We have developed a method that enables calculation of the degree of partial melting and source composition for cogenetic primary magmas, in the context of the dynamic melting model of Langmuir et al. (1977). This method uses variations of between-magma concentration ratios for two incompatible trace elements that have different bulk distribution coefficients, and does not require assumptions regarding source incompatible element concentrations or ratios. Source concentrations can be calculated after obtaining the partial melting degree.
The dynamic melting inversion, or DMI, method builds on the approach of Maaløe (1994). The major difference between our method and those of Maaløe (1994) or Treuil and Joron (1975) is that ours is based on the dynamic melting model, instead of batch or fractional melting, and, therefore, works within what many would consider to be a more realistic melting context. Consequently, the results obtained are expected to more accurately reflect the melting process.
Application of the DMI method to several suites of alkalic volcanic rocks, the Koloa volcanics, the Honolulu volcanics,
and basalts from southeastern Australia, suggests that melilitites are formed by 2-4% partial melting, and alkali olivine basalts represent 8-11% partial melts, of a LREE-enriched mantle source. The viability of the method is supported by the observed intersuite consistency and the high level of agreement obtained by using different element pairs for the same basalts. Our results, in accord with numerous previous studies, quantitatively document the derivation of basalts with positive eNd from LREE-enriched sources. The near-ubiquity of this result for alkalic suites argues that the often-proposed "recent source enrichment" occurs as an integral, initial phase of the total melting process. Although our method does not address this initial melting phase, we believe that future progress in quantifying the production and sources of mantle-derived basalts will depend on efforts that do so.
The DMI method works very well for cogenetic pairs of primary alkalic basalts. Further work may extend application of the method to different kinds of basalts produced in different tectonic settings, given that observed or inferred primary magma compositions exhibit sufficient variation in trace element concentrations.
Langmuir, et al., Earth. Planet. Sci. Lett. 36, 133-156 (1977).
Maaløe, Geochim. Cosmochim. Acta 58, 2519-2525 (1994).
Treuil & Joron Soc. Ital. Mineral. Petrol. 31, 125-174 (1975).