Inversion of batch melting equations and the trace element pattern of the mantle

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Abstract
The inversion of trace element data for batch melting models consists of using concentrations measured in a series of cogenetic lavas to derive the trace element pattern of their source. The necessary minimum assumptions include the absence of late crystallization/contamination processes (primary liquids), the identification of the possible residual phases, and a homogeneous equilibrium melting situation for which partition coefficients can be estimated. The problem is shown to be, in general, over‐determined provided the number of samples exceeds the number of the elements for which source concentration is desired. There are several important restrictions: (1) transition elements are of little value because they are sensitive to subtle crystallization effects, (2) olivine and orthopyroxene reject almost perfectly all the remaining trace elements and their abundance must be constrained independently from petrological information. After the reliability of the theory was checked using synthetic examples, three case studies were carried out on Grenada alkali basalts and Kohala and Honolulu basaltic series (Hawaii). Rare earth elements, Th, and Ba data were inverted and suggest that except for Honolulu, the mantle source is LREE depleted in accord with Nd isotope data. Garnet behaves generally as a perfectly residual phase. Some tentative mineralogical compositions of the mantle, from which the different series are derived, are proposed. There is no indication that the present theory could not be used for major elements as well.