The Generation and Compaction of Partially Molten Rock

The equations governing the movement of the melt and the matrix of a partially molten material are obtained from the conservation of mass, momentum, and energy using expressions from the theory of mixtures. The equations define a length scale dc called the compaction length, which depends only on the material properties of the melt and matrix. A number of simple solutions to the equations show that, if the porosity is initially constant, matrix compaction only occurs within a distance ~<5C of an impermeable boundary. Elsewhere the gravitational forces are supported by the viscous stresses resulting from the movement of melt, and no compaction occurs. The velocity necessary to prevent compaction is known as the minimum fluidization velocity. In all cases the compaction rate is controlled by the.properties of the matrix. These results can only be applied to geological problems if the values of the permeability, bulk and shear viscosity of the matrix can be estimated. All three depend on the microscopic geometry of the melt, which is in turn controlled by the dihedral angle. The likely equilibrium network provides some guidance in estimating the order of magnitude of these constants, but is no substitute for good measurements, which are yet to be carried out. Partial melting by release of pressure at constant entropy is then examined as a means of produced melt within the earth. The principal results of geological interest are that a mean mantle temperature of 1350 °C is capable of producing the oceanic crustal thickness by partial melting. Local hot jets with temperatures of 1550 °C can produce aseismic ridges with crustal thicknesses of about 20 km on ridge axes, and can generate enough melt to produce the Hawaiian Ridge. Higher mantle temperatures in the Archaean can produce komatiites if these are the result of modest amounts of melting at depths of greater than 100 km, and not shallow melting of most of the rock. The compaction rate of the partially molten rock is likely to be rapid, and melt-saturated porosities in excess of perhaps 3 per cent are unlikely to persist anywhere over geological times. The movement of melt through a matrix does not transport major and trace elements with the mean velocity of the melt, but with a slower velocity whose magnitude depends on the distribution coefficient. This effect is particularly important when the melt fraction is small, and may both explain some geochemical observations and provide a means of investigating the compaction process within the earth. I N T R O D U C T I O N There is an obvious need for a simple physical model which can describe the generation of a partially molten rock, and the separation of the melt from the residual solid, which will be referred to as the matrix. If such a model is to be useful it must lead to differential equations which can be solved by standard methods. The principal aim of this paper is to propose such a model, derive the governing equations, and obtain some solutions for particularly simple cases. The model is concerned with the physics, rather than the chemistry, of the process, though the formulation is sufficiently general to allow the inclusion of complicated phase equilibria. Several effects whose importance is unclear have not been included, in order to obtain the simplest model which can describe the generation and extraction of magma. Generation of a magma containing few solid crystals requires two operations. A partially mohen rock must first be generated, either by supplying heat or by reducing the pressure and so changing the solidus temperature. Once such a rock has been formed, the melt must UounuJ of Petrology, Vol. 25, Pirt 3, pp. 713-765, 19841 at W asngton U niersity at St L ouis on M arch 5, 2013 http://petroxfordjournals.org/ D ow nladed from