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

Grose, Christopher J. and Afonso, Juan C. (2019) New Constraints on the Thermal Conductivity of the Upper Mantle from Numerical Models of Radiation Transport. Geochemistry, Geophysics, Geosystems, 20 (5). pp. 2378-2394. ISSN 1525-2027. doi:10.1029/2019gc008187.

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To address uncertainties in the values and mathematical form of the radiative thermal conductivity k_(rad) 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 k_(rad) 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 k_(rad) 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 k_(rad) increases net cooling by about 25%.

Item Type:Article
Related URLs:
URLURL TypeDescription
Grose, Christopher J.0000-0002-8318-1649
Afonso, Juan C.0000-0001-9938-6692
Additional Information:© 2019 American Geophysical Union. Received 14 JAN 2019; Accepted 7 APR 2019; Accepted article online 13 APR 2019; Published online 22 MAY 2019. Thanks to Alexander Goncharov and Hans Keppler for helpful comments regarding their experimental results, and to John Howell for insightful comments regarding the n2 factor in the radiation source function. George Rossman also provided insight on the available spectral data and values in the far infrared. Thanks to two reviewers for critical comments. The work of J. C. Afonso has been supported by two Australian Research Council Discovery Grants (DP120102372 and DP110104145). J. C. Afonso also acknowledges support from the Research Council of Norway through its Centers of Excellence funding scheme, Project 223272. C. J. Grose acknowledges support from NSF (grant 1826310). This is contribution 1341 from the Australian Research Council Centre of Excellence for Core to Crust Fluid Systems ( and 1308 in the GEMOC Key Centre ( Data Statement: As this is a modeling study we do not report new data. Quantitative information consists of model results which are illustrated in the figures and discussed in the text. Modeling details are described in the supporting information. A MATLAB code for calculating k_(rad) using our effective medium theory is also available in the supporting information.
Group:Seismological Laboratory
Funding AgencyGrant Number
Australian Research CouncilDP120102372
Australian Research CouncilDP110104145
Research Council of Norway223272
Subject Keywords:thermal conductivity; heat transport; potts model; radiation; effective medium theory; scattering
Issue or Number:5
Record Number:CaltechAUTHORS:20190415-132901215
Persistent URL:
Official Citation:Grose, C. J., & Afonso, J. C. C. (2019). New constraints on the thermal conductivity of the upper mantle from numerical models of radiation transport. Geochemistry, Geophysics, Geosystems, 20, 2378–2394.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94709
Deposited By: Tony Diaz
Deposited On:16 Apr 2019 18:59
Last Modified:16 Nov 2021 17:07

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