Grain-size dynamics beneath mid-ocean ridges: Implications for permeability and melt extraction

摘要

Grain size is an important control on mantle viscosity and permeability, but is difficult or impossible to measure in situ. We construct a two-dimensional, single phase model for the steady state mean grain size beneath a mid-ocean ridge. The mantle rheology is modeled as a composite of diffusion creep, dislocation creep, dislocation accommodated grain boundary sliding, and a plastic stress limiter. The mean grain size is calculated by the paleowattmeter relationship of Austin and Evans (2007). We investigate the sensitivity of our model to global variations in grain growth exponent, potential temperature, spreading-rate, and mantle hydration. We interpret the mean grain-size field in terms of its permeability to melt transport. The permeability structure due to mean grain size may be approximated as a high permeability region beneath a low permeability region. The transition between high and low permeability regions occurs across a boundary that is steeply inclined toward the ridge axis. We hypothesize that such a permeability structure generated from the variability of the mean grain size may focus melt toward the ridge axis, analogous to Sparks and Parmentier (1991)-type focusing. This focusing may, in turn, constrain the region where significant melt fractions are observed by seismic or magnetotelluric surveys. This interpretation of melt focusing via the grain-size permeability structure is consistent with MT observation of the asthenosphere beneath the East Pacific Rise.Key Points: class="unordered" style="list-style-type:disc">The grain-size field beneath MORs can vary over orders of magnitude The grain-size field affects the rheology and permeability of the asthenosphere The grain-size field may focus melt toward the ridge axis class="kwd-title">Keywords: mid-ocean ridge, permeability, grain size, simulation class="head no_bottom_margin" id="__sec2title">IntroductionMid-ocean ridges (MOR) are a fundamental feature of terrestrial plate tectonics and the simplest of the main tectono-volcanic systems. The asthenospheric dynamics beneath and near MORs are driven mostly by spreading of lithospheric plates, which is a consequence of far-field tectonic stresses (e.g., slab pull). The passive asthenospheric flow caused by imposed plate spreading is dominantly controlled by the material properties of the asthenosphere and, in particular, its viscosity. Furthermore, asthenospheric flow beneath a ridge causes melting; this melt segregates to fuel MOR volcanism and production of oceanic crust. Melt segregation is controlled by the permeability of the partially molten asthenosphere. Both mantle permeability and viscosity are sensitive to mantle grain size, a key property that has received little consideration in most previous models.Grain size is a fundamental structural property of a polycrystalline material that can vary in response to conditions including stress, strain rate, temperature, and the presence of melt. Grain size growth and reduction are assumed to be consequences of independent and simultaneous processes [e.g., Austin and Evans, ; Hall and Parmentier, ]. In situations where these rates are balanced, a steady state grain size can be established. However, predictions of grain dynamics are complicated by the nonlinear relationships between the grain size, viscosity, and stress, which can lead to reinforcing feedbacks.Ductile strain localization is a well-studied example of a grain-size feedback [Poirier, ; Jessell and Lister, ; Drury et al., ; Jin et al., ; Braun et al., ; Montési and Hirth, ; Bercovici and Ricard, ]. It occurs when the viscosity is positively correlated with grain size. Deformational work reduces the local grain size, which in turn reduces the viscosity. A decrease in viscosity allows the local strain rate to increase, which further reduces the local grain size. This feedback mechanism is the basis for an instability that can emerge from an inhomogeneous initial viscosity and/or grain-size field and lead to strain localization. In the simple form discussed here, it does not rely on the presence of fluid or melt. However, strain localization in the presence of melt may lead to the generation of melt bands, which can lead to additional feedbacks on the localization process [Katz et al., ; Rudge and Bercovici, ].A second feedback in which grain size plays a role is associated with reactive flow of magma through a permeabile mantle matrix [Kelemen et al., ; Aharonov et al., ; King et al., ]. Magma rising under buoyancy is undersaturated in SiO2 and hence dissolves pyroxene and precipitates olivine; this process leaves a dunite residue as evidence of extensive reaction [Morgan and Liang, ^,]. If pyroxene is a pinning phase that limits the growth of olivine grains [Evans et al., ^{href="#b16" rid="b16" class=" bibr popnode">2001}], then reactive dissolution may enable more rapid growth of olivine. Since permeability depends on the square of grain size [e.g., von Bargen and Waff, ^{href="#b45" rid="b45" class=" bibr popnode">1986}], this would increase permeability, strengthening channelization and reactive dissolution, and enabling further olivine grain growth [Braun, ^{href="#b10" rid="b10" class=" bibr popnode">2004}].These two examples of feedback mechanisms emphasize the importance of grain-size variations in time and space for controlling the dynamics of mantle processes. Unfortunately, there are no direct measurements of in situ grain size in the Earth's mantle. Mantle xenoliths [Twiss, ^{href="#b44" rid="b44" class=" bibr popnode">1977}; Ave Lallemant et al., ^{href="#b4" rid="b4" class=" bibr popnode">1980}] and ophiolites [Braun, ^{href="#b10" rid="b10" class=" bibr popnode">2004}] can provide estimates for the range of grain sizes in the upper mantle, however, such studies provide no information about spatial variations in grain size on the scale of mantle dynamics beneath a ridge axis. Moreover, it is difficult to assess how much these samples have evolved during emplacment, and thus how representative the recorded grain sizes are of normal mantle conditions. Similarly seismic attenuation, which is a strong function of grain size [Karato, ^{href="#b27" rid="b27" class=" bibr popnode">2003}], typically cannot resolve grain-size variations on the length-scales that are important for controlling ridge dynamics.An alternative approach for assessing grain-size variations in the mantle is to couple numerical models with experimentally derived flow laws and grain-size evolution models. Behn et al. [^{href="#b7" rid="b7" class=" bibr popnode">2009}] used this approach to estimate grain size as a function of depth in the oceanic upper mantle. As part of their study they compared the models of Hall and Parmentier [^{href="#b19" rid="b19" class=" bibr popnode">2003}] and Austin and Evans [^{href="#b3" rid="b3" class=" bibr popnode">2007}] with experimental data for deformed wet and dry olivine. They found that the Austin and Evans [^{href="#b3" rid="b3" class=" bibr popnode">2007}] model provided closer agreement with the laboratory experiments. Behn et al. [^{href="#b7" rid="b7" class=" bibr popnode">2009}] modeled grain size in a one-dimensional vertical column with a composite rheology of dislocation and diffusion creep. The steady state grain size was calculated under the assumption that a constant fraction of mechanical work acts to reduce grain size. They found that the mean grain-size reaches a minimum of 15–20 mm at a depth of approximately 150 km. They also found that the structure of mean grain size is a good fit to the low seismic shear-wave velocity zone in the upper oceanic mantle. They predicted that dislocation creep is the dominant deformation mechanism for all depths of the upper mantle. However, Behn et al. [^{href="#b7" rid="b7" class=" bibr popnode">2009}] did not calculate the influence of mantle corner flow, and so the near-ridge strain-rate structure was oversimplified. Moreover, the assumption of a constant fraction of mechanical work reducing the mean grain size, as opposed to a fraction of dislocation work [Austin and Evans, ^{href="#b3" rid="b3" class=" bibr popnode">2007}], removed a potentially important coupling between the deformation mechanism and mean grain size.The goal of this study is to characterize the variations in grain-size beneath a mid-ocean ridge, with particular focus upon the implications for the permeability structure beneath the ridge. The permeability structure is an important control on melt migration and has been implicated as a key component in focusing of partial melt toward the ridge axis. In such focusing models [e.g., Sparks and Parmentier, ^{href="#b42" rid="b42" class=" bibr popnode">1991}; Spiegelman, ^{href="#b43" rid="b43" class=" bibr popnode">1993}; Ghods and Arkani-Hamed, ^{href="#b18" rid="b18" class=" bibr popnode">2000}; Hebert and Montési, ^{href="#b21" rid="b21" class=" bibr popnode">2010}], the cold thermal boundary of the lithosphere gives rise to a permeability barrier due to freezing of melt within the pore space of the mantle. The buoyancy-driven vertical transport of melt is inhibited beneath this barrier by a compaction pressure gradient that balances melt buoyancy. If the thermal boundary were perpendicular to the gravity vector, then melt would be trapped at this boundary. However, the thermal boundary layer is inclined toward the ridge axis, such that a component of the compaction pressure gradient, which acts normal to the permeability barrier, drives melt toward the ridge axis. However, permeability-based models of melt focusing have yet to consider the contribution of spatial variations in grain size beneath the ridge axis. This leaves open the question whether a gradient in grain size can act as a permeability barrier and, if so, what effect would this have on melt transport beneath a mid-ocean ridge.In this study we construct a two-dimensional, single phase model for the steady state grain size beneath a mid-ocean ridge. The model employs a composite rheology of diffusion creep, dislocation creep, dislocation accommodated grain boundary sliding, and a plastic stress limiter. Our choice of rheology allows for a nonlinear coupling between the mean grain size and strain rate; the mean grain size is reduced by dislocation creep and grain boundary sliding, which then affects the strain rate of diffusion creep and grain boundary sliding. The mean grain size is calculated using the paleowattmeter model [Austin and Evans, ^{href="#b3" rid="b3" class=" bibr popnode">2007}]. The dynamics of the model are described by Stokes flow and the rheology is taken from experimental flow laws.The manuscript is organized as follows. We develop the model in section 2. First the standard Stokes flow dynamics are briefly outlined, then the composite rheology and mean grain-size evolution model are presented in detail. Section 2 concludes by examining the sensitivity of the composite rheology to variations in experimentally determined parameters for two different grain boundary sliding parameterizations. In section 3, we present a reference case for grain-size dynamics beneath a mid-ocean ridge and explore the sensitivity of the model to grain boundary sliding parameters, water concentration, and parameter perturbations within the mean grain-size evolution equation. In section 4, we investigate the influence of mean grain size upon the permeability structure for an ultra-slow, slow, and fast spreading-rate ridge. The permeability structure due to mean grain size is then interpreted in the context of melt transport.