  Partial melting of asthenospheric mantle generates magma that supplies
volcanic systems. The timescale of melt extraction from the mantle has been
hotly debated. Microstructural measurements of permeability typically suggest
relatively slow melt extraction (1 m/yr) whereas geochemical (Uranium-decay
series) and geophysical observations suggest much faster melt extraction (100
m/yr). The deglaciation of Iceland triggered additional mantle melting and
magma flux at the surface. The rapid response has been used to argue for
relatively rapid melt extraction. However, this episode must, at least to some
extent, be unrepresentative, because the rates of magma eruption at the surface
increased about thirty-fold relative to the steady state. Our goal is to
quantify this unrepresentativeness. We develop a one-dimensional,
time-dependent and nonlinear (far from steady-state), model forced by the most
recent, and best mapped, Icelandic deglaciation. We find that 30 m/yr is the
best estimate of the steady-state maximum melt velocity. This is a factor of
about 3 smaller than previously claimed, but still relatively fast. We
translate these estimates to other mid-ocean ridges accounting for differences
in passive and active upwelling and degree of melting. We find that fast melt
extraction greater than about 10 m/yr prevails globally.
