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).