Geochemistry of crustal formation and evolution

Terrestrial planets produce crusts as they differentiate. The Earth’s bi-modal crust, with a high-standing granitic continental crust and a low-standing basaltic oceanic crust, is unique in our solar system and links the evolution of the interior and exterior of this planet. Here I present geochemical observations to constrain processes accompanying crustal formation and evolution. My approach includes geochemical analyses, quantitative modeling, and experimental studies. The Archean crustal evolution project represents my perspective on when Earth’s continental crust began forming. In this project, I utilized critical element ratios in sedimentary records to track the evolution of the MgO content in the upper continental crust as a function time. The early Archean subaerial crust had >11 wt. % MgO, whereas by the end of Archean its composition had evolved to about 4 wt. % MgO, suggesting a transition of the upper crust from a basalt-like to a more granite-like bulk composition. Driving this fundamental change of the upper crustal composition is the widespread operation of subduction processes, suggesting the onset of global plate tectonics at ~ 3 Ga (Abstract figure). Three of the chapters in this dissertation leverage the use of Eu anomalies to track the recycling of crustal materials back into the mantle, where Eu anomaly is a sensitive measure of the element’s behavior relative to neighboring lanthanoids (Sm and Gd) during crustal differentiation. My compilation of Sm-Eu-Gd data for the continental crust shows that the average crust has a net negative Eu anomaly. This result requires recycling of Eu-enriched lower continental crust to the mantle. Mass balance calculations require that about three times the mass of the modern continental crust was returned into the mantle over Earth history, possibly via density-driven recycling. High precision measurements of Eu/Eu* in selected primitive glasses of mid-ocean ridge basalt (MORB) from global MORs, combined with numerical modeling, suggests that the recycled lower crustal materials are not found within the MORB source and may have at least partially sank into the lower mantle where they can be sampled by hot spot volcanoes. The Lesser Antilles Li isotope project provides insights into the Li systematics of this young island arc, a representative section of proto-continental crust. Martinique Island lavas, to my knowledge, represent the only clear case in which crustal Li is recycled back into their mantle source, as documented by the isotopically light Li isotopes in Lesser Antilles sediments that feed into the fore arc subduction trench. By corollary, the mantle-like Li signal in global arc lavas is likely the result of broadly similar Li isotopic compositions between the upper mantle and bulk subducting sediments in most arcs. My PhD project on Li diffusion mechanism in zircon is being carried out in extensive collaboration with multiple institutes and employs analytical, experimental and modeling studies. This ongoing project, finds that REE and Y play an important role in controlling Li diffusion in natural zircons, with Li partially coupling to REE and Y to maintain charge balance. Access to state-of-art instrumentation presented critical opportunities to identify the mechanisms that cause elemental fractionation during laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) analysis. My work here elucidates the elemental fractionation associated with plasma plume condensation during laser ablation and particle-ion conversion in the ICP.

Essays on Matching Markets and Their Equilibria

Matching theory and matching markets are a core component of modern economic theory and market design. This dissertation presents three original contributions to this area. The first essay constructs a matching mechanism in an incomplete information matching market in which the positive assortative match is the unique efficient and unique stable match. The mechanism asks each agent in the matching market to reveal her privately known type. Through its novel payment rule, truthful revelation forms an ex post Nash equilibrium in this setting. This mechanism works in one-, two- and many-sided matching markets, thus offering the first mechanism to unify these matching markets under a single mechanism design framework. The second essay confronts a problem of matching in an environment in which no efficient and incentive compatible matching mechanism exists due to matching externalities. I develop a two-stage matching game in which a contracting stage facilitates subsequent conditionally efficient and incentive compatible Vickrey auction stage. Infinite repetition of this two-stage matching game enforces the contract in every period. This mechanism produces inequitably distributed social improvement: parties to the contract receive all of the gains and then some. The final essay demonstrates the existence of prices which stably and efficiently partition a single set of agents into firms and workers, and match those two sets to each other. This pricing system extends Kelso and Crawford's general equilibrium results in a labor market matching model and links one- and two-sided matching markets as well.