| The Bugaboo Batholith is a mid-Cretaceous, composite granitoid intrusion consisting of biotite granite and granodiorite. It intruded metasediments, of the late Proterozoic Horsethief Creek Group, producing a metamorphic aureole ca. 1000 meters wide. Prior to contact metamorphism, rocks in the area of the Bugaboo Batholith experienced chlorite-zone regional metamorphism in the Jurassic, transforming the pelitic rocks into variably crenulated phyllites.; Field, petrographic, and mineral-chemical observations suggest the following series of reactions to account for the development of the observed series of mineral assemblage zones within the aureole (Qtz = quartz; Chl = chlorite; Pg = paragonite; Ms = muscovite; Bt = biotite; And = andalusite; Crd = cordierite; Ab = albite; Kfs = K-feldspar): (1) Chl + Qtz + AlVIAl IVMg–1Si–1 = Crd + H2O; (2) Pg + Qtz = Ab + And + H2O; (3) Ms + Chl + Qtz = And + Bt + Crd + H2O; (4) Ms + Qtz = And + Kfs + H2O; (5) Bt + And + Qtz = Crd + Kfs + H2O.; Between the isograds corresponding to reactions 3 and 4, textural evidence suggests forward progress of the reaction Ms + Crd = Bt + And + Qtz + H 2O with increasing grade, but chemical data are difficult to interpret, possibly indicating bulk compositional control on Mg/(Mg+Fe) in biotite and cordierite.; Petrologic hypotheses derived from field and petrographic relationships were tested using mass balance methods. The assessment of mass balance, whether graphical or algebraic, depends on three assumptions. (1) The assemblages are in equilibrium. (2) The mineralogical makeup of the assemblage is known. (3) The constituents needed to describe compositional variation of the system are known. Algebraic methods have no inherent advantage over graphical approaches when the number of ‘significant’ compositional variables in the system is less than four. In cases with four or more ‘significant’ variables, algebraic approaches have significant advantages. The meaning of ‘significant’ in this context is closely linked to assumptions 2 and 3 above, which serve to define the model chemical system. The choice of which phases and elements to include in the model system is one that must be carefully considered in light of the mineralogical and chemical makeup of the assemblage, and is inherently subjective.; For those cases where algebraic analysis is deemed appropriate, a new formulation for carrying out mass balance calculations is presented that is based on nonlinear programming. This new approach has significant advantages over existing approaches with respect to flexibility in the treatment of analytical uncertainties and constraint of the solution. |
