A general mixing equation with applications to Icelandic basalts

Abstract The mixing equation applied by Vollmer [1] to Pb and Sr isotope ratios is shown to be a general equation applicable to consideration of element and isotope ratios. The mixing equation is hyperbolic and has the form: Ax + Bxy + Cy + D = 0 where the coefficients are dependent on the type of plot considered: i.e. ratio-ratio, ratio-element, or element-element. Careful use of this equation permits testing whether mixing is a viable process, places constraints on end member compositions, allows distinction between mixing of sources and mixing of magmas, and should allow distinction between recent mixing and long-term evolution of sources. The available chemical data for postglacial basalts from Iceland and along the Reykjanes Ridge are not consistent with either mixing of magmas or simple mixing of an enriched ocean island source with a depleted ocean ridge source. If the available analyses for basalts are representative of the source regions, the data are consistent with at least two models neither of which can be properly tested with the available data. (1) There are two separate mixing trends: one beneath Iceland with the alkali basalt source and a depleted Iceland source as end members; the second along the Reykjanes Ridge with a heterogeneous ocean ridge basalt source and a source similar to that for intermediate basalts on Iceland as end members. The depleted Iceland source and the depleted ocean ridge source are not the same. (2) The chemistry of the basalts is not determined by mixing. Instead the basalts are derived from a multiplicity of sources with a similar history which have been isolated for hundreds of millions of years.