Fluid‐mechanical models of crack propagation and their application to magma transport in dykes

Abstract

The ubiquity of dykes in the Earth's crust is evidence that the transport of magma by fluid‐induced fracture of the lithosphere is an important phenomenon. Magma fracture transports melt vertically from regions of production in the mantle to surface eruptions or near‐surface magma chambers and then laterally from the magma chambers in dykes and sills. In order to investigate the mechanics of magma fracture, the driving and resisting pressures in a propagating dyke are estimated and the dominant physical balances between these pressures are described. It is shown that the transport of magma in feeder dykes is characterized by a local balance between buoyancy forces and viscous pressure drop, that elastic forces play a secondary role except near the dyke tip and that the influence of the fracture resistance of crustal rocks on dyke propagation is negligible. The local nature of the force balance implies that the local density difference controls the height of magma ascent rather than the total hydrostatic head and hence that magma is emplaced at its level of neutral buoyancy (LNB) in the crust. There is a small overshoot beyond this level which is calculated to be typically a few kilometres. Magma accumulating at the LNB will be intruded in lateral dykes and sills which are directed along the LNB by buoyancy forces since the magma is in gravitational equilibrium at this level. Laboratory analogue experiments demonstrate the physical principle of buoyancy‐controlled propagation to and along the LNB. The equations governing the dynamics of magma fracture are solved for the cases of lithospheric ascent and of lateral intrusion. Volatiles are predicted to be exsolved from the melt at the tips of extending fractures due to the generation of low pressures by viscous flow into the tip. Chilling of magma at the edges of a dyke inhibits cross‐stream propagation and concentrates the downstream flow into a wider dyke. The family of theoretical solutions in different geometries provides simple models which describe the relation between the elastic and fluid‐mechanical phenomena and from which the lengths, widths and rates of propagation can be calculated. The predicted dimensions are in broad agreement with geological observations.