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).