ABSTRACT

A mathematical formulation of the mantle-crust development is carried out from the view point of material transfer. The enrichment of elements into melts during the process of magma generation and the transport rate within the earth are the essential factors. Based upon the approximation of dilute ideal solution, the enrichment factors for minor elements during partial melting, equilibrium freezing, fractionation freezing and zone melting are calculated. It is shown that the log-linear pattern of lanthanide concentration is realized not only by the melting process of the whole mantle but also by a repetition of local melting. Numerical integration of the equation of development is carried out and it is compared with the observed data by PATTERSON and TATSUMOTO for U-Pb system. A model with the following characteristics is proposed: (1) Repetition of local melting of the mantle materials. (2) Upward transfer into the crust and mixing. (3) Continuous material exchange between the upper and the lower mantle. It is concluded that the mantle differentiation and the mantle convection hypotheses do not contradict with each other under reasonable physical and chemical conditions.