The process of regional metamorphism during a geosynclinal subsidence of the earth's crust is physically interpreted as interactions among heat flow, water flow, and chemical reactions. Physical state variables are: temperature T, rock pressure Ps, and water pressure Pf. A candition Pf≤Ps appears to be satisfied in actual metamorphic belts.
A formulation of physical model of regional metamorphism is carried out. The following quantities are the essential factors: rate of subsidence of the crust (W), relaxation time of thermal equilibrium (tT), relaxation time of osmotic equilibrium (tos), and rate of metamorphic reactions (Jc). The rate of geosynclinal subsidence is obtained as an order of 0.1cm/year. The rock pressure Ps is increased by several kilobars during an order of 107 years.
Three types of metamorphic reactions are adopted as models, and variations of temperature and water pressure during a process of regional metamorphism are calculated. The physical state of the crust and the upper mantle is inferred in the light of the calculated results. The flow diffusivity of water within the crust is estimated as an order of 10-2cm2/sec. It is shown that the normal temperature gradient has no significance during metamorphism and that the heat flow from the mantle toward the crust is an essential factor to determine the types of regional metamorphism. An extraordinary feature of Sanbagawa metamorphic belt in the south-western Japan is briefly discussed in relation to the physical structure of the earth's interior.
