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letters to nature 604 NATURE | VOL 397 | 18 FEBRUARY 1999 | www.nature.com arise from the attempt to interpret complex behaviour within the limits of a favoured structure. The main conclusions drawn from the present ®rst-principles quantum simulations, together with those of ref. 23, are in accordance with a model that is deduced from, and is claimed to be consistent with, all known experimental data 33 . M

Magmatic sheet intrusions (dykes) constitute the main form of magma transport in the Earth’s crust. The size distribution of dykes is a crucial parameter that controls volcanic surface deformation and eruption rates and is required to realistically model volcano deformation for eruption forecasting. Here we present statistical analyses of 3,676 dyke thickness measurements from different tectonic settings and show that dyke thickness consistently follows the Weibull distribution. Known from materials science, power law-distributed flaws in brittle materials lead to Weibull-distributed failure stress. We therefore propose a dynamic model in which dyke thickness is determined by variable magma pressure that exploits differently sized host-rock weaknesses. The observed dyke thickness distributions are thus site-specific because rock strength, rather than magma viscosity and composition, exerts the dominant control on dyke emplacement. Fundamentally, the strength of geomaterials is scale-dependent and should be approximated by a probability distribution.

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[1] Ongoing deglaciation in Iceland not only causes uplift at the surface but also increases magma production at depth due to decompression of the mantle. Here we study glacially induced decompression melting using 3-D models of glacial isostatic adjustment in Iceland since 1890. We find that the mean glacially induced pressure rate of change in the mantle increases melt production rates by 100-135%, or an additional 0.21-0.23 km 3 of magma per year beneath Iceland. Approximately 50% of this melt is produced underneath central Iceland. The greatest volumetric increase is found directly beneath Iceland's largest ice cap, Vatnajökull, colocated with the most productive volcanoes. Our models of the effect of deglaciation on mantle melting predict a significantly larger volumetric response than previous models which only considered the effect of deglaciation of Vatnajökull, and only mantle melting directly below Vatnajökull. Although the ongoing deglaciation significantly increases the melt production rate, the increase in melt supply rate at the base of the lithosphere is delayed and depends on the melt ascent velocity through the mantle. Assuming that 25% of the melt reaches the surface, the upper limit on our deglaciation-induced melt estimates for central Iceland would be equivalent to an eruption the size of the 2010 Eyjafjallajökull summit eruption every seventh year.