Studies on the processes of magma generation and migration are reviewed, with special reference to geochemical and numerical modeling. A full set of governing equations for describing melting and melt migration by porous flow are introduced, in which the relationships between the equations (conservation of mass, momentum and energy) and the variables are investigated. Based on the governing equations, characteristics of the melt-solid flow systems with chemical reactions are described, which shows that the chemistry of the melt and solid can be used to investigate the processes involved quantitatively (e. g., the style of melt migration). Application of these theories and numerical modeling to the magmatism at mid-ocean ridges revealed that more than 80 per cent of the melt produced beneath the ridges is transported towards the surface without significant chemical reaction on ascent within a short period of time (e. g., less than 1,000 years). Magmatism and metamorphism in subduction zones are also modeled, which suggests that transportation of H
2O and melting depend strongly on the age of the subducting slab. Associated with subduction of young (<10 m. y.) slabs and ridges, transition in terms of magmatism and metamorphism occurs within 10 m. y., from (1) normal arc melting in mantle wedge, (2) forearc mantle melting (high-Mg andesitic) to (3) slab melting in which a significant amount (〜100 km
3) of granitic melt is produced. The model results newly show that, this event of ridge subduction should cause synchronous formation of granitic batholith by slab melting and regional paired-metamorphic belts, such as Ryoke-Sanbagawa belt in Japan. These results show that the geochemical and numerical modeling is a useful approach in order to understand the melt generation and migration processes and their roles in the Earth's history.
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