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Melt Migration in a Heterogeneous Mantle

The generation and segregation of melt from the earth's interior is a fundamental, but only partially understood, process. Melt segregation involves interacting physical processes on a wide range of length scales. Melt, generated at the millimeter scale of individual mineral grains, migrates through porous solid mantle, perhaps in an interconnected network of channels that forms at scales of tens of meters. This melt, driven by buoyancy forces and stresses that develop in solid mantle, flows on scales of hundreds of kilometers (Figure 1). It has been suggested that high-porosity pyroxene-free dunite channels may serve as pathways for efficient extraction of melt formed in the deep mantle. With postdocs Alan Schemenz and Marc Hesse, and Profs. Marc Parmentier and Jan Hesthaven (Applied Math, Brown University), we examined the dynamics of reactive dissolution along a solubility gradient in an upwelling and viscously deformable mantle column. Three dynamics regimes are identified through linear stability analysis (Hesse et al., 2011): channel regime where melt localizes into high porosity channels, wave regime where melt migrates in the form of compaction-dissolution waves, and a stable regime. The compaction-dissolution waves are different from the solitary waves discussed in the magma dynamics literature in that the wave speed of the former is smaller than that of the buoyancy-driven melt migration. A parameter study shows that compaction-dissolution waves may play an important role for melt migration beneath mid-ocean ridges.

To better understand the first order characteristics of high-porosity melt channels and compaction-dissolution waves, we conducted two-dimensional (2D) numerical simulations of reactive dissolution in an upwelling and chemically heterogeneous porous medium (Liang et al. 2010, 2011; Schiemenz et al, 2011). With the help of high-order accurate numerical methods, we are able to study the detailed structures of high-porosity channels and show the spatial and temporal relations among compaction-dissolution waves, high-porosity melt channels, and dunite channels. Only the upper part of high-porosity channel is pyroxene-free dunite. The lower parts are harzburgite and lherzolite (Figure 2). It is surprisingly difficult to initiate high-porosity channels at great depth (i.e., near mantle solidus). In general, the temporal evolution of an upwelling melting column follows four distinct stages: initiation of compaction-dissolution waves; development of dunite channels; reorganization of the wave and channel fields; and quasi steady-state evolution of the waves and channels (Figure 3). This cascade of different melt migration styles occurs over a period of 5~50 Ma (depending on compaction length). The spatial and temporal distributions of lithology, porosity, and melt flow fields documented in our 2D simulations have important geochemical (and geophysical) implications. Transient melt flow in the wave regime, for example, results in significant lateral mixing and chromatographic fractionation even when mantle source compositions are independent of time (Figure 4). Small-scale variations in isotope ratios recorded in basalts and peridotites may result, at least in part, from the dynamics of melt migration in the asthenospheric mantle, in addition to (or rather than) convective mixing in the mantle source. We are actively pursuing this and related melt migration problems through a combination of high-order numerical simulations in 2D and 3D, and simple geochemical modeling of trace element and isotope variations in basalts and residual peridotites reported in the literature.

Perspective students should contact Professor Liang or Professor Parmentier for more information.


Related References:
Liang, Y. (2008) Simple models for concurrent melting and melt migration in an upwelling heterogeneous mantle column: Analytical solutions. Geochim. Cosmochim. Acta. 72, 3804-3821 (doi: 0.1016/j.gca.2008.05.050).

Liang, Y. and Peng, Q. (2010) Non-modal melting in an upwelling mantle column: Steady-state models with applications to REE depletion in abyssal peridotites. Geochim. Cosmochim. Acta 74, 321-339 (doi: 10.1016/j.gca.2009.09.029).

Liang, Y. and Parmentier, E. M. (2010) A two-porosity double lithology model for partial melting, melt migration and melt-rock reaction in the mantle: The nature of channel melt and the role of matrix dissolution. J. Petrol. 51, 125-152 (doi:10.1093/petrology/egp086).

Liang, Y., Schiemenz, A., Hesse, M., Parmentier, E. M., and Hesthaven, J. S. (2010) High-porosity channels for melt migration in the mantle: Top is the dunite and bottom is the harzburgite and lherzolite. Geophys. Res. Lett. 37, L15306, doi: 10.1029/2010GL044162.

Schiemenz, A., Liang, Y., Parmentier, E. M. (2011) A high-order numerical study of reactive dissolution in an upwelling heterogeneous mantle: I. Channelization, channel lithology, and channel geometry. Geophysical Journal International, 186, 641-664, doi: 10.1111/j.1365-246X.2011.05065.x.

Hesse, M., Schiemenz, A., Liang, Y., and Parmentier, E. M. (2011) Compaction-dissolution waves in an upwelling mantle column. Geophysical Journal International, doi: 10.1111/j.1365-246X.2011.05177.x.

Liang, Y., Schiemenz, A., Hesse, M., and Parmentier, E. M. (2011) Waves, channels, and the preservation of chemical heterogeneities during melt migration in the mantle. 38, L20308, Geophys. Res. Lett. doi:10.1029/2011GL049034.

Brown faculty collaborators:

Jan Hesthaven
Marc Parmentier

Other project collaborators:

Marc Hesse, Alan Schiemenz, Seshu Tirupathi, Chenguang Sun, Conroy Baltzell

Figure 1. Multiscales of melt generation and segregation in the mantle. The largest scale defines the setting in which melting occurs. At the smallest scale partial melting occurs by chemical reactions between different mineral grains. The intermediate scale that controls the rate of melt transport can be broadly described as a porous block with multiple scales of porosity. High porosity melt channels consisting primarily of the mineral olivine are thought to be a consequence of rising melt dissolving minerals clinopyroxene (cpx) and orthopyroxene (opx) while precipitating olivine. Here D refers to the rock dunite that comprises almost entirely of olivine with small amount of cpx and spinel. H represents harzburgite composed of olivine + opx ± cpx ± spinel.

Figure 2. Steady-state distributions of (a) porosity and (d) the soluble mineral opx in a short upwelling column. (b) Close-up view of the porosity field in the highlighted area near the top of the wider channel. (c) Close-up view of the opx field in the highlighted region near the bottom of the wider dunite channel. Dark blue regions in Figure 1d mark the opx-free dunite channels. White curves in Figures 1b and 1c are streamlines of the melt. The two dunite channels were initiated by two small but sustained Gaussian perturbations in porosity at the bottom of the upwelling column. Steady state is established after one solid overturn (t ≥ 2). Porosity and opx modal abundance are normalized to their respective background values (2% and 15%, respectively) at the bottom of the upwelling column.

Figure 3. Distributions of (a–d) porosity and (e–h) the soluble mineral opx at four selected times in an upwelling column. Dark blue regions in Figures 2f–2h mark the opx-free dunite channels. Curves in Figures 2e–2h are melt streamlines. Dimensions of the waves are outlined by the dashed rectangles in Figures 2b and 2d. Porosity and opx abundance are normalized to their background values (1% and 20%, respectively) at the bottom of the upwelling column. Time is measured in units of solid upwelling time which is the time needed to advance the solid by one compaction length. One solid overturn takes 6.75 time units in this example.

Figure 4. Distributions of (a–c) 86Sr/87Sr and (d–f) 143Nd/144Nd isotopic ratios in the melt and solid at three selected times in an upwelling column. The isotopic ratios were calculated using the porosity, opx, and velocity fields from the case shown in Figure 3 while neglecting diffusion and dispersion in the melt. The white lines in each panel are melt streamlines.

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Research at Brown: Yan Liang: Melt Migration in a Heterogeneous Mantle
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