AFC3D: A 3D graphical tool to model assimilation and fractional crystallization with and without recharge in the R environment

Abstract AFC3D is an original graphical free software developed in the framework of the R scientific environment and dedicated to the modelling of assimilation and fractional crystallization without (AFC) and with (AFC-r) recharge, facilitating the search for the solutions of the equations originally proposed by DePaolo (1981, 1985) and first solved in a graphical way by Aitcheson and Forrest (1994). The software presented here allows a graphical 3D representation of ρ (mass of assimilated crust/mass of original magma) as a function of r (rate of crustal assimilation/rate of fractional crystallization) and β (recharge rate of magma replenishment / rate of assimilation) for each element/isotope, finding a coherent set of (r, β, ρ) parameter triples in a mostly automated way. Mathematically optimized solutions are derived, which can and should then be discussed and evaluated from a geological and petrological point of view by the end user. The presented contribution presents the software and a series of models published in the literature, which are discussed as case studies of application and whose solutions are sometimes enhanced based on the results provided by the software.