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Jackson & Pollack 1984
Jackson, M.J. and Pollack, H.N. (1984). On the sensitivity of parameterized convection to the rate of decay of internal heat sources. Journal of Geophysical Research 89: doi: 10.1029/JB080i012p10103. issn: 0148-0227.

Thermal histories for the earth based on parameterized mantle convection models have previously indicated that the earth departs significantly from a steady thermal state. The non-steady state is manifested by a present-day excess of heat loss over heat production. We investigate the dependence of the heat production/heat loss ratio and mantle viscosity on heat source decay rate by varying the relaive and absolute concentrations of the heat-producing isotopes of K, U, and Th in the mantle. We examine three models with progressively increasing effective half-lives, respectively characterized by K/U ratios of 6¿104 (''chondritic''), 1¿104 (''terrestrial''), and 0.25¿104(''low K/U''). Each of these models can be constrained to yield a common present-day heat flow, mantle temperature, and mantle viscosity, thus demonstrating the inability of those present-day constraints to differentiate between widely varying blends of the earth's nuclear fuel. The present-day heat production/heat loss ratio ranges from about 73% for the chondritic model to about 86% for the low K/U model. Other possible criteria diagnostic of the earth's radioisotope mix are the present-day isotopic abundances. The low K/U model requires U and Th greater by a factor of 2.5 over the chondritic model and K less by a factor of 10. However, measurements of concentrations in candidate mantle rocks reveal a range that far exceeds the relatively small variations that distinguish the different compositional models. Paleothermal conditions also may be indicative of the earth's radiosotope blend. The thermal state in the Archean calculated for the low K/U earth model is characterized by a mean mantle temperature about 100¿C hotter and heat flow about 2 times greater than the present-day, whereas a chondritie earth model yields a mantle temperature 300¿C hotter and heat flow 4 times greater. However, current estimates of paleo-heat and mantle melting temperatures are burdened with uncertainties sufficiently large to preclude their use as criteria diagnostic of the earth's radioisotope endowment.

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Journal
Journal of Geophysical Research
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American Geophysical Union
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