Tectonic pumping of pervasive granitic melts

Abstract

Finite element 2D models are used to study how tectonic stresses pump pervasive granitic melts within migmatites. We start by assuming elliptical melt-filled veins (of different orientations) interconnected by the assumption that they share the same pressure. The melt is then redistributed in the vein array by the application of lateral compression or extension. The effective permeability of vein networks is thought to be up to 13 orders of magnitude higher than the matrix permeability of 10−19m2. This allows us to approximate pressure equilibration and neglect irreversible compaction in the matrix. This simple configuration allows solution of constitutive equations for the equation of state in the viscoelastic matrix, the melt in the vein array, and the mechanical equilibrium along with force balance on the walls of the deforming veins. A rectangular box is pressurized by a constant load applied to one side and continuously deformed by shift of another side with constant velocity.New veins cannot initiate and pre-existing veins cannot migrate bodily down pressure gradients. However, potential flaws are cut in-line with the tip of every pre-defined vein. This means that veins not only close, open, and shear as they rotate, but can also undergo limited propagation at rates dictated by the bulk deformation of the matrix. We use constant viscosities ηs, in the range 1017–1018Pas, deformation rates ė vary between 10−10 and 10−9s−1, and a total strain up to 4–5%.Isolated veins parallel and normal to σ1 have melt pressures between P0 and P0+4ηsė. The mean vein pressure differs from these extremes and is equilibrated by driving melt from shrinking veins into veins parallel to σ1 which widen and lengthen. The above assumptions result in an asymptotic pattern of stress distribution and the amount of melt redistributed at given strain approaching the kinematic limit with time. This occurs whatever the viscosity of the matrix and the strain rate. Multilayered systems are modeled by pre-defining a single vertical vein crossing the planar horizontal boundary between two uniform media. Compression parallel to the layering expels melt from the part of the vein in the more viscous layer to open and extend that part of the same vein in the less viscous layer. Melt moves in the opposite direction during lateral extension. If sheet-like bodies become sufficiently tall to become buoyant, horizontal sheets resulting from lateral compression are likely to rise to higher crustal levels as diapirs while vertical sheets resulting from lateral extension are more likely to ascend as dikes.