Non-modal melting in an upwelling mantle column: Steady-state models with applications to REE depletion in abyssal peridotites and the dynamics of melt migration in the mantle

Simple models for trace element fractionation during concurrent melting and melt migration in an upwelling steady-state mantle were developed. Based on petrologic considerations, we divided the mantle column into two regions: a single-lithology lower region that consists of partially molten garnet and spinel lherzolites and a double-lithology upper region where high-porosity dunite channels or melt-filled fractures are embedded in a porous lherzolite/harzburgite matrix. Analytical solutions for the case of a constant and uniform relative melting suction rate and a linearly variable relative melt suction rate were obtained. Key parameters and the first order characteristics of melting and melt migration in a 1-D steady-state mantle column were examined through forward calculations and Monte Carlo simulations. Melting in the upwelling single-lithology column is equivalent to non-modal batch melting, whereas melting and melt migration in the double-lithology region can be viewed as a nonlinear combination of batch melting and fractional melting, depending on the amount of melt extracted to the channel. The degree of melting (F), the degree of melting at the depth of melt-channel initiation (F_d) and the relative rate of melt suction (R) are important in controlling the extent of depletion of the incompatible trace element in the matrix. Spatially variable R affects the abundance of an incompatible trace element in the melt and residual solid the most in near fractional melting. There is a strong nonlinear trade off among the three parameters. Given F_d, it is possible to constrain F and R from incompatible trace element abundances in residual peridotite.To explore the dynamics of melt migration in the mantle, we used the two melting models developed in this study and published REE and Y abundances in diopside in abyssal peridotites from the Central Indian Ridge to infer their melting and melt migration history. Overall, the degrees of melting inferred from the trace element data are not sensitive to the value of F_d used in the inversion and ranges from 10% to 15%. The relative rate of melt suction depends slightly on the choice of F_d and ranges from 0.85 to 1.0 for F_d = 0.05 and 0.75 to 0.97 for F_d = 0. Further, the estimated R is inversely correlated with F, a robust feature independent of the choice of F_d. The upward decrease of R in an upwelling mantle column can be understood in terms of melt focusing in the lower part of the double-lithology region. And finally, given F and R, we found that the permeability and porosity of the lherzolite/harzburgite matrix also increase as a function of F in the melting column, with melt fractions ranging from 0.2% to 0.7% for a grain size of 5 mm.