Magma Dynamics with the Enthalpy Method: Benchmark Solutions and Magmatic Focusing at Mid-ocean Ridges

Magma genesis and transport link mantle convection with surface volcanism and hence with the long-term chemical and morphological evolution of the Earth' s crust.Modeling the dynamics of magma^ mantle interaction in tectonic settings remains a challenge, however, because of the complexity of multi-component thermodynamics and melt segregation in a permeable, compactible, and actively deforming mantle matrix.Here I describe a flexible approach to formulating the thermochemistry of such models based on the Enthalpy Method, a technique commonly used in simulations of alloy solidification.This approach allows for melting and freezing based on a familiar binary phase diagram, consistent with conservation of energy and two-phase compaction and flow.I present an extension of the Enthalpy Method to more than two thermodynamic components.Simulation of a onedimensional upwelling and melting column provides a benchmark for the method.Two-dimensional simulations of the melting region that feeds magma to a rapidly spreading mid-ocean ridge demonstrate the utility of the Enthalpy Method.These calculations provide a new estimate of the efficiency of magmatic focusing along the base of the oceanic lithosphere.Modeled focusing efficiency varies with mantle permeability and resistance to compaction.To yield 5^7 km of oceanic crust with $20% melting of a homogeneous, sub-ridge mantle, a focusing efficiency of greater than 70% is required.This, in turn, suggests that matrix permeability and bulk viscosity are at the high end of previously estimated values.