Replenishment rates of crustal magma and their bearing on potential sources of thermal energy

Abstract A general model of magma intrusion into the crust is developed which is based on a viscous-dissipation, forced-convection flow process driven by gravitational-buoyancy forces. Although some of the points in this general model have been studied before, it is possible with the present model to go further and calculate magma volumetric intrusion rates from fundamental properties and parameters. Equations for forced convection in a conduit with viscous dissipation are combined with results for the temperature dependence of magma viscosity. The volumetric intrusion rate is shown to be not a function of viscosity as might be expected, but rather a function primarily of the rate of change of viscosity with temperature. The model predictions for intrusion rate correlate well with field results for several sites where data exist for both intrusion or extrusion rate and for the temperature-dependent behavior of magma viscosity. The model predicts magma chamber replenishment rates equivalent to thermal energy rates on the order 10 GW (gigawatts) for a single active magma site. Assuming active magma sites on a 50-km spacing along volcanic lineaments leads to an estimate of a renewable magma intrusion rate into the crust of the western U.S. on the order of 2 TW (terawatts).

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