7.16).

The adiabatic gradient can also tell us much about melting in the mantle.
For most rocks, the melting curve is very different from the adiabatic gradient
(Fig. 7.17), and the two curves intersect at some depth. Imagine a mantle rock
rising along an adiabat. At the depth at which the two curves intersect, the rock
will begin to melt and then rises along the melting curve. At some point, the melted
material separates from the solid residue and, being less dense, rises to the surface.
Since melt is liquid, it has a coefficient of thermal expansion

∼

greater than that
of the solid rock. The adiabat along which the melt rises is therefore considerably
different from the mantle adiabat (perhaps 1 ◦ Ckm − 1 instead of 0.4 ◦ Ckm − 1 ).
One way of comparing the thermal states of rising melts is to define a potential
temperature T p ,which is the temperature an adiabatically rising melt would have
at the Earth's surface. T p is therefore the temperature at the theoretical intersection
of the adiabat with z

α

0, the surface. Integrating Eq. (7.94)gives the potential
temperature T p for a melt at depth z and temperature T :

=

T p = T e − α gz / c P (7.95)

The potential temperature T p is a constant for that melt and so is unaffected by
adiabatic upwelling.
Equation (7.94) can also be used to estimate temperature gradients in the outer
core, where temperatures are constrained by the solidus of iron (Section 8.3).