MELT EXTRACTION MODELING WITH PERCOLATION THEORY

Knowledge of the porousity and permeability of melt channels in and near magmatic source regions is crucial to our understanding of magma transport in the deep crust and upper mantle. One approach to the study of melt transport is the use of percolation theory which investigates the interconnectedness of objects as a function of their shape and abundance. Percolation theory models can be used to statistically predict when a series of melt channels becomes interconnected to form a permeable network, how tortuous a path the melt travels through it,and how much of the channel network potentially can be "drained" of the melt inside it. In order to model a partially molten region we performed simulations by randomly placing two-dimensional rectangles on a 1001 x 1001 lattice. These rectangles represent the channels (or "cracks") that melt travels through as it accumulates from micron-scale grain boundaries into meter-scale dikes. Both the aspect ratio and the orientation of the rectangles can be controlled during modeling to simulate the effects of deformation. A simplifying assumption necessary to apply this model is that the channels have fixed dimensions and therefore do not expand or contract in response to changes in melt flow or deformational forces. These simulations demonstrate that the rectangles' aspect ratio and orientational distribution exert significant effects on the properties of the network.