Acceleration of buoyancy-driven fractures and magmatic dikes beneath the free surface

By performing buoyancy-driven fracture experiments in brittle gelatin we observe that the ascent velocity of a fracture containing a finite volume of fluid increases when approaching the free surface. We theoretically describe this free-surface effect and quantify it by introducing an effective depth-dependent fracture toughness and developing an ascent model on the basis of linear fracture mechanics. We develop a successful inversion approach and resolve the actual and critical fracture length and the ascent velocity far away from the free surface from the observation of the fracture tip migration alone. Other parameters, as the fluid volume included in the fracture and the in situ fracture toughness, can be derived. Applying the model and inversion to the 1998 eruption at Piton de la Fournaise, Reunion Island, reveals estimates of the length and critical length of the feeding magma batch, the magma batch volume and the in situ fracture toughness. It further indicates that the ascent velocity of the magma batch was probably much smaller at greater depths and that the batch might have been initiated several months or years before the eruption.