A bi-directional mixing model for lead isotope evolution

Abstract

This paper explores the characteristics of two-reservoir evolutionary models for radiogenic isotopes. It extends the studies of Russell (1972) to the case of bi-directional transport. Like that earlier study, it is based on the hypothesis that the characteristic lead isotope patterns of oceanic basalts and conformable ores betray the existence of at least two major geochemical systems of global extent and great age. The lead-207 deficiency of the oceanic basalt leads is considered to be a fundamental characteristic of the systems. Analytical solutions are obtained for both the case of constant and variable transport rate coefficients. It is shown that both will predict isotopic patterns in accord with those observed, but that the time-variable transport coefficients provide quantitative agreement over a much wider range of parameters. The model of Armstrong (1968) is shown to correspond to a special case of the analytical solutions here derived; study of this case confirms that the Armstrong model cannot provide for the lead-207 discrepancy mentioned above. Otherwise numerical agreement with that model seems acceptable. The most remarkable feature of the models studied is the constancy of the value obtained for the beginning time of evolution of the two systems. Constant rate coefficients give times in the range 3100 ± 300 m.y., and variable rate coefficients give times in the range 3100 ± 200 m.y. This value is compared with the youngest ages of volcanism observed for the moon and the oldest ages for the earth, as discussed by Whetherill (1972). The model also provides information about the distribution of Th/U in an evolving earth.