[1] Modeling of melt formation and transport in all tectonic settings requires the inclusion of water, since water has large effects on mantle solidi as well as physical properties of liquids. To facilitate the inclusion of water in melting models this paper presents a new parameterization for melt fraction as a function of pressure, temperature, water content and modal cpx, based on knowledge gained from recent advances in the fields of thermodynamic modeling as well as experimental investigations of peridotite melting and hydrous equilibria. The parameterization is computationally efficient and can be modified easily as better experimental data become available. We compare it to other published parameterizations and test it in simple calculations of adiabatic decompression melting (mid-ocean ridge) and hydrous melting (subduction zone).

Magma transport in brittle rock occurs by diking. Understanding the dynamics of diking and its observable consequences is essential to deciphering magma propagation in volcanic areas. Furthermore, diking plays a key role in tectonic phenomena such as continental rifting and plate divergence at mid-ocean ridges. Physics-based models of propagating dikes usually involve coupled transport of a viscous fluid with rock deformation and fracture. But the behaviour of dikes is also affected by the exchange of heat with the surroundings and by interaction with rock layering, pre-existing cracks, and the external stress field, among other factors. This complexity explains why existing models of propagating dikes are still relatively rudimentary: they are mainly 2D, and generally include only a subset of the factors described above. Here, we review numerical models on dike propagation focusing on the most recent studies (from the last 15-20 years). We track the influence of two main philosophies, one in which fluid dynamics are taken to control the behavior and the other which focuses on rock fracturing. It appear that uncertainties in the way that rock properties such as fracture toughness vary from laboratory to field scale remains one of the critical issues to be resolved. Finally, we present promising directions of research that include emerging approaches to numerical modeling and insights from hydraulic fracturing as an industrial analogue.

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