Two terrestrial lead isotope paradoxes, forward transport modelling, core formation and the history of the continental crust

A combined solution for the two major terrestrial lead paradoxes has been sought. These are the 'future' paradox (upper crustal and upper mantle Pb isotope compositions plot in the future field in ²⁰⁷Pb/²⁰⁴Pb vs. ²⁰⁶Pb/²⁰⁴Pb space) and the Th/U mantle paradox (The Th/U ratio of the upper mantle is ca. 2.6, whereas Pb isotopes indicate a value of 3.8). Constraints considered other than U-Th-Pb data include siderophile element concentrations of the mantle (which restrict core formation scenarios), W isotopes and the oldest lunar ages (bracketing the accretion and core formation time scale to 60-100 Ma), and noble gas systematics (requiring a two-layered mantle structure dating back to just after accretion). Further, Nd isotopes allow a test of the validity of crustal growth models used. The transport balance model used includes a continental crust divided into four parts; upper (high U/Pb) and lower (low U/Pb), as well as older and younger. The latter division is generated by erosion removing proportionally more younger than older crust. After 2 Ga ago erosion transfers U to the ocean floor in preference to Pb and Th, as a consequence of U solubility in an oxidizing environment. Within the constraints imposed on the model, the future paradox cannot be solved by postulating a delayed core formation. An additional low U/Pb reservoir required for this can be found in the continental crust. Solving the future paradox requires that particularly the older lower crust reservoir is conservative, which limits the amount of continental crust that can have been recycled into the mantle over Earth's history. On the other hand, a solution of the mantle Th/U paradox requires a considerable amount of continent recycling, particularly in the last 1-2 Ga. A restricted family of crustal history scenarios allows a solution to both paradoxes. These are characterized by < 10% of the present amount of continental crust existing just after Earth accretion, rapid crustal growth, with relatively insignificant recycling into the mantle, during the Archaean, and increasing continent recycling in the Proterozoic, reaching ca. 60% of the rate of continent formation today. Scenarios in which delamination of lower crust accounts for over 5% of continent recycling do not provide solutions. The result portrays a non-steady-state Earth in which the net mass of continental crust is at present still growing at 2 × 10¹⁵ g/a, and the U content of the upper mantle is increasing.