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Calculations of mantle convection generally use constant rates of internal heating and time-invariant core-mantle boundary temperature. In contrast, parameterized convection calculations, sometimes called thermal history calculations, allow these properties to vary with time but only provide a single average temperature for the entire mantle. Here I consider three-dimensional spherical convection calculations that run for the age of the Earth with heat-producing elements that decrease with time, a cooling core boundary condition, and a mobile lid. The calculations begin with a moderately hot initial temperature, consistent with a relatively short accretion time for the formation of the planet. I find that the choice of a mobile or stagnant lid has the most significant effect on the average temperature as a function of time in the models. However, the choice of mobile versus stagnant lid has less of an effect on the distribution of hot and cold anomalies within the mantle, or planform. I find the same low-degree (one upwelling or two upwelling) temperature structures in the mobile-lid calculations that have previously been found in stagnant-lid calculations. While having less of an effect on the mean mantle temperature, the viscosity of the asthenosphere has a profound effect on the pattern of temperature anomalies, even in the deep mantle. If the asthenosphere is weaker than the upper mantle by more than an order of magnitude, then the low-degree (one or two giant upwellings) pattern of temperature anomalies results. If the asthenosphere is less than an order of magnitude weaker than the upper mantle, then the pattern of temperature anomalies has narrow cylindrical upwellings and cold downgoing sheets. The low-degree pattern of temperature anomalies is more consistent with the plate model than the plume model.

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