Computer simulation of Pb and Sr isotope evolution of the Earth's crust and upper mantle

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Isotope evolution in a differentiated (crust and upper mantle) and chemically heterogeneous Earth has been computed for a model with isotopic exchange between crust and mantle at an exponentially decreasing rate. To simulate the effects of subduction, cells of crust and mantle are selected at random, their contents mixed and then redistributed into the cells from which they came—to give new chemically heterogeneous but momentarily isotopically homogeneous systems. Daughter isotopes in each cell grow according to equations appropriate for closed chemical systems. Rock age distributions and isotopic data created by the computer calculation mimic nature. Pb isotope data changes through geologic time are illustrated to demonstrate that two-stage interpretations applied to Pb data for rocks with complex histories may be misleading. The intercept of the Pb ore growth curve and regressions fit to Pb data gives minimum values only for the duration of heterogeneous U Pb systems, not the time when heterogeneous distribution first occurred. An intercept derived time of about 3 b.y., in the Pb system is shown to be quantitatively compatible with an average Rb Sr age of crustal rocks of 1.5 b.y. and with a constant degree of chemical heterogeneity for all of Earth history.