Geology Reference
In-Depth Information
25
24
400 kJ/mol
23
22
200 kJ/mol
21
20
19
18
1000
1100
1200
1300
1400
1500
1600
Temperature (
°
C)
Figure 4.4. Dependence of viscosity on temperature. Each curve is labelled with
its activation energy.
Examples of the dependence of viscosity on temperature for two different acti-
vation energies are shown in Figure 4.4. Activation energies are not easy to deter-
mine, and there is some debate about which value applies to the upper mantle.
The value also depends on whether the mantle is really a linear viscous fluid or
has a more nonlinear dependence on stress [39]. Pressure tends to increase the
activation energy (strictly speaking, it increases the activation enthalpy), so the
sensitivity of viscosity to temperature is likely to be even stronger in the deep
mantle.
4.4 Inevitable convection
This strong dependence of mantle viscosity on temperature plays a very important
role in mantle convection. It is the reason the lithosphere is much stronger than
the underlying mantle. It also controls the form of mantle plumes, as we will
see in Chapter 7. Also, Tozer [40] argued in 1965, at a time when convection
throughout the mantle was still controversial, that the temperature dependence of
mantle viscosity made convection virtually inevitable in an Earth-sized planet.
Tozer's argument was that the planet would presumably be heated to some degree
by the release of gravitational energy as it accreted from fragments orbiting the
Sun. Radioactivity would then slowly heat it more. The conductivity of rocks is low,
and conduction would only cool the planet to a depth of around 500 km over the
age of the Earth. Sooner or later the deeper interior would become hot enough that
the mantle viscosity was reduced to a value that permitted convection. Thereafter
the mantle temperature and viscosity would self-regulate to remove whatever heat
