Provided that parental melts for the gabbros are known or can be reasonably predicted, fractional crystallization models can be formulated that allow the compositions of liquids, minerals, and bulk solids to be calculated as a function of temperature or liquid fraction remaining. The fractional crystallization models presented here are based on existing experimental results on mostly ferrobasaltic lavas (e.g., Thy and Lofgren, 1992, 1994; Toplis and Carroll, 1995). The models employ mass balance calculations for each oxide as a function of the solid fraction incrementally going from 0 to 1 in small and constant steps of the remaining liquid (<0.01). The compositions of the stable phase assemblage in equilibrium with the coexisting liquid are determined from simple and complex experimentally determined exchange coefficients, either as constants or as linear functions of temperature. In addition, stoichiometric constraints have been imposed on all silicate minerals. The temperature for each increment is estimated from a linear relationship with liquid MgO content. The redox conditions are constrained by the FMQ oxygen buffer using the equations formulated by Kilinc et al. (1983). The FMQ buffer is suggested by the coexisting Fe-Ti oxide minerals (Fig. F19). The instantaneous solid modes along the cotectics are modeled as constants based on the results of Thy and Lofgren (1994) and Toplis and Carroll (1995). The plagioclase-olivine cotectic is approximated by 0.264 olivine and 0.736 plagioclase (as total solids in weight fractions). The olivine-plagioclase-augite cotectic is constrained by 0.092 olivine, 0.463 plagioclase, and 0.446 augite. The Fe-Ti oxide minerals are modeled by 0.13 ilmenite and 0.07 magnetite, based on Thy and Lofgren (1994). Because of insufficient experimental constraints, the model calculations exclude low-Ca pyroxene and apatite and have been terminated at temperatures of 1000°C. Because the petrographic observations suggest that low-Ca pyroxene replaces olivine as a fractionating phase, this exclusion will have little effect on the liquid line of descent. The saturation of augite is based on Sugawara (2000), whereas the saturation of Fe-Ti oxides is based on Thy and Lofgren (1994) and Toplis and Carroll (1995). Details of the calculation method can be obtained from the author.
The parental magmas for the gabbros are not preserved in the recovered core, and no example of chilled margins has been identified from Hole 1105A (Shipboard Scientific Party, 1999) or from the nearby Hole 735B (Robinson, Von Herzen, et al., 1989; Dick, Natland, Miller, et al., 1999). However, possible parental basalts have been dredged from the Atlantis II Fracture Zone at several locations (Dick et al., 1991b; Natland et al., 1991; Johnson and Dick, 1992). Two glass analyses from pillow lavas have been tested as parental magma in the calculations. The first is from the rim of a pillow dredged from the northeastern side of the transform (Natland et al., 1991, table 1, anal. 5-3; Johnson and Dick, 1992, table 5). The other and more primitive glass analysis is from a sample dredged from the triple junction (Mahoney et al., 1989; Natland et al., 1991, table 1, anal. AII93-5, 6-1).
The results of modeling perfect fractional crystallization based on these possible parental magmas are illustrated in Figures F25 and F26. The modeling for sample 5-3 assumes coprecipitation of olivine (Fo84) and plagioclase (An69) from 1184°C, augite (Mg/[Mg + Fetotal] = 0.82) in addition from 1155°C, and magnetite and ilmenite from 1100°C. The calculations are terminated at a liquid fraction of 0.13 (equal to 1000°C). The modeling result for sample 5-3 is summarized in Table T8 with the first entry (zero solid fraction) being the starting composition normalized to 100%. The modeling for sample AII93-5 (only shown in Fig. F25) assumes coprecipitation of olivine (Fo88) and plagioclase (An69) from 1221°C, augite (Mg/[Mg + Fetotal] = 0.80) in addition from 1139°C, and magnetite and ilmenite from 1100°C. The calculations are terminated at liquid fractions of 0.14. The compositions of the mafic silicates when Fe-Ti oxides appear on the liquidus are very similar for the two models, whereas plagioclase compositions reflect differences in sodium content of the two compositions. The calculations show that olivine gabbro differentiation can be accounted for by up to 65% fractionation and that only the residual 35% will be saturated in Fe-Ti oxide minerals.
The resultant liquid lines of descent initially show increasing FeO with moderate increases in SiO2. After Fe-Ti oxides appear, FeO and TiO2 decrease while SiO2 increases markedly to dacitic compositions at temperatures of ~1000°C and liquid fractions remaining of 0.15-0.10 (Fig. F26A; Table T8). The actual liquid iron enrichment path will be strongly dependent on the composition of the assumed starting composition. This is illustrated in Figure F26A, where the two liquid curves represent the two slightly different compositions for the same sampleم-3 given by Natland et al. (1991) and Johnson and Dick (1992), respectively (the highest iron enrichment in Fig. F26A results from the analysis of Johnson and Dick, 1992). The calculated liquid line of descent is typically tholeiitic and not very different than that suggested by Toplis and Carroll (1996) for the Skaergaard intrusion.
The average mode of the Hole 1105A olivine gabbros suggests a solid fractionate with higher plagioclase content (olivine = 11 wt%, plagioclase = 54 wt%, and augite = 35 wt%) than used in the modeling. Using such high plagioclase modes result in unrealistic fractionation paths, with Al2O3 being depleted from the liquid at fairly high temperatures (~1020°-1030°C) and thus the inability of plagioclase to be in equilibrium with the late-stage melts. Also the Fe-Ti oxide modes actually observed in the Hole 1105A gabbros suggest much lower contents of 0.12 ilmenite and 0.02 magnetite (maximum values). Despite this, the adopted model calculation for sample 5-3 duplicates reasonably well the observed cryptic variation (Fig. F25). The early income of augite suggests that few, if any, of the gabbros are troctolitic. However, it should be taken into account that the actual temperature of appearance of augite is a best estimate and need not be accurate for the particular starting composition. The actual income of Fe-Ti oxides is poorly predicted by the modeling, which suggests a later appearance of Fe-Ti oxides relative to the model assumption. Delays in Fe-Ti oxide crystallization may principally be caused by departures from the FMQ oxygen buffer toward reduced conditions (e.g., closed-system crystallization with respect to oxygen).
The crystallization modeling additionally allows the bulk solid fractionate and liquid compositions to be calculated for the chosen parental melt composition. Models for a range of trapped liquids contents (0%, 10%, 20%, and 30%) are shown in Figure F26. Several features can be observed:
Most of these observations were expected and support the fractional crystallization modeling. The strong linear variation in the Fe-Ti oxide gabbros between the two apparent end-members is not consistent with perfect fractional crystallization, which predicts trends perpendicular to the observed variation (Fig. F26A). It is possible, although not experimentally predicted, that the instantaneous mode of Fe-Ti oxides initially shows exponential increase. This would amount to a delay in the effects of Fe-Ti oxide fractionation on the liquid line of descent. It is perhaps equally or more likely that the strong linear trend is caused by failure to sample the pure end-member gabbros (olivine and Fe-Ti oxide gabbros) (Fig. F26A).