Channeling instability of upwelling melt in the mantle

Abstract

We present results of a theoretical study aimed at understanding melt extraction from the upper mantle. Specifically, we address mechanisms for focusing of porous flow of melt into conduits beneath mid‐ocean ridges in order to explain the observation that most oceanic residual peridotites are not in equilibrium with mid‐ocean ridge basalt. The existence of such conduits might also explain geological features, termed replacive dunites, that are observed in exposed mantle sections. We show here, by linear analysis, that flow in a chemically reactive porous media is unstable in the presence of a solubility gradient, such as induced by adiabatic ascent of melt underneath mid‐ocean ridges. The initially homogeneous flow becomes focused in time to produce elongated high‐porosity fingers that act as conduits for transport of fast flowing melt. This instability arises due to a positive feedback mechanism in which a region of slightly higher than average porosity causes increased influx of unsaturated flow, leading to increased dissolution which further reduces the Porosity. Even in the presence of matrix compaction and chemical diffusion the instability is demonstrated to be robust. Our analysis also indicates the existence of growing, traveling waves which transport and amplify porosity and concentration perturbations.

Spatial distribution of melt conduits in the mantle beneath oceanic spreading ridges: Observations from the Ingalls and Oman ophiolites

“…There may be several ways to generate such spatial relationships, but we favor the hypothesis that the dunites represent a coalescing melt transport network, in which flux from many small veins feeds a few large ones, and flow is ultimately focused to a narrow region beneath oceanic spreading ridges (Figure 8). This result is broadly consistent with the hypothesis that mantle melt extraction may occur within a fractal branching network [Hart, 1993] and with recent analytical and numerical results on formation of dissolution channels via flow of a solvent through a partially soluble, compacting porous medium [Aharonov et al, 1995;Kelemen et al, 1995b;Spiegelman et al, 2000]. We are intrigued by the possibility that such networks may arise spontaneously in nature, in this case as a result of reactive porous flow where disequilibrium arises from the release of gravitational potential energy during ascent of melt.…”

“…At longer times the fastest growing channels entrain more of the total flux, starving their neighbors, leading to a decreasing number of more widely spaced features [Kelemen et al, 1995b]. As discussed by Aharonov et al [1995], scaling relationships based on a linear stability analysis suggest that unstable formation of dissolution channels in viscously compacting porous media could give rise to a coalescing channel network ( Figure 5A). …”

“…(1) The dunites formed part of a coalescing network of channels, in which many small channels fed a few larger ones [e.g., Aharonov et al, 1995;Kelemen et al, 1995b;Spiegelman et al, 2000]. (2) The dunites formed as porous reaction zones around melt-filled cracks [e.g., Suhr, 1999].…”

“…However, for porosity in 0.01-m channels of 0.001 and m = 3, then the porosity in dunites 10 m wide would be $0.1, which may be reasonable. Alternatively, there may be a maximum porosity within channels, which is reached when the increasing rate of viscous compaction (due to the exponential decrease in bulk viscosity as Figure A1 of Aharonov et al [1995]. (C, D, E, and F) Results of numerical modeling of the reactive infiltration instability [Spiegelman et al, 2000], in a two-dimensional system undergoing porous flow and viscous compaction, with a fixed flux of solvent through the bottom boundary, a free top boundary, wrap-around side boundaries (image is repeated once).…”

“…Melt extraction in fractures spanning the melting region in mantle undergoing passive, corner flow beneath a spreading ridge cannot satisfy this constraint, because such fractures, formed parallel to the direction of maximum compressive stress, would reach the top of the mantle over a region more than 80 km wide [Sleep, 1984]. Instead, focusing of melt extraction in a narrow region beneath the ridge axis requires either (1) very highly focused solid mantle upwelling [Buck and Su, 1989;Jousselin et al, 1998;Nicolas and Rabinowicz, 1984;Rabinowicz et al, 1984], or (2) a variety of porous flow mechanisms including``suction'' due to corner flow [Phipps Morgan, 1987;Spiegelman and McKenzie, 1987]; anisotropic permeability along mineral foliation [Phipps Morgan, 1987] or in stress controlled planes of high porosity [Daines and Kohlstedt, 1997;Zimmerman et al, 1999]; channels at the base of thè`l ithosphere,'' beneath a permeability barrier created by melt crystallization [Sparks and Parmentier, 1991;Spiegelman, 1993]; and coalescence of dissolution channels forming as a result of reactive porous flow [Aharonov et al, 1995;Kelemen et al, 1995b;Spiegelman et al, 2000].…”