Finally, knowledge of the bulk partition coefficient, D, is required in
order to fully resolve the group of equations above. To accomplish this,
we perform thermodynamic simulations using rhyolite-MELTS 1.1.x (Gualda
& Ghiorso, 2015). Simulations assume a parental magma composition
listed in Table 2, a fixed pressure of 200 MPa, ca. 5 wt %
H2O and an QFM+1 for the oxygen fugacity. The choice of
parental magma composition is influenced by several observations . The
pressure of 200 MPa is chosen due to the clustering of SMB samples along
the 200 MPa minimum (Gualda et al. , 2012, Gualda et al. ,
2023) of the Qz-Ab-Or ternary (supplementary Fig. 2), while the water
content and oxygen fugacity are relatively unconstrained. However, the
concentration of water must be sufficiently high to precipitate biotite
as an early crystallizing phase (consistent with SMG mineralogy). The
sensitivity of the results to these choices is explored by altering the
wt % H2O content to 2 wt % and the pressure to 500 MPa
(supplementary Fig. 3 and 4). The starting temperature is set to assure
the system is entirely comprised of melt and equilibrium crystallization
proceeds in increments of 0.5ºC until >95% of the mass is
incorporated in the solid (usually ca. 730ºC). Equillibrium
crystallization is chosen because what is required for closure of the TE
model is D as a function of mass crystallized. For trace element
calculations, we model the evolution of both Sr and Rb using partition
coefficients, KD, reported in Table 3. The phase
abundances predicted by rhyolite-MELTS as a function of crystallinity
are shown in Fig. 11 as well as the associated evolution of the bulk
partition coefficients for Sr and Rb. Example model outputs are included
in Fig. 10.
Table 3. Table of partition coefficients used in trace element
calculations.