Simple 2-D models for melt extraction at mid-ocean ridges and island arcs

Abstract

A general set of 2-D equations for the conservation of mass and momentum of a two-phase system of melt in a deformable matrix is used to derive analytic solutions for the corner flow of a constant porosity melt-saturated porous medium. This solution is used to model the melt extraction processes at mid-ocean ridges and island arcs. The models indicate that flow of melt is controlled by pressure gradients induced by the Laplacian of the matrix velocity field and by the dimensionless percolation velocity which measures the relative contributions of buoyancy-driven flow to advection by the matrix. The models can account for many features of ridge and arc volcanism. Matrix corner flow at ridges causes melt to be drawn to the ridge axis enabling the extraction of small melt fractions from a wide melting zone while showing a narrow zone of volcanism at the surface. At subduction zones melts do not percolate vertically but are drawn to the junction of the upper plate and subducting slab by corner flow in the mantle wedge. For subduction zones, if the dimensionless percolation velocity is below a critical value, slab-derived fluids will be carried down by the matrix and cannot interact with the mantle wedge. The geochemistry of island arcs will be controlled by the geometry of melt streamlines. This model is consistent with geophysical and geochemical data from the Aleutian arc.