### The deep roots of volcanos: localization instabilities in a continuum model of magma dynamics

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Richard Katz, Columbia University
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The broad regions deep in the Earth that feed molten rock (magma) to volcanos at the surface are generally inaccessible to direct observation. Progress in understanding these regions requires the use of models. The dynamics of magma in the mantle can be described with equations that enforce the conservation of mass, momentum, energy and chemistry for a continuum of two interpenetrating fluids of vastly different viscosity. In this theory (McKenzie 1984), low viscosity magma is considered a Darcy fluid that percolates through the pores of the extremely high viscosity mantle rock. The crystalline mantle is known to undergo creeping thermal convection over geologic time and may be described mathematically as a Stokes fluid.

Access to high-performance computational tools (e.g. PETSc) has enabled us to solve these equations without neglecting important rheological non-linearities and hence to develop magma-dynamics simulations of unprecedented fidelity. Here we will describe two recent results on channelization of magma observed in natural and experimental systems. First, as demonstrated in experiments, shear of partially molten mantle rocks causes localization of an initially uniform melt distribution into highly concentrated melt bands oriented at about 15 degrees to the shear plane (Holtzman et al. 2003). Our computational model behaves consistently and predicts that the band angle is a function of the stress-dependence of the matrix shear viscosity. We have confirmed this result with linear analysis. Second, as observed in exhumed sections of mantle rock (Kelemen 1995), buoyant upward percolation of magma leads to highly channelized flux. Our flow models capture this reactive infiltration instability and make predictions about melt focusing and ascent rates. We will discuss both these models and their predictions for patterns of global volcanism.

**Abstract Author(s): **Richard Katz and Marc Spiegelman