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trying to calculate. The situation can be retrieved with a bit of algebra. Squaring
both sides yields
v 2
( 0 αT D/ 12 μ ) 2 (4 κD/v ) ,
=
so
v 3
( 0 αT D/ 12 μ ) 2 (4 κD )
D 3 ( 0 αT 2 κ 1 / 2 / 12 μ ) 2
=
=
and finally
D 0 αT κ
6 μ
2 / . 3
v
=
.
(5.18)
This expression involves only g , the temperature and some material properties.
Let's try evaluating it with T
1300 C and other quantities as used before. This
=
10 9 m/s, which is 0.115 m/yr or 11.5 cm/yr. Thus our extended
theory yields a result within a factor of 2 of observed plate velocities, which are
around 5 cm/yr.
It is time to review this chapter. We have reproduced the observed velocities
of tectonic plates using a theory that assumes plate motions are governed by a
balance between the (thermal, negative) buoyancy of a sinking plate and the viscous
resistance of the fluid mantle. The theory, in its extended form, also assumes that
plates are a cool thermal boundary layer formed by conductive cooling to the
Earth's surface. The only inputs have been the inferred temperature and viscosity
of the mantle, and some other material properties established by experiments. Thus
we have used a simple theory of convection to predict the velocities of tectonic
plates, and have achieved an agreement that is within the expected uncertainties of
the approximate theory and the uncertainties of the inputs. We now have a possible
answer to the question: 'What drives the plates?' The answer is that the plates drive
themselves, because they are the active part of a form of mantle convection.
Does this 'prove' that this is why plates move? No, there might be a theory
involving other forces that can also match the observations. But it does show that
our simple theory can explain the observations, so it is a candidate for a good theory
of why plates move. Finally, I hope there is no mystery in how we got to this point.
We examined viscous fluid flow and we examined thermal expansion and thermal
buoyancy. Then we put those things together to deduce plate velocities, using
observational or experimental inputs to evaluate the required terms. Convection can
be understood in fairly simple physical terms. It is not just something mysterious
that happens 'down there'.
In the interpretation made here, tectonic plates do not ride passively on something
mysteriously overturning down there. Tectonic plates are the active components
in a form of mantle convection - they are the cool thermal boundary layer of
gives v
=
3.6
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