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, K_D, 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.