Dike propagation through an elastic plate

Abstract

We study the vertical propagation of a magma‐filled crack which rises due to buoyancy through an elastic plate of finite thickness. The plate rests on a magma source of large volume. Full time‐dependent solutions of the coupled problem with elastic deformation and viscous flow in a thin fracture are obtained numerically. A range of initial conditions corresponding to different regimes of fracture filling, from passive conditions at negligible magma velocity to forceful injection, are investigated. Three phases are distinguished during ascent. In a first phase, as the dike grows out of the initial magma‐filled fracture, the elastic pressure distribution adjusts to a fully developed distribution, with values close to buoyancy in a nose region and smaller values in a conduit region below the nose. Subsequently, the dike develops increasingly wider conduit and nose regions. Close to the plate upper boundary, stress and displacement fields become sensitive to the width of the plate. The initial conditions determine quantitative characteristics of subsequent dike propagation and, in particular, the flux of magma into the dike. As a dike propagates away from source, magma encounters increasingly colder rock but flows through an increasingly wider channel. This provides a self‐shielding mechanism against freezing. At the upper boundary, eruption initially occurs out of the inflated nose region and is driven by the relaxation of elastic stresses.