The thermal profile in the Earth's interior is influenced by many factors. One of the least understood and studied processes is that resulting from adiabatic heating and viscous dissipation. With the exception of the work by Jarvis and McKenzie1 very little has been done on the effects of compressibility on mantle circulation. It is quite common for geophysicists to add the adiabatic temperature gradient a posteriori2 to temperature profiles derived from Boussinesq (incompressible) equations. Recently it has been shown3 with the mean-field method4 that there exists a strong coupling between the Theological parameters, such as the activation volume, and the thermodynamic constants governing adiabatic heating. Here we point out the important consequences brought about by incorporating the effects of equations of state and rheology in the dissipative heating term of the energy equation. We demonstrate explicitly the ways in which compression may raise the interior mantle temperature and illustrate how this effect can, in turn, be used for constraining some of the intrinsic parameters associated with the equation of state in the mantle.
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Yuen, D., Quareni, F. & Hong, HJ. Effects from equation of state and rheology in dissipative heating in compressible mantle convection. Nature 326, 67–69 (1987). https://doi.org/10.1038/326067a0