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We present a sequence of numerical experiments studying thermal plumes that arise from the basal thermal boundary layer in a spherical axisymmetric convecting fluid, reporting the geoid, topographic (swell), and heatflow anomalies. We consider the influence of spherical geometry, temperature and pressure dependence of rheology, internal heat generation, pressure-dependent coefficient of thermal expansion, the Clapeyron slope of the endothermic phase transformation, and compositional layering at the base of the mantle on the structure and dynamics of thermal plumes and resulting geophysical anomalies. This fluid system simplifies a number of complexities within the Earth (e.g., it is not compressible, does not include plate motions, enforces axisymmetric symmetry, and has a simple equation of state); however, this system is computationally tractable and provides an opportunity to evaluate each effect in a systematic fashion. With the assumptions listed above, we are formally unable to reproduce the observed hotspot swell, heatflow, and geoid anomalies from the resulting thermal plumes. The calculations that most closely approach the observed geoid, topographic, and heatflow anomalies contain all the effects mentioned above. One particularly interesting aspect of these calculations is that when we include a depth-dependent coefficient of thermal expansion, the plume conduits in the lower 500 km of the mantle are more than 200 km in diameter wider than with an otherwise identical, uniform coefficient of thermal expansion calculation. We speculate that the lack of mobile plates in our calculations, which would both advect upwelling material away from the plume conduit and change the global cooling mechanism, is a major shortcoming and that it may be possible to reconcile thermal plume calculations with the geoid, topographic, and heatflow observations if we included mobile plates.

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