Parental magma compositions inferred from the chemical compositions of olivine-controlled derivative melts

Abstract

The melt portion of a parental magma, undergoing equilibrium olivine crystallization, passes through a succession of compositions unique to its initial composition. Because the succession of compositions follows uniquely from the parental magma's composition, a liquid line of descent model fit to several of the derivative-melt compositions can recover an estimate of the parental magma's composition. We have developed an algorithm to accomplish the model fitting and thus far equipped it to treat olivine fractionation including departures from perfect equilibrium crystallization. Here we report validation tests on the method, which we call “Derivative-Magma Analysis” (DMA), applied to computer-synthesized data and two instances of laboratory-synthesized data (one as a single-blind test). For the computer- and laboratory-synthesized data, DMA recovered the parental-magma compositions within common analytical accuracy. For the most difficult oxide to estimate, MgO, the recovered values deviated from the measured values by less than 0.5 wt% for the two laboratory-synthesized datasets. For other major-element oxides, recovered values typically deviate from nominal values by less than 0.2 wt%. DMA also reliably estimated the compositions of the olivines that coexisted with each derivative melt. Applied to the Kilauean summit eruption of 1959, DMA estimates a parental magma with Mg# = 73 (MgO ≈ 16 wt%). This value, while significantly higher than estimates from some authors who favor low-Mg parental magmas, rules out the extremely high-MgO parental magmas favored by other authors.