The Importance of the Size and Distribution of Mantle Heterogeneities to the Interpretation of Isotope Ratios and Trace Element Abundances in Basalts

夏威夷等海洋岛屿是由火山喷发形成的。为火山提供燃料的岩浆是由地球内部的部分融化产生的。在大洋岛屿和海底大洋中脊取样的大洋玄武岩，为了解难以接近的地球的组成以及地幔中岩浆产生和运输的过程和时间尺度提供了重要线索。地球化学中的一个基本观察是，地幔中大洋玄武岩的源区是不均匀的，由不同大小和分布的化学和岩石学上不同的区域组成。这种不均匀的地幔来源的部分熔融导致了地表喷发的各种玄武岩岩浆。地幔不均质性的大小和分布尚不清楚，但可能在控制玄武岩中观察到的化学变化方面发挥了重要作用。长期存在的地球化学问题之一是将玄武岩中观察到的不均质性映射到地幔源区的化学和岩性不均质性。这种映射是非线性的，其数学表达式是未知的。本文旨在研究地幔不均质性的大小和分布对大洋玄武岩的同位素比值和微量元素丰度的影响。该项目的结果将使地球化学家能够建立玄武岩与其地幔来源之间的非线性映射。该项目将通过为本科生提供研究机会，以及通过培训研究生和博士后学者培养具有竞争力的STEM劳动力来促进STEM教育。这项拟议研究的主要目标是：(1)找到玄武岩与其地幔来源之间的非线性映射的函数形式；(2)建立一个框架，用于理解和解释在空间和时间上相关的大洋玄武岩中同位素比和微量元素丰度的变化；(3)通过一些案例研究来检验新模型，在这些案例研究中，可以获得时间或空间的地球化学数据。要建立非线性映射，需要知道非均质性的性质(化学和岩性、大小和分布)、熔融的类型(批量和分批)、熔体迁移过程(沟道化和颗粒尺度多孔流)，以及残余矿物和渗流熔体之间化学不平衡的程度。时间和空间变量将被添加到地球化学文献中广泛使用的熔融模型中。这些随时间变化的熔融模型将使地球化学家能够系统地研究地幔源区不均质性的大小和分布在控制提取熔体中的同位素比值和不相容的微量元素丰度变化中的作用。二维模型将使用一维含时熔化模型来构造。这些物理上更真实的模型将被用来研究大洋中脊玄武岩和大洋岛屿玄武岩中锶-钕-氢-铅同位素的变化和选定的不相容的微量元素比率。这项拟议工作的一个重要成果是为岩石学家和地球化学家提供了一套新的解释工具，用于研究时空相关的地幔和地幔衍生样品。这一奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Oceanic islands such as Hawaii are formed by volcanic eruptions. Magmas that feed the volcanos are produced by partial melting in the interior of the Earth. Oceanic basalts, which are sampled at oceanic islands and along mid-ocean ridges on the seafloor, provide important clues to understanding the composition of the inaccessible Earth and the processes and time scales of magma generation and transport in the mantle. A fundamental observation in geochemistry is that the source regions of oceanic basalts in the mantle are heterogeneous and consist of chemically and lithologically distinct domains of variable size and distribution. Partial melting of such heterogeneous mantle sources gives rise to a diverse range of basaltic magmas erupted on the surface. The size and distribution of mantle heterogeneities are unknown, but may have played an important role in controlling chemical variations observed in basalts. One of the long-standing problems of geochemistry is the mapping of heterogeneities observed in basalts into the chemical and lithological heterogeneities in the mantle source. Such a mapping is nonlinear and its mathematical expression is unknown. The thesis of this project is to investigate how the size and distribution of mantle heterogeneities affect the isotope ratios and trace element abundances in oceanic basalts. Results from this project will enable geochemists to establish the nonlinear mapping between basalts and their mantle sources. The project would advance STEM education by providing research opportunities for undergraduate students and by developing of a competitive STEM workforce through training of graduate students and postdoc scholar. The primary objectives of this proposed study are (1) to find the functional forms for the nonlinear mapping between basalts and their mantle sources; (2) to develop a framework for understanding and interpreting variations in isotope ratios and trace element abundances in spatially and temporally associated oceanic basalts; and (3) to test the new models through selected case studies where temporal or spatial geochemical data are available. To establish the nonlinear mapping, one needs to know the nature of heterogeneity (chemical vs. lithological, size and distribution), the style of melting (batch vs. fractional), the process of melt migration (channelized vs. grain-scale porous flow), and the extent of chemical disequilibrium between residual minerals and the percolating melt. Time and spatial variables will be added to the widely used melting models in the geochemical literature. These time-dependent melting models will enable geochemists to systematically study the roles of the size and distribution of heterogeneities in the mantle source in controlling the variations of isotope ratios and incompatible trace element abundances in extracted melts. Two-dimensional models will be constructed using the one-dimensional time-dependent melting models. These physically more realistic models will be used to examine variations of Sr-Nd-Hf-Pb isotope and selected incompatible trace element ratios in mid-ocean ridge basalts and ocean island basalts. An important outcome of the proposed work is a set of new interpretation tools to petrologists and geochemists in their studies of spatially and temporally correlated mantle and mantle-derived samples.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.