Diapiric ascent of magmas through power law crust and mantle

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Abstract
There has never been a convincing explanation of the way in which diapirs of molten granite can effectively rise through mantle and crust. We argue here that this is mainly because the country rocks have previously been assumed to be Newtonian, and we show that granitoid diapirs rising through thermally graded power law crust may indeed rise to shallow crustal levels while still molten. The ascent velocity of diapirs is calculated through an equation with the form of the Hadamard‐Rybczynski equation for the rise of spheres through Newtonian ambient fluids. This well‐known equation is corrected by factors dependent on the power law exponent n of the ambient fluid and the viscosity contrast between the drop and the ambient fluid. These correction factors were derived from results reported in the fluid mechanical and chemical engineering literature for the ascent of Newtonian drops through power law fluids. The equation allows calculation of the ascent rates of diapirs by direct application of rheological parameters of rocks. The velocity equation is numerically integrated for the ascent of diapirs through a lithosphere in which the temperature increases with depth. The depth of solidification of the diapir is systematically studied as a function of the geothermal gradient, buoyancy of the body, solidus temperature of the magma, and rheological parameters of the wall rock. The results show that when the wall rock behaves as a power law fluid, the diapir's ascent rate increases, without a similar increase in the rate of heat loss. In this way, diapirs rising at 10 to 102 m/yr can ascend into the middle or upper crust before solidification. Strain rate softening rather than thermal softening is the mechanism that allows diapirism to occur at such rates. The thermal energy of the diapir is used to soften the country rock only at late stages of ascent. The transport of magmas through the lower crust and mantle as diapirs is shown to be as effective as magmatic ascent through fractures.