Modeling of trace-element distribution in magma chambers using open-system models

Abstract With the increasing amount of geochemical data available for magmatic systems, there is an increasing need for more accurate mathematical models to describe trace-element distributions in magma chambers. Several mechanisms are thought to be active in magma chambers, including fractional crystallization, assimilation, and replenishment. Most previously published mathematical models have considered only one or two of these mechanisms to be active at the same time. This article presents two models, the “batch-” and “continuous replenishment” models, allowing fractional crystallization, assimilation, and replenishment to be concurrent mechanisms. Both the degree of fractionation, F , and arbitrary time, t , may be used as the independent variable. The enclosed FORTRAN 77 program implements these models. It allows the concurrent modeling of the behavior of up to ten trace elements in a magma chamber undergoing concurrent fractional crystallization, assimilation and replenishment, or any combination of these processes.