When dikes go critical: Fracture toughness and propagation dynamics using earthquake catalogs

Dikes represent magma filled fractures that may propagate from a magma chamber to the surface producing an eruption, or alternatively may stall at some depth resulting only in deformation and seismicity. A crucial parameter for the modeling of dike propagation is fracture toughness, which can be defined as the critical stress intensity factor that is necessary for a fracture to propagate. Despite the fact that fracture toughness is a well defined physical quantity adopted from material science, its meaning and possible variation in volcanic environments remains poorly understood. Dike volume can provide valuable information on the level of fracture toughness and on its balance with viscous flow that ultimately determines the dynamics of dike propagation. Recently it has been shown that intrusion volume can be derived from the cumulative seismic moment release of earthquakes that accompany dike propagation. Here it is shown that a similar methodology can be utilized in order to reconstruct the volume history of dikes using high-quality earthquake catalogs from 8 volcanoes (Augustine, Bardarbunga, Cumbre Vieja, Etna, Hierro, Kilauea, Okmok, Redoubt) spanning different volcanological and tectonic settings. The pre-eruption dike volume is compared to Monte Carlo simulations of critical volume performed for a range of fracture toughness and density difference using realistic values of elastic moduli and Poisson ratio. The volume history for each eruption is also utilized for estimating magma flux rate in the dike in order to infer whether fracture toughness or viscous flow dominates dike propagation. Results show that in all the volcanoes considered fracture toughness of 100 MPa m^1/2 can explain pre-eruption volumes indepedently of volcano type and length scale of the dike. In 6 out of 8 eruptions studied dike propagation fluctuated between being dominated by fracture toughness and viscous flow, while only in two cases propagation was driven almost exclusively by viscous flow.