The Generation and Compaction of Partially Molten Rock

The equations governing the movement of the melt and the matrixof a partially molten material are obtained from the conservationof mass, momentum, and energy using expressions from the theoryof mixtures. The equations define a length scale _c called thecompaction length, which depends only on the material propertiesof the melt and matrix. A number of simple solutions to theequations show that, if the porosity is initially constant,matrix compaction only occurs within a distance _c of an impermeableboundary. Elsewhere the gravitational forces are supported bythe viscous stresses resulting from the movement of melt, andno compaction occurs. The velocity necessary to prevent compactionis known as the minimum fluidization velocity. In all casesthe compaction rate is controlled by the properties of the matrix.These results can only be applied to geological problems ifthe values of the permeability, bulk and shear viscosity ofthe matrix can be estimated. All three depend on the microscopicgeometry of the melt, which is in turn controlled by the dihedralangle. The likely equilibrium network provides some guidancein estimating the order of magnitude of these constants, butis no substitute for good measurements, which are yet to becarried out. Partial melting by release of pressure at constantentropy is then examined as a means of produced melt withinthe earth. The principal results of geological interest are that a meanmantle temperature of 1350?C is capable of producing the oceaniccrustal thickness by partial melting. Local hot jets with temperaturesof 1550?C can produce aseismic ridges with crustal thicknessesof about 20 km on ridge axes, and can generate enough melt toproduce the Hawaiian Ridge. Higher mantle temperatures in theArchaean can produce komatiites if these are the result of modestamounts of melting at depths of greater than 100 km, and notshallow melting of most of the rock. The compaction rate ofthe partially molten rock is likely to be rapid, and melt-saturatedporosities in excess of perhaps 3 per cent are unlikely to persistanywhere over geological times. The movement of melt througha matrix does not transport major and trace elements with themean velocity of the melt, but with a slower velocity whosemagnitude depends on the distribution coefficient. This effectis particularly important when the melt fraction is small, andmay both explain some geochemical observations and provide ameans of investigating the compaction process within the earth.