Mixing Loops, Mixing Envelopes, and Scattered Correlations among Trace Elements and Isotope Ratios Produced by Mixing of Melts Derived from a Spatially and Lithologically Heterogenous Mantle

Mixing has been widely used in the interpretation of radiogenic isotope ratios and highly incompatible trace element variations in basalts produced by melting of a heterogeneous mantle. The binary mixing model is constructed by considering mass balance of endmember components, which is independent of physical state and spatial distribution of the endmembers in the mantle source. Variations of radiogenic isotope ratios and highly incompatible trace elements in basalts also depend on the size and spatial distribution of chemical and lithological heterogeneities in the mantle source. Here we present a new mixing model and a mixing scheme that take into account of the size, spatial location, and melting history of enriched mantle (EM) and depleted mantle (DM) parcels in the melting column. We show how Sr, Nd, and Hf concentrations and isotope ratios in the aggregated or pooled melt collected at the top of the melting column vary as a function of location of the EM parcel in the melting column. With changing location of the EM parcel in the upwelling melting column, compositions of the pooled melt do not follow a single mixing curve expected by the binary mixing model. Instead, they define a mixing loop that has an enriched branch and a depleted branch joined by two extreme points in composition space. The origin of the mixing loop can be traced back to four types of EM distribution or configuration in the melting column. The shape of the mixing loop depends on the relative melting rate of the EM to that of the DM and the number and spacing of EM parcels in the melting column. Probabilities of sampling the enriched and depleted branches in the pooled melt are proportional to volume fractions of the enriched and depleted materials in the mantle source. Mixing of pooled melts from a bundle of melting columns results in mixing envelopes in the isotope ratio correlation diagrams. The mixing envelope is a useful tool for studying chemical variations in mantle-derived melts. As an application, we consider scattered correlations in Sr-87/Sr-86 vs. Nd-143/Nd-144 and Nd-143/Nd-144 vs. Hf-176/Hf-177 in mid-ocean ridge basalts. We show that such correlations arise naturally from melting of a spatially heterogeneous mantle.