A geochemical approach to model periodically replenished magma chambers: Does oscillatory supply account for the magmatic evolution of EPR 17–19°S? Eric Rannou a, * , Martial Caroff b , Carole Cordier b a UMR No 6205 ‘‘Laboratoire de Mathe ´matiques,’’ Universite ´ de Bretagne Occidentale, 6 Avenue Le Gorgeu, C.S. 93837, 29238 Brest Cedex 3, France b UMR No 6538 ‘‘Domaines Oce ´aniques,’’ IUEM, Universite ´ de Bretagne Occidentale, 6 Avenue Le Gorgeu, C.S. 93837, 29238 Brest Cedex 3, France Received 21 November 2005; accepted in revised form 6 July 2006 Abstract We propose a new approach to model the geochemical evolution of continuously replenished and tapped steady-state magma cham- bers. 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, nois- es 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 km 3 per 20 km segment). Lastly, variations in crystallization rate do not significant- ly alter the results. Ó 2006 Elsevier Inc. All rights reserved. 1. Introduction The linkage between energetics and material balances in the magmatic systems can be numerically treated either through geochemical models which formalize physical pro- cesses (e.g., Ghiorso and Sack, 1995; Edwards and Russell, 1998; Spera and Bohrson, 2002, 2004) or though mass bal- ance models in which physics is not directly apparent, but enclosed into a few integrative parameters. In the physicochemical models, the modeling exercise appeals directly to physical laws in order to address com- plex natural systems. However such modeling processes must make use of a great number of input parameters, the values of which are not highly constrained. For instance, to model instantaneous heat transfer in a magma chamber, heat loss to country rocks (roughly proportional to the surface area of the reservoir) must be taken into ac- count together with the effects of thermal and/or solutal convection, replenishment by hot liquids, wall-rock assim- ilation, etc. In such an approach, the realism of the method is counterbalanced by the difficulty to obtain a set of useful output parameters. Alternatively, there are models based on integrative methods, which can be used to reduce the number of parameters and make their estimation easier without too much simplification. Two kinds of integrative procedures have been devel- oped for modeling the behavior of replenished magma res- ervoirs from geochemical data (see Caroff and Fleutelot, 2003, for a review). The first group uses mass balance cal- culations to explore trace element variations in long-lived 0016-7037/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.gca.2006.07.007 * Corresponding author. Fax: +33 298016790. E-mail address: Eric.Rannou@univ-brest.fr (E. Rannou). www.elsevier.com/locate/gca Geochimica et Cosmochimica Acta 70 (2006) 4783–4796