QUANTIFICATION OF CRUSTAL CONTAMINATION IN OPEN MAGMATIC SYSTEMS

The DePaolo (1981a, Earth Planet. Sci. Lett.53,189-202) equations for assimilation with fractional crystallization (AFC) are extended and solved to yield directly the fraction of crust assimilated during AFC with or without magma replenishment or recharge. Errors in the computed crust/magma ratio are also presented. Using graphical methods and a sufficient number of elements no assumptions need be made about the value of the ratios r (=rate of assimilation/rate of fractional crystallization) and beta (= rate of recharge/rate of assimilation); in fact, the method yields independent estimates of these ratios in addition to the crust/magma ratio. Thus the average relative sizes of the fluxes of wall-rock melt, replenishing magma, and fractionating phases are known and can be incorporated in a budget for the whole magma-crust system. The method for calculating the crust/magma ratio is extended to encompass variable values of r, beta, and bulk distribution coefficient (D). Simple (bulk) mixing is effectively a special case of AFC where beta or r --> infinity and/or D = 0. Only for highly incompatible elements (D<0.1) do bulk mixing calculations approximate the true crust/magma ratio if AFC processes operated. For more compatible elements (e.g., oxygen) bulk mixing calculations considerably overestimate the crust/magma ratio if r and beta are constant. The complications of compositional stratification and diffusion in magma chambers are considered qualitatively. Two examples illustrate the application of the methods developed here. For the upper zone of the Lille Kufjord intrusion in northern Norway, an example of mid-crustal AFC without magma recharge, either r = 0.04 and the crust/magma ratio is 0.04, or r = 0.08 and the crust/magma ratio is 0.06. For lavas of the Andean Central Volcanic Zone, an example of deep AFC with possible recharge, r = 0.15, beta = 3.2, and the crust/magma ratio is 0.16.