Melting by numbers: Assessing the effective melt fertility of crustal rocks

Partial melting of rocks and the corresponding metamorphic reactions can be simulated through a Lagrangian description, which considers a discrete mineral distribution at sample scale and an infinite heat source. Our model aims to determine the effective melt productivity of crustal rocks linked to texture and composition of the source. In addition, it allows to assess the degree of melt fertility of greywackes and sandstones as a function of erosion and weathering of the source regions and of the tectonic environment in which the sediments were deposited. Our model is represented by a grid of cells, each containing a mineral phase or melt. The infinite heat source can be calibrated according to the melting equations. Melt extraction is ruled by the melt abundance in the source, and the melt sink is also an infinite reservoir. Our model presents three configurations each characterized by a specific melt fertility. Firstly, the spatial distribution of minerals can be random or anisotropic. Secondly, the relative abundance of each mineral phase mimics the initial composition. Finally, the conditions of melt extraction reflect the tectonic environment in place when melt is extracted. The chemical reactivity is simply modelled from the equations of melting, yielding the maximum melt productivity as a function of reactants. The composition of the sediments is represented by a ternary diagram, built on quartz, micas and plagioclase. It mimics depositional environments issued from actual tectonic environments such as continental block erosion, continental basement reworking, or magmatic arc setting. Melting occurs when the effective bulk composition (or mineral assemblage) corresponds to the melting reaction stoichiometry. For a large range of sedimentary protoliths, the melt generated at the eutectic is of granitic composition. In other cases, optimum melt productivity cannot be reached, but the melt is removed when reaching a significant abundance. In other cases, such as an anisotropic mineral distribution, i.e. implying less chances to have the adequate minerals in contact, induces melt layering, similar to the one observed in stromatic migmatites. In order to enhance melt productivity and melt transfer, a deformation field is imposed to the model, mimicking simple or pure shear in a vertical plane, maintaining the 2D pattern of the model. Simple shear is efficient in bringing adequate minerals in contact and thus favors melt production. The source compositio