Mathematics – Logic
Scientific paper
Jan 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990gecoa..54...87d&link_type=abstract
Geochimica et Cosmochimica Acta, vol. 54, Issue 1, pp.87-102
Mathematics
Logic
7
Scientific paper
We have used a computer model (TRACES) to simulate low pressure differentiation of natural basaltic magmas in an attempt to investigate the chemical dynamics of open system magmatic processes. Our results, in the form of simulated liquid lines of descent and the calculated equilibrium mineralogy, were determined for perfect fractional crystallization; fractionation paired with recharge and eruption (PRF); fractionation paired with assimilation (AFC); and fractionation paired with recharge, eruption, and assimilation (FEAR). These simulations were calculated in an attempt to assess the effects of combinations of petrogenetic processes on major and trace element evolution of natural systems and to test techniques that have been used to decipher the relative roles of these processes. If the results of PRF calculations are interpreted in terms of a mass balance based fractionation model (e.g., Bryan et al., 1969), it is possible to generate low residuals even if one assumes that fractional crystallization was the only active process. In effect, the chemical consequences of recharge are invisible to mass balance models. Pearce element ratio analyses, however, can effectively discern the effects of PRF versus simple fractionation. The fractionating mineral proportions, and therefore, bulk distribution coefficients ( ) of a differentiating system are dependent on the recharge or assimilation rate. Comparison of the results of simulations assuming constant with the results calculated by TRACES show that the steady state liquid concentrations of some elements can differ by a factor of 2 to 5. If the PRF simulation is periodic, with episodes of mixing separated by intervals of fractionation, parallel liquidus mineral control lines are produced. Most of these control lines do not project back to the parental composition. This must be an important consideration when attempting to calculate a potential parental magma for any natural suite where magma chamber recharge has occurred. Most basaltic magmas cannot evolve to high silica compositions without magnetite fractionation. Small amounts of rhyolite assimilation (assimilation/fractionation < 0.1), however, can drive evolving basalts to more silica rich compositions. If mass balance models are used to interpret these synthetic AFC data, low residuals are obtained if magnetite is added to the crystallizing assemblage. This approach works even for cases where magnetite was not a fractionating phase. Thus, the mass balance results are mathematically correct, but are geologically irrelevant.
Defant Marc J.
Nielsen Roger L.
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