Recent asymptotic analysis for the slow, steady ascent of a zero-traction sphere in a power-law fluid with temperature-dependent viscosity is applied to the derivation of a model for magmatic diapirism in the Earth's mantle and continental crust. As an example, the model is applied to the case of a mantle diapir rising through country rock that is treated as a strongly shear-thinning fluid. It is found that, within the geologically relevant timescale of 10~5 years, the diapir would only encounter two of the four possible asymptotic regimes that the earlier analysis uncovered, before stalling at a considerably greater depth below the Earth's surface than was predicted by an earlier model. The implications of this result for the modelling of magmatic diapirism are discussed.
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