Trace element and isotopic effects of combined wallrock assimilation and fractional crystallization

Equations describing trace element and isotopic evolution in a magma chamber affected simultaneously by fractional crystallization and wallrock assimilation are presented for a model where the mass assimilation rate(?_a) is an arbitrary fraction(r) of the fractional crystallization rate(?_c). The equations also apply to recharge of a crystallizing magma. Relatively simple analytical expressions are obtained for both radiogenic isotope variations (Nd, Sr, Pb) and stable isotopes (O, H) including the effects of mass-dependent fractionation. Forr = 1 a modified zone refining equation is obtained for trace element concentrations, but forr < 1 behavior is a combination of zone refining and fractional crystallization. Asr → ∞, simple binary mixing is approached. The isotopic and trace element “mixing” trends generated can be much different from binary mixing, especially forr < 1. The model provides the basis for a more general approach to the problem of wallrock assimilation, and shows that binary mixing models are insufficient to rule out crustal assimilation as a cause of some of the isotopic variations observed in igneous rocks, including cases where clustering of isotopic values occurs partway between presumed endmember values. The coupled assimilation-fractional crystallization model provides an explanation for certain trace element and isotopic properties of continental margin orogenic magmas (e.g. Sr concentration versus⁸⁷Sr/⁸⁶Sr) which had previously been interpreted as evidence against assimilation. So-called “pseudoisochrons” can be understood as artifacts of contamination using this model. A significant correlation exists between country rock age and low¹⁴³Nd/¹⁴⁴Nd ratios in continental igneous rocks, clearly suggestive that crustal contamination is generally important.