Simple models for dynamic melting in an upwelling heterogeneous mantle column: Analytical solutions

Abstract

Several lines of evidence suggest that the melt generation and segregation regions of the mantle are heterogeneous, consisting of chemically and lithologically distinct domains of variable size and dimension. Partial melting of such heterogeneous mantle source regions gives rise to a diverse range of basaltic magmas. In order to better assess the role of source heterogeneity during mantle melting, we have undertaken a theoretical study of trace element distribution and fractionation during concurrent melting and melt migration in an upwelling, chemically heterogeneous, two-porosity double lithology melting column. Analytical solutions for the abundance of a trace element in the matrix and channel were obtained under the assumptions that the porosity, melt and solid velocities, and solid–melt partition coefficients are constant and uniform. For simplicity, we neglected diffusion and dispersion in the melt. Chemical source heterogeneities of arbitrary size and shape were integrated into the simple melting models by allowing trace element abundance in the source region to vary as a function of time and space. Concurrent melting and melt migration in an upwelling heterogeneous mantle may be approximated as a quasi-steady state problem in which time-dependent concentration patterns produced by melting of heterogeneous source regions are superimposed on a reference steady-state concentration distribution established by melting of the ambient or background mantle. Chromatographic fractionation is especially important for the matrix melt and solid when chemical heterogeneities are involved during melting and melt migration in the mantle, giving rise to significant phase-shift between two incompatible trace elements in the matrix melt and scattered correlations among incompatible trace elements in residual peridotites. Mixing is the chief mass transfer process in the dunite channel where the chromatographic effect is negligible for most of the incompatible trace elements. The lack of chromatographic fractionation among incompatible trace elements and isotopic ratios in MORB suggests either most MORB are channel melts or mixing in magma conduit and chamber is very efficient such that the phase-shift is averaged out during magma transport and storage processes. Advection brings melt produced by smaller-degree of melting in the deeper part of the melting column to the overlying melting region, increasing the incompatible trace element abundance in the matrix and the channel. This advection-induced self-enrichment is especially important when heterogeneous sources are involved and may account for some of the enriched incompatible trace element patterns observed in residual peridotite that were previously interpreted to be a result of mantle metasomatism. Systematic studies of high-resolution spatially correlated mantle samples may help to constrain the melting history and the size and nature of chemical heterogeneities in the mantle.