Distribution of Temperature and Heat Flux in the Earth: The Influence of Sphericity of the Mantle

Abstract

The structure of thermal convection is determined by the spatial distribution of temperature in the mantle. However, in the literature, when modeling various manifestations of convection, little attention is paid to the degree of correspondence of the temperature distribution calculated in the model with the real temperature in the mantle, and often the temperature distribution is not even presented. In this paper, we analyze the effect on the distribution of temperature and heat fluxes of internal heat sources and the sphericity of the mantle, as well as the effects of dissipation and adiabatic compressibility. Using the Cartesian model leads to a large discrepancy between the calculated distribution of the heat flux and temperature with the observational data. It is shown that the effect of sphericity of the mantle can be approximately interpreted as an additional effective negative internal heat source. At the same time, for the parameters of the modern Earth, it turned out by chance that this effective source is approximately equal in modulus (or rather somewhat more) to the real positive internal heat source (due to radioactivity and secular cooling) and compensates for it. Therefore, the numerous literature results of modeling mantle convection in Cartesian coordinates including internal heat sources are poorly consistent with the actual temperature in the mantle. For the convection model in the modern mantle, this discrepancy can be approximately eliminated by simply eliminating real internal heat sources from the convection equations. The depth distribution of temperature in the mantle of the modern Earth is presented, which is optimally consistent with both the available measurement data (reference points) and the results of refined numerical modeling.