Stretching chemical heterogeneities by melt migration in an upwelling mantle: An analysis based on time-dependent batch and fractional melting models

The source region of basalt in the upper mantle is heterogeneous and may consist of depleted background mantle and blobs of enriched mantle. The size, shape, and distribution of the enriched blobs in the upper mantle are unknown but may play an important role in controlling variations in isotope ratios and trace element abundances in basalts and residual peridotites. During decompression melting, the mass flux of interstitial melt increases while the mass flux of residual solid decreases upward from the solidus, resulting in an acceleration of the effective transport velocity for an incompatible trace element in the residue. Consequently, a blob of chemical heterogeneity is stretched during its transit through the melting column. Here we quantify the melt migration induced size change by allowing trace element abundances and isotope ratios in the mantle source to vary as a function of time and space. We use simple analytical solutions for the time-dependent batch melting and fractional melting models to illustrate how a trace element or an isotope ratio varies spatially and temporally in an upwelling and chemically heterogeneous melting column. We show that an enriched blob as marked by isotope or incompatible trace element anomaly is variably stretched along the direction of melt flow during its transit through the melting column. The amount of stretching depends on the extent of melting, style of melt extraction (batch vs. fractional), porosity of the melting column, and partition coefficient, and can be quantified by a dimensionless parameter called the stretching factor. For radiogenic isotopes U, Th, Pb, Sr, Nd, and Hf, a factor of 2∼8 stretching is expected for the residue and a factor of at least 30 is found for the channel melt. For near fractional melting beneath mid-ocean ridge, an enriched Nd isotope signal takes approximately 10 times more time to transit through the low-porosity matrix than through the high-porosity channel. Hence chemical heterogeneities observed in residual peridotites and extracted melts are decoupled both spatially and temporally, which has important implications for the interpretation of isotope and trace element characteristics of the basalts and residual peridotites.