Compaction and Crystallization in Magma Chambers: Towards a Model of the Skaergaard Intrusion

Abstract

The geochemical variations within the Skaergaard intrusion provide an opportunity to discover what features of the intrusion can be understood using the simplest form of the equations governing the two-phase flow of melt and matrix. The equations governing the conservation of mass, momentum and energy are first simplified by using the extended Boussinesq approximation, and then solved numerically to study the time-dependent behaviour of a compacting solidifying layer at the base of a magma chamber when variations in the horizontal plane can be neglected. The most important result is that the concept of a trapped liquid fraction, which has been widely used to model the bulk composition of layered intrusions, is a useful concept to describe the steady-state behaviour of compacting layers. This result is at first sight surprising, because there is relative movement between the melt and crystals during compaction, and the system is therefore open. The reason why it is useful is because both the melt and the crystals are moving downwards in a frame fixed to the upper surface of the compacting layer. Because the mass of all elements must be conserved, what goes into the top of the layer as melt and solid must come out of its bottom as a solid when the behaviour is not time dependent. However, when time-dependent behaviour occurs, the concept of a trapped liquid fraction ceases to be useful.The governing equations are used to model the concentration of phosphorus, uranium and rubidium in the lower part of the Skaergaard intrusion, where they behave incompatibly. The observed behaviour requires the viscosity of the solid part of the compacting layer to have a value of 10 Pa s.