{"title":"A REE Inverse Model From Bulk Distribution Coefficients and Boundary Conditions: Results for Shield and Rejuvenated Stage Hawaiian Volcanoes","authors":"M. J. Carr, M. D. Feigenson, E. Gazel","doi":"10.1029/2024GC011651","DOIUrl":null,"url":null,"abstract":"<p>A major challenge in mantle geochemistry is determining the source composition and melt fraction involved in melting. We provide a new Rare-Earth Element (REE) inverse model that provides source concentration, source and melt mineral modes, and melt fraction based on the difference between separate determinations of bulk distribution coefficients and constrained by boundary conditions. An analytical inverse of the batch melting equation provides expressions for source, <span></span><math>\n <semantics>\n <mrow>\n <msubsup>\n <mi>C</mi>\n <mi>o</mi>\n <mi>i</mi>\n </msubsup>\n </mrow>\n <annotation> ${C}_{o}^{i}$</annotation>\n </semantics></math>, and bulk distribution coefficient of the mantle, <span></span><math>\n <semantics>\n <mrow>\n <msubsup>\n <mi>D</mi>\n <mi>o</mi>\n <mi>i</mi>\n </msubsup>\n </mrow>\n <annotation> ${D}_{o}^{i}$</annotation>\n </semantics></math>, with two unknowns, the initial concentration of La in the mantle, <span></span><math>\n <semantics>\n <mrow>\n <msubsup>\n <mi>C</mi>\n <mi>o</mi>\n <mrow>\n <mi>L</mi>\n <mi>a</mi>\n </mrow>\n </msubsup>\n </mrow>\n <annotation> ${C}_{o}^{La}$</annotation>\n </semantics></math>, and <i>P</i><sup><i>i</i></sup>, the bulk distribution coefficient of the melt. We traverse through a range of <span></span><math>\n <semantics>\n <mrow>\n <msubsup>\n <mi>C</mi>\n <mi>o</mi>\n <mrow>\n <mi>L</mi>\n <mi>a</mi>\n </mrow>\n </msubsup>\n </mrow>\n <annotation> ${C}_{o}^{La}$</annotation>\n </semantics></math> steps and examine thousands of melt modes, <i>P</i><sup><i>i</i></sup>, at each step. Thousands of trial melt modes fail by generating <span></span><math>\n <semantics>\n <mrow>\n <msubsup>\n <mi>D</mi>\n <mi>o</mi>\n <mi>i</mi>\n </msubsup>\n </mrow>\n <annotation> ${D}_{o}^{i}$</annotation>\n </semantics></math> that are inconsistent with partition coefficients. Many surviving trials cannot be inverted to estimate a mantle mode. Other boundary conditions eliminate even more trials. Surviving trials are ordered by the difference between <span></span><math>\n <semantics>\n <mrow>\n <msubsup>\n <mi>D</mi>\n <mi>o</mi>\n <mi>i</mi>\n </msubsup>\n </mrow>\n <annotation> ${D}_{o}^{i}$</annotation>\n </semantics></math> calculated from the REE data of a lava suite and <span></span><math>\n <semantics>\n <mrow>\n <msubsup>\n <mi>D</mi>\n <mi>c</mi>\n <mi>i</mi>\n </msubsup>\n </mrow>\n <annotation> ${D}_{c}^{i}$</annotation>\n </semantics></math> calculated from partition coefficients and mantle mode. We select the solution with the closest fit that passes all the boundary conditions. We tested our new model with lava suites from Hawaii where different lines of evidence suggest that they melted from different mantle sources, Mauna Kea representing shield-stage lava and submarine Kiekie representing rejuvenated stage lava. Our inverse determination of mantle composition and melting parameters was consistent with earlier models based on assumptions of HREE composition.</p>","PeriodicalId":50422,"journal":{"name":"Geochemistry Geophysics Geosystems","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1029/2024GC011651","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geochemistry Geophysics Geosystems","FirstCategoryId":"89","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1029/2024GC011651","RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"GEOCHEMISTRY & GEOPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
A major challenge in mantle geochemistry is determining the source composition and melt fraction involved in melting. We provide a new Rare-Earth Element (REE) inverse model that provides source concentration, source and melt mineral modes, and melt fraction based on the difference between separate determinations of bulk distribution coefficients and constrained by boundary conditions. An analytical inverse of the batch melting equation provides expressions for source, , and bulk distribution coefficient of the mantle, , with two unknowns, the initial concentration of La in the mantle, , and Pi, the bulk distribution coefficient of the melt. We traverse through a range of steps and examine thousands of melt modes, Pi, at each step. Thousands of trial melt modes fail by generating that are inconsistent with partition coefficients. Many surviving trials cannot be inverted to estimate a mantle mode. Other boundary conditions eliminate even more trials. Surviving trials are ordered by the difference between calculated from the REE data of a lava suite and calculated from partition coefficients and mantle mode. We select the solution with the closest fit that passes all the boundary conditions. We tested our new model with lava suites from Hawaii where different lines of evidence suggest that they melted from different mantle sources, Mauna Kea representing shield-stage lava and submarine Kiekie representing rejuvenated stage lava. Our inverse determination of mantle composition and melting parameters was consistent with earlier models based on assumptions of HREE composition.
地幔地球化学的一个主要挑战是确定熔融过程中涉及的源成分和熔体分数。我们提供了一种新的稀土元素(REE)反演模型,它可以提供源浓度、源和熔融矿物模式,以及基于单独测定的体分布系数和边界条件约束之间的差值的熔融分数。批量熔融方程的分析逆模型提供了源 C o i ${C}_{o}^{i}$ 和地幔体分布系数 D o i ${D}_{o}^{i}$ 的表达式,其中有两个未知数,即地幔中 La 的初始浓度 C o L a ${C}_{o}^{La}$ 和熔体的体分布系数 Pi。我们遍历了 C o L a ${C}_{o}^{La}$ 的一系列步骤,并在每个步骤中检验了数千种熔体模式 Pi。数以千计的试验熔融模式因产生与分区系数不一致的 D o i ${D}_{o}^{i}$ 而失败。许多幸存的试验无法反演以估计地幔模式。其他边界条件则会消除更多的试验。根据熔岩套件的 REE 数据计算出的 D o i ${D}_{o}^{i}$ 与根据分区系数和地幔模式计算出的 D c i ${D}_{c}^{i}$ 之间的差值,对存活的试验进行排序。我们选择最接近拟合且通过所有边界条件的解。我们用夏威夷的熔岩套件测试了我们的新模型,不同的证据表明它们熔化自不同的地幔源,莫纳凯亚代表屏蔽期熔岩,而海底基基代表再生期熔岩。我们对地幔成分和熔融参数的反向确定与早期基于 HREE 成分假设的模型是一致的。
期刊介绍:
Geochemistry, Geophysics, Geosystems (G3) publishes research papers on Earth and planetary processes with a focus on understanding the Earth as a system. Observational, experimental, and theoretical investigations of the solid Earth, hydrosphere, atmosphere, biosphere, and solar system at all spatial and temporal scales are welcome. Articles should be of broad interest, and interdisciplinary approaches are encouraged.
Areas of interest for this peer-reviewed journal include, but are not limited to:
The physics and chemistry of the Earth, including its structure, composition, physical properties, dynamics, and evolution
Principles and applications of geochemical proxies to studies of Earth history
The physical properties, composition, and temporal evolution of the Earth''s major reservoirs and the coupling between them
The dynamics of geochemical and biogeochemical cycles at all spatial and temporal scales
Physical and cosmochemical constraints on the composition, origin, and evolution of the Earth and other terrestrial planets
The chemistry and physics of solar system materials that are relevant to the formation, evolution, and current state of the Earth and the planets
Advances in modeling, observation, and experimentation that are of widespread interest in the geosciences.