5. TRACE ELEMENT MODELING AND RHYOLIT-MELTS CALIBRATION
We implement a trace element (TE) model based on Gelman et al.(2014) in order to investigate if the range in trace elements recorded by the SMB is consistent with crystallization and variable melt loss from a single parental magma composition. The box model considers the evolution of the concentration of a given trace element during crystallization in three separate reservoirs: crystal, melt, and lost melt (in alternate simulations we consider crystal, melt, and lost crystals). The reason for this formulation is because accumulating feldspars (melt loss) can explain SMB samples enriched in Sr, while accumulating melt (crystal loss) can explain SMB samples depleted in Sr. In the model, crystal and melt reservoirs are coupled or grouped together and comprise the synthetic sample (Fig. 9). Lost melt, on the other hand, is removed from the sample (Fig. 9 and 10). Strictly speaking, however, the fundamental equations used to solve for the evolution of the trace elements of interest (Sr and Rb) assume fractional crystallization. This choice is governed by the diffusivity of the trace element of interest and the longevity of the magma system at elevated temperatures. Gelman et al. (2014) demonstrated that for Sr the results are relatively insensitive to this choice. In the box model, the sample is initially considered entirely molten and subsequently the mass of the trace element is partitioned between crystals and melt as crystallization persists. Either reservoir (crystal or melt) can be incrementally lost; however, only lost melt or crystals are separated or “lost” from the sample (Fig. 9 and 10). If no mass is lost, all of the melt will convert to crystal and the final sample concentration (concentration of TE of interest in crystal reservoir once all melt has crystallized) will be equivelant to the starting concentration of the parental melt. However, if a portion of melt is lost, only the melt that remains is converted to the crystal reservoir that comprise the final sample (Fig. 10). Here, the final concentration of the sample relative to the initial concentration of the sample will change as total sample mass has decreased, while, depending on the compatibility of the TE of interest, the mass of the TE in the crystals potentially remains the same. Allowing crystal loss similarly decreases the sample mass; however, the effect on the final concentration of the sample will be the inverse of the case of melt loss (loss of melt for a compatible TE increases TE concentration in the final sample relative to initial whereas crystal loss decreases the final concentration).