| Abstrakt: |
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, Coi ${C}_{o}^{i}$, and bulk distribution coefficient of the mantle, Doi ${D}_{o}^{i}$, with two unknowns, the initial concentration of La in the mantle, CoLa ${C}_{o}^{La}$, and Pi, the bulk distribution coefficient of the melt. We traverse through a range of CoLa ${C}_{o}^{La}$ steps and examine thousands of melt modes, Pi, at each step. Thousands of trial melt modes fail by generating Doi ${D}_{o}^{i}$ 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 Doi ${D}_{o}^{i}$ calculated from the REE data of a lava suite and Dci ${D}_{c}^{i}$ 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. Plain Language Summary: Determining the composition of our planet's interior is a major goal of geochemistry. The most common approach is to make forward models based on reasonable assumptions about the source composition and the melting process to calculate synthetic compositions that match the observed lava. Successful forward models may be difficult to achieve, but nevertheless remain dependent on initial assumptions. In principle, inverse models make fewer assumptions and achieve more objective results. Even so, most published inverse models for mantle melting require assumptions about the source. The inverse modeling described here relies on boundary conditions and the match between observed and calculated bulk distribution coefficients to determine the behavior of mantle parameters as a function of the initial lanthanum concentration (CoLa ${C}_{o}^{La}$). Certain behavior patterns allow determination of the optimum CoLa ${C}_{o}^{La}$, allowing a complete inverse. Successful inverse models for Hawaiian lava suites define two distinct mantle types, in agreement with past observations about these volcanoes. Key Points: Melt modes and mantle La concentrations generate trial source and bulk distribution profiles, but most solutions fail boundary conditionsTrial solutions are ranked by comparing observed and calculated bulk distribution profiles. The best fit over a range of La is the solutionOptimum source and bulk distribution profiles provide melt extents for shield stage Hawaiian tholeiites and rejuvenated basalts [ABSTRACT FROM AUTHOR] |
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