A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17–19°S?

We propose a new approach to model the geochemical evolution of continuously replenished and tapped steady-state magma chambers. We use a sinusoidal function to model cyclic magma supply. The temporal evolution of a reservoir is described using differential equations, in which the amount of refilling magma does not depend on the size of the chamber. These equations can be used to calculate incompatible trace element concentrations and magma quantities. We examine the geochemical consequences of episodic injections, noises and wall-rock assimilation. We also explore possible variations in crystallization rate. To show its potential, the theoretical treatment has been applied to the EPR 17–19°S, a site with a strong magma budget which has been the subject of several geological/geophysical studies. The practical application requires geological parameters to be constrained, as well as the extreme values of the lava concentration range. A first step specifies the incompatible trace element composition of the replenishing melt, which corresponds in the EPR case to a magnesian liquid (MgO = 9.5 wt%). It is then possible to determine other parameters such as cycle period (750 years), magma residence time (300 years), and reservoir size (from 4.1 to 8.6 km3 per 20 km segment). Lastly, variations in crystallization rate do not significantly alter the results