Hi Cosmo
You raise some interesting points. How do we know what we know about the temperature structure of the earth? The main source of our information is from studying the propogation of seismic waves generated by earthquakes through the centre of the earth.
This site seems to give a good introduction to the basics. To quote:
An earthquake occurs when rocks in a fault zone suddenly slip past each other, releasing stress that has built up over time. The slippage releases seismic energy, which is dissipated through two kinds of waves, P-waves and S-waves. The distinction between these two waves is easy to picture with a stretched-out slinky. If you push on one end of a slinky, a compression wave passes through the slinky parallel to its length. If instead you move one end of the slinky up and down rapidly, a ripple wave moves through the slinky. The compression waves are P-waves, while the ripple waves are S-waves. While both kinds of waves refract, or bend, when they cross a boundary into a different material, these two types of waves behave differently depending on the composition of the material they are passing through. One of the biggest differences is that S-waves cannot travel through liquids while P-waves can.
This is an important point, as the only part of the earth which S waves do not propogate through is the outer core. This tells us that whatever the inside of the earth is made of, in most places it cannot be hot enough to melt. We think much of the mantle is made of a rock known as peridotite, so we can use laboratory studies to plate upper limits on its temperature. At the core/mantle boundary (CMB), there's actually quite a narrow temperature range at which you can have solid peridotite and molten iron, so we can estimate the temperature of this boundary quite precisely (3000 C I seem to recall).
The other thing that seismic waves can tell us about is where there is an abrupt change in physical properties such as P and S wave propogation speed. When seismic waves meet these boundaries, some energy is reflected back towards the surface. These boundaries can be chemical and physical in nature. The principal two we see in the mantle are at 410 km at 660 km depth; laboratory studies of peridotite shows that as pressure increases it undergoes a number of 'phase transitions' - basically the crystalline structure alters to become more compact. The change in density changes the wave propogation speed. It is thought that the 410km and 660km discontinuities correspond to two of these phase transitions, which allows us to use the lab experiments to fix the mantle temperature at these points - about 1500 C at 440 km and 1900 C at 660 km.
so, in summary, temperature at:
440 km 1500 C
660 km 1900 C
CMB 3000 C
So I'm afraid there's no evidence of cooling beneath the crust (although the temperature gradient does decrease substantially - if it didn't the mantle would be hot enough to melt). There is also no evidence of any liquid bodies either, except the outer core.
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