Modeling the Shape and Velocity of Magmatic Intrusions, a New Numerical Approach. Issue 3 (11th March 2023) - Furst, S.; Maccaferri, F.; Pinel, V.
Abstract: Dykes are magma‐filled fractures propagating through the brittle crust. Understanding the physics of dyking process is essential to mitigate the volcanic hazard associated with the opening of new eruptive fissures at the surface. Often, physics‐based models view either fracturing of the host rock or viscous flow of the magma as the dominating energy sink during dyke propagation. Here, we provide a numerical model that captures the coupling of fracturing at the crack tip and the transport of a viscous fluid. Built with the boundary element technique, our model allows for computation of the shape and velocity of a growing fluid‐filled crack accounting for the viscosity of the fluid: the fluid flow induces a viscous pressure drop acting at the crack walls, and modifies the shape of the crack. The energy conservation equation provides the constraints to solve for the crack growth velocity, assuming that brittle fracturing and viscous flow are the main processes that dissipate energy. Using a parameter range that represents typical magmatic intrusions, we obtain crack shapes displaying some typical characteristics, including a tear‐drop head and an open tail that depend on rock rigidity, magma viscosity, and buoyancy. We show that viscous forces significantly contribute to the energy dissipated during the propagation of magmatic dykes. Applied to the 1998 intrusion at Piton de la Fournaise (La Réunion Island), we provide ranges of dyke lengths and openings by adjusting the numerical velocity to the one deduced from the migration of volcano‐tectonic events. Plain Language Summary: Magma is a viscous fluid that can propagate through the crust by fracturing rocks and flowing through them. These magma‐filled fractures are called dykes. Magma pressure is the force ensuring the opening of the fracture and maintaining the flow of magma. Although physics‐based models provide simplified but reliable representations of dykes, few consider both fracture creation and viscous flow simultaneously. Here, we present a new model for magmatic dyke propagation, implementing viscous flow equations into an existing model, such that the dyke shape, trajectory, and velocity are determined together. We show that the viscous dissipation within the magma is a major contribution to the energy balance for a range of viscosity and velocity values which are typical for magmatic intrusions. The dyke shapes obtained with our model compare well with the ones obtained with previous models. The velocity derived from the model has been compared with that derived from the spatio‐temporal evolution of seismic events recorded before the 1998 eruption at Piton de la Fournaise. Our new modeling scheme may represent a step forward in predicting the timing and location of future eruptions at monitored volcanoes. Key Points: We present a new modeling scheme to compute the shape and velocity of a growing fluid‐filled crack Our magmatic dykes show a tear drop head and open tail, on a wide range of propagation velocities We reproduce the velocity and fit important parameters for the 1998 Piton de la Fournaise intrusion