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 10(2) 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.