Abstract
Abstract. An inverse method is devised to probe Earth's thermal state without assuming its mineralogy. This constrains thermal conductivity (κ) in the lower mantle (LM) by combining seismologic models of bulk modulus (B) and pressure (P) vs. depth (z) with a new result, ∂ln(κ) / ∂P ∼ 7.33/BT, and available high temperature (T) data on κ for lengths exceeding millimeters. Considering large samples accounts for the recently revealed dependence of heat transport properties on length scale. Applying separation of variables to seismologic ∂B/∂P vs. depth isolates changes with T. The resulting LM dT / dz depends on ∂2B/∂P2 and ∂B/∂T, which vary little among dense phases. Because seismic ∂B/∂P is discontinuous and model dependent ∼ 200 km above the core, unlike the LM, our results are extrapolated through this tiny layer (D′′). Flux and power are calculated from dT / dz for cases of high (oxide) and low (silicate) κ. Geotherm calculations are independent of κ, and thus of LM mineralogy, but require specifying a reference temperature at some depth: a wide range is considered. Limitations on deep melting are used to ascertain which of our geotherm, flux, and power curves best represent Earth's interior. Except for an oxide composition with miniscule ∂2B/∂P2, the LM heats the core, causing it to melt. Deep heating is attributed to cyclical stresses from > 1000 km daily and monthly fluctuations of the barycenter inside the LM.
Highlights
The models yield smoothly varying properties and their derivatives over most of the lower mantle (LM), the changes of which are taken in this report to represent combined effects of P and T varying with depth
Gradual changes in chemical composition could be hidden in our choices for B if changes in mineralogy lead to a linear response of ∂B/∂P
Mineralogy depending linearly on density and on P would lead to an equation equivalent to Eq (6)
Summary
Heat moves when a temperature (T ) difference exists, where the net flow is from hotter to colder regions. This phenomenon is important to Earth because it is dynamic. 1.1 Recent findings on heat transport properties relevant to mantle studies. One incorrect presumption is that the physical properties representing heat flow (thermal conductivity, κ, or its close relative thermal diffusivity, D) are independent of the distance along the thermal gradient. This static view is inconsistent with Fourier’s heat equation, as follows.
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