Weibull-distributed dyke thickness reflects probabilistic character of host-rock strength

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.