New Constraints on the Thermal Conductivity of the Upper Mantle From Numerical Models of Radiation Transport

Abstract

To address uncertainties in the values and mathematical form of the radiative thermal conductivity krad in the mantle, we developed new models for the transport, scattering, and absorption of thermal radiation in semitransparent multiphase polycrystalline assemblages. We show that the Rosseland diffusion equation correctly describes the diffusion of thermal radiation and infer the form of the effective spectral coefficients through numerical experimentation. We show that the scattering coefficient depends on the grain size and on interphase contact statistics in complicated ways, but that simplifications can be employed in practice. The effective opacity of a composite random material is a harmonically weighted mixture in the limit of infinitely large grain size and an arithmetically weighted mixture in the limit of infinitesimal grain size. Using existing absorption spectra for major upper mantle minerals, we estimate krad as a function of temperature, grain size, and petrology. In mantle assemblages, the scattering effect is important for small grain sizes (<1 mm), but the grain size effect on the effective opacity of a multiphase medium is important for grain sizes up to 10 cm. We calculate that upper mantle krad is about 2–3.5 W·m−1·K−1 for a representative mean grain size range of 0.01 to 1 cm. This translates to a total thermal conductivity of 5.5–7 W·m−1·K−1. Application of our model to the cooling of oceanic lithosphere shows that krad increases net cooling by about 25%.

Structure and dynamics of the oceanic lithosphere-asthenosphere system

“…Incorporating this range for the lattice conductivity introduces variation in the optimal mantle potential temperature of˘115˝C, and plate thickness of˘5 km. Furthermore, there remains significant debate surrounding the magnitude of the radiative component of thermal conductivity and how it may vary as a function of pressure and temperature (Shankland et al, 1979;Hofmeister, 2005;Grose and Afonso, 2019b). Therefore, tighter experimental constraints on thermal conductivity are likely to provide the largest reduction in the range of parameters obtained by lithospheric cooling models.…”

High-pressure evolution of the refractive index of MgO up to 140 GPa

“…2,3 The change of refractive index with pressure is also of direct importance to geophysics because radiative thermal conductivity, which is believed to increase with depth in the Earth, is proportional to n 2 . 4,5 Furthermore, refractive index of materials at high pressure allows the determination of diamond-diamond separation in diamond anvil cell (DAC) experiments, which in turn is a key parameter needed to determine thermal/electrical conductivities of materials in DAC experiments. The existent large discrepancy in the thermal conductivities of the Earth's mantle and core, [6][7][8][9][10][11][12][13][14][15] based on DAC experiments, may be rooted in the inadequate assessment of samples' thickness at high pressure.…”

Anisotropic thermal conductivity of antigorite along slab subduction impacts seismicity of intermediate-depth earthquakes

“…S 9 ): (A) olivine Λ DryOl , Λ WetOl 41 , 47 , ρ Ol 83 and Cp Ol 83 ; (B) antigorite Λ Atg (this study), ρ Atg 32 , 44 , Cp Atg 32 . The aggregate thermal conductivity of the hydrous layer was computed with the geometric average of olivine and antigorite contributions 84 (Note S 3 ): Λ HydLayer (Λ Ol ) φOl (Λ Atg ) φAtg . We chose to use geometric averaging because it provides the best correlation between the computed and the measured thermal conductivity of a random grainy medium 85 .…”