Constraints on Archean crust formation from open system models of Earth evolution

Establishing the mode and rate of formation of the continental crust is crucial for quantifying mass exchange between Earth's crust and mantle. The limited crustal rock record, particularly of early Archean rocks, has led to a variety of different models of continental growth. Here, we present an open-system model of silicate Earth evolution incorporating the Sm-Nd and Lu-Hf isotope systematics with the aim to constrain crustal growth during the Archean and its effect on the chemical and isotopic evolution of Earth's crust-mantle system. Our model comprises four reservoirs: the bulk continental crust (CC), depleted upper mantle (UM), lower mantle (LM), and an isolated reservoir (IR) where recycled crust is stored transiently before being mixed with the LM. The changing abundance of isotope species in each reservoir is quantified using a series of first order linear differential equations that are solved numerically using the fourth order Runge-Kutta method at 1 Myr time steps for 4.56 Gyr (the age of the Earth). The model results show that only continuous and exponential crustal growth reproduces the present-day abundances and isotope ratios in the terrestrial reservoirs. Our preferred crustal growth model suggests that the mass of the CC by the end of Hadean (4.0 Ga) and end of Archean (2.5 Ga) was similar to 30% and similar to 75% of the present-day mass of the CC, respectively. Models proposing formation of most (similar to 90%) of the present-day CC during the initial 1 Gyr or nearly 50-60% during the last 1 Gyr are least favorable. Significant mass exchange between crust and mantle, that is, both the formation and recycling of crust, started in the Hadean with Sm-Nd and Lu-Hf isotope evolution typical for mafic rocks. Depletion of the UM (in incompatible elements) during the early Archean is mitigated by the input of recycled crust, so that the UM maintained a near-primitive Hf-Nd isotope composition. The LM also retained a near-primitive Hf-Nd isotope composition during the Archean, but for different reasons. In contrast to the UM, the crustal return flux into the LM is transiently stored (similar to 1 Gyr) in an isolated reservoir (IR), which limits the mass flux into and out of the LM. The IR in our model is distinct from other mantle reservoirs and possibly related to stable crustal blocks or, alternatively, to recycled crust in the mantle that remains temporarily isolated, perhaps at the core-mantle boundary (LLSVPs).