The upper mantle is widely considered to be heterogeneous, possibly comprising a "marble-cake" mixture of heterogeneous domains in a relatively well-mixed matrix. The extent to which such domains are capable of producing and expelling melts with characteristic geochemical signatures upon partial melting, rather than equilibrating diffusively with surrounding peridotite, is a critical question for the origin of ocean island basalts (OIB) and mantle heterogeneity, but is poorly constrained. Central to this problem is the characteristic length scale of heterogeneous domains. If radiogenic osmium signatures in OIB are derived from discrete domains, then sub-linear correlations between Os isotopes and other geochemical indices, suggesting melt-melt mixing, may be used to constrain the length scales of these domains. These constraints arise because partial melts of geochemically distinct domains must segregate from their sources without significant equilibration with surrounding peridotite. Segregation of partial melts from such domains in upwelling mantle is promoted by compaction of the domain mineral matrix, and must occur faster than diffusive equilibration between the domain and its surroundings. Our calculations show that the diffusive equilibration time depends on the ratios of partition and diffusion coefficients of the partial melt and surrounding peridotite. Comparison of time scales between diffusion and melt segregation shows that segregation is more rapid than diffusive equilibration for Os, Sr, Pb, and Nd isotopes if the body widths are greater than tens of centimeter to several meters, depending on the aspect ratio of the bodies, on the melt fraction at which melt becomes interconnected in the bodies, and on the diffusivity in the solid. However, because Fe-Mg exchange occurs significantly more rapidly than equilibration of these isotopes under solid-state and partially molten conditions, it is possible that some domains can produce melts with Fe/Mg ratios reflecting that of the surrounding mantle but retaining isotopic signatures of heterogeneous domains. Although more refined estimates on the rates of, and controls on, Os mobility are needed, our preliminary analysis shows that heterogeneous domains large enough to remain compositionally distinct in the mantle (as solids) for ∼109 yr in a marble-cake mantle, can produce and expel partial melts faster than they equilibrate with surrounding peridotite.
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We gratefully acknowledge Shun Karato, Eiichi Takahashi, David Kohlstedt, Daisuke Yamazaki, Ken Koga, Ritsuo Morishita, and Ben Holtzmann for assistance and for stimulating discussions, and Glenn Gaetani and Harry Becker for their comments. We also thank constructive reviews by Stan Hart, John Lassiter, Jim van Orman, and Fred Frey. This work was supported by NSF 9876255.
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