Unmixing model - calculation of trapped melt fraction
While the TE model employed in earlier sections was used to calculate
melt and crystal loss using only Sr, we make use of an alternate
approach to calculate the trapped melt fraction and the range of
crystallinities over which melt is lost. When plotting the Rb against Sr
concentrations for the SMB (bulk) samples, the data collapses primarily
onto a straight line defined by the samples belonging to the transect in
Fig. 1b. We assume that the spread in Rb and Sr concentrations for the
analyzed samples (yellow samples in prior figures and in Fig. 13) is due
primarily to unmixing of fixed liquid and crystal end member
compositions for reasons outlined in the previous section. The choice of
parental magma composition is listed in Table 2 and is validated by
field observations, the fact that the spread in major, minor, trace
element with respect to wt % SiO2 is minimized at
compositions near the assumed parental magma composition, and the
ability of the starting composition to satisfy the observed major,
minor, and trace element data. The extent of crystallization (mass
fraction) before melt loss can be solved for by calculating the
evolution of Rb and Sr in the liquid and solid assuming fractional
crystallization where melt and crystals aren’t separated from one
another and fitting the tie-lines between liquid and solid to the
samples composition (Fig. 13). In this case, the crystallized mass
fraction, MC, that minimizes the scatter about the
mixing line is 0.24. The trapped melt fraction of each sample is then
calculated as the relative contribution of each endmember – the solid
and liquid at MC = 0.24 of a parental magma composition
listed in Table 2. Using rhyolite-MELTS, we convert mass to volume and
solve for the trapped melt volume (Fig. 13). The results are similar to
the melt and crystal loss results, except this technique allows us to
obtain the tie-line along which unmixing primarily occurs (i.e. how much
mass has crystallized before the onset of unmixing). This allows us to
quantify trapped melt fraction profiles from the trace element record of
the samples and compare to numerical models of (mechanical) compaction
by repacking (Florez et al. , 2024).