A quasi-asymptotic model for the ascent of magmatic diapirs

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.