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Drainage of supraglacial lakes to the ice-sheet bed can occur when a hydrofracture propagates downward, driven by the weight of the water in the lake. For supraglacial lakes in the grounding zones of Antarctic glaciers, the mechanics of drainage is complicated by their proximity to the grounding line. Recently, a series of supraglacial lake-drainage events through hydrofractures was observed in the Amery Ice Shelf grounding zone, East Antarctica. The lake depth at drainage varied considerably between events, raising questions about the mechanisms that induce hydrofracture, even at low lake depths. Here we use a modelling approach to investigate the contribution of tidally driven flexure to hydrofracture propagation. We model the viscoelastic response of a marine ice sheet to tides, the stresses that are induced, and the contribution of tidal stresses to hydrofracture propagation. Our results show that ocean tides and lake-water pressure together control supraglacial lake drainage through hydrofractures in the grounding zone. We give a model-based criterion that predicts supraglacial lake drainage as a function of daily maximum tidal amplitude and lake depth. Our model-based criterion agrees with remotely sensed data, indicating the importance of tidal flexure to processes associated with hydrofracturing such as supraglacial lake drainage, rifting and calving., Comment: 23 pages, 10 figures

Partially molten rock is a densely packed, melt-saturated, granular medium, but it has seldom been considered in these terms. In this manuscript, we extend the continuum theory of partially molten rock to incorporate the physics of granular media. Our formulation includes dilatancy in a viscous constitutive law and introduces a non-local fluidity. We analyse the resulting poro-viscous--granular theory in terms of two modes of liquid--solid segregation that are observed in published torsion experiments: localisation of liquid into high-porosity sheets and radially inward liquid flow. We show that the newly incorporated granular physics brings the theory into agreement with experiments. We discuss these results in the context of grain-scale physics across the nominal jamming fraction at the high homologous temperatures relevant in geological systems., Comment: 31 pages, 9 figures, 4 appendicies

Subsurface sandstone reservoirs sealed by overlying, low-permeability layers provide capacity for long-term sequestration of anthropogenic waste. Leakage can occur if reservoir pressures rise sufficiently to fracture the seal. Such pressures can be generated within the reservoir by vigorous injection of waste or, over thousands of years, by natural processes. In either case, the precise role of intercalated mudstones in the long-term evolution of reservoir pressure remains unclear; these layers have variously been viewed as seals, as pressure sinks or as pressure sources. Here, we use the geological record of episodic fluid venting in the Levant Basin to provide striking evidence for the pressure-source hypothesis. We use a Bayesian framework to combine recently published venting data, which record critical subsurface pressures since $\sim$2~Ma, with a stochastic model of pressure evolution to infer a pressure-recharge rate of $\sim$30~MPa/Myr. To explain this large rate, we quantify and compare a range of candidate mechanisms. We find that poroelastic pressure diffusion from mudstones provides the most plausible explanation for these observations, amplifying the $\sim$3~MPa/Myr recharge caused primarily by tectonic compression. Since pressurised mudstones are ubiquitous in sedimentary basins, pressure diffusion from mudstones is likely to promote seal failure globally.

Fluid venting phenomena are prevalent in sedimentary basins globally. Offshore, these localised fluid-expulsion events are archived in the geologic record by the resulting pockmarks at the sea-floor. Venting is widely interpreted to occur via hydraulic fracturing, which requires near-lithostatic pore pressures for initiation. One common driver for these extreme pressures is horizontal tectonic compression, which pressurises the entire sedimentary column over a wide region. Fluid expulsion leads to a sudden, local relief of this pressure, which then gradually recharges through continued compression, leading to episodic venting. Pressure recharge will also occur through pressure diffusion from neighbouring regions that remain pressurised, but the combined role of compression and pressure diffusion in episodic venting has not previously been considered. Here, we develop a novel poroelastic model for episodic, compression-driven venting. We show that compression and pressure diffusion together set the resulting venting period. We derive a simple analytical expression for this venting period, demonstrating that pressure diffusion can significantly reduce the venting period associated with a given rate of compression. Our expression allows this rate of compression to be inferred from observations of episodic venting. We conclude that pressure diffusion is a major contributor to episodic fluid venting in mudstone-dominated basins.

Basal crevasses are macroscopic structural discontinuities at the base of ice sheets and glaciers. Motivated by observations and the mechanics of elastic fracture, we hypothesise that in the presence of basal water pressure, spatial variations in basal stress can promote and localise basal crevassing. We quantify this process in the theoretical context of linear elastic fracture mechanics. We develop a model evaluating the effect of shear stress variation on the growth of basal crevasses. Our results indicate that sticky patches promote the initiation of basal crevasses, increase their length of propagation into the ice and, under some conditions, give them curved trajectories that incline upstream. A detailed exploration of the parameter space is conducted to gain a better understanding of the conditions under which sticky-patch-induced basal crevassing likely occurs beneath ice sheets and glaciers., Comment: 29 pages, 9 figures

The size distribution of grains is a fundamental characteristic of polycrystalline solids. In the absence of deformation, the grain-size distribution is controlled by normal grain growth. The canonical model of normal grain growth, developed by Hillert, predicts a grain-size distribution that bears a systematic discrepancy with observed distributions. To address this, we propose a change to the Hillert model that accounts for the influence of heterogeneity in the local environment of grains. In our model, each grain evolves in response to its own local environment of neighbouring grains, rather than to the global population of grains. The local environment of each grain evolves according to an Ornstein-Uhlenbeck stochastic process. Our results are consistent with accepted grain-growth kinetics. Crucially, our model indicates that the size of relatively large grains evolves as a random walk due to the inherent variability in their local environments. This leads to a broader grain-size distribution than the Hillert model and indicates that heterogeneity has a critical influence on the evolution of microstructure., Comment: 24 pages, 8 figures, to be published in Acta Materialia

It is generally accepted that melt extraction from the mantle at mid-ocean ridges (MORs) is concentrated in narrow regions of elevated melt fraction called channels. Two feedback mechanisms have been proposed to explain why these channels grow by linear instability: shear flow of partially molten mantle and reactive flow of the ascending magma. These two mechanisms have been studied extensively, in isolation from each other, through theory and laboratory experiments as well as field and geophysical observations. Here, we develop a consistent theory that accounts for both proposed mechanisms and allows us to weigh their relative contributions. We show that interaction of the two feedback mechanisms is insignificant and that the total linear growth rate of channels is well-approximated by summing their independent growth rates. Furthermore, we explain how their competition is governed by the orientation of channels with respect to gravity and mantle shear. By itself, analysis of the reaction-infiltration instability predicts the formation of tube-shaped channels. We show that with the addition of even a small amount of extension in the horizontal, the combined instability favours tabular channels, consistent with the observed morphology of dunite bodies in ophiolites. We apply the new theory to MORs by calculating the accumulated growth and rotation of channels along streamlines of the solid flow. We show that reactive flow is the dominant mechanism deep beneath the ridge axis, where the most unstable orientation of high-porosity channels is sub-vertical. Channels are then rotated by the solid flow away from the vertical. The contribution of the shear-driven instability is confined to the margins of the melting region. Within the limitations of our study, the shear-driven feedback is not responsible for significant melt focusing or for shallowly dipping seismic anisotropy [abridged]., Comment: [32 pages, 17 figures.] This is a pre-copyedited, author-produced PDF of an article accepted for publication in Geophysical Journal International following peer review. The version of record is available online at https://doi.org/10.1093/gji/ggab112

Tidal heating is expected to impart significant, non-spherically-symmetric structure to Jupiter's volcanic moon Io. A signature of spatially variable tidal heating is generally sought in observations of surface heat fluxes or volcanic activity, an exploration complicated by the transient nature of volcanic events. The thickness of the lithosphere is expected to change over much longer timescales, and so may provide a robust link between surface observations and the tidal heating distribution. To predict long-wavelength lithospheric thickness variations, we couple three-dimensional tidal heating calculations to a suite of one-dimensional models of magmatic segregation and volcanic eruption. We find that the lithospheric thickness could either be correlated with the radially integrated heating rate, or weakly anti-correlated. Lithospheric thickness is correlated with radially integrated heating rate if magmatic intrusions form at a constant rate in the lithosphere, but is weakly anti-correlated if intrusions form at a rate proportional to the flux through volcanic conduits. Utilising a simple isostasy model we show how variations in lithospheric thickness can predict long-wavelength topography. The relationship between lithospheric thickness and topography depends on the difference in chemical density between the lithosphere and mantle. Assuming that this difference is small, we find that long-wavelength topography anti-correlates with lithospheric thickness. These results will allow future observations to critically evaluate models for Io's lithospheric structure, and enable their use in constraining the distribution of tidal heating., Comment: Published in Icarus

Magmatic segregation and volcanic eruptions transport tidal heat from Io's interior to its surface. Several observed eruptions appear to be extremely high temperature ($\geq$ 1600 K), suggesting either very high degrees of melting, refractory source regions, or large amounts of viscous heating on ascent. To address this ambiguity, we develop a model that couples crust and mantle dynamics to a simple compositional system. We analyse the model to investigate chemical structure and evolution. We demonstrate that magmatic segregation and volcanic eruptions lead to differentiation of the mantle, the extent of which depends on how easily high temperature melts from the more refractory lower mantle can migrate upwards. We propose that Io's highest temperature eruptions originate from this lower mantle region, and that such eruptions act to limit the degree of compositional differentiation., Comment: Accepted at Journal of Geophysical Research: Planets

Magmatism and volcanism transfer carbon from the solid Earth into the climate system. This transfer may be modulated by the glacial/interglacial cycling of water between oceans and continental ice sheets, which alters the surface loading of the solid Earth. The consequent volcanic-carbon fluctuations have been proposed as a pacing mechanism for Pleistocene glacial cycles. This mechanism is dependant on the amplitude and lag of the mid-ocean ridge response to sea-level changes. Here we develop and analyse a new model for that response, eliminating some questionable assumptions made in previous work. Our model calculates the carbon flux, accounting for the thermodynamic effect of mantle carbon: reduction of the solidus temperature and a deeper onset of melting. We analyse models forced by idealised, periodic sea level and conclude that fluctuations in melting rate are the prime control on magma and carbon flux. We also discuss a model forced by a reconstruction of eustatic sea level over the past 800 kyr. It indicates that peak-to-trough variations of magma and carbon flux are up to about 20% and 10% of the mean flux, respectively. Peaks in mid-ocean ridge emissions lag peaks in sea-level forcing by less than about 20 kyr and the lag could well be shorter. The amplitude and lag are sensitive to the rate of melt segregation. The lag is much shorter than the time it takes for melt to travel vertically across the melting region., Comment: 28 pages including supplementary material. 9 figures plus 6 supplementary figures. Accepted for publication in Earth and Planetary Science Letters

The observed variability of trace-element concentration in basaltic lavas and melt inclusions carries information about heterogeneity in the mantle. The difficulty is to disentangle the contributions of source heterogeneity (i.e., spatial variability of mantle composition before melting) and process heterogeneity (i.e., spatial and temporal variability in melt transport). Here we investigate the end-member hypothesis that variability arises due to source heterogeneity alone. We model the attenuation of trace-element variability introduced into the bottom of a one-dimensional, steady-state melting column. Our results show that the melting column can be considered to be a filter that attenuates variability according to the wavelength of heterogeneity, the partition coefficient of the trace element, melt productivity and the efficiency of melt segregation. We further show that while the model can be fit to the observations, this requires assumptions inconsistent with constraints on the timescales of magma assembly. Hence, we falsify the end-member hypothesis and, instead, conclude that observed variability requires heterogeneity of melt transport. This might take the form of channels or waves and would almost certainly interact with source heterogeneity., Comment: 44 pages, 13 figures, to be published in G-cubed

Rocky planetesimals in the early solar system melted internally and evolved chemically due to radiogenic heating from Al-26. Here we quantify the parametric controls on magma genesis and transport using a coupled petrological and fluid mechanical model of reactive two-phase flow. We find the mean grain size of silicate minerals to be a key control on magma ascent. For grain sizes larger than $\approx$ 1 mm, melt segregation produces distinct radial structure and chemical stratification. This stratification is most pronounced for bodies formed at around 1 Myr after formation of Ca,Al-rich inclusions. These findings suggest a link between the time and orbital location of planetesimal formation and their subsequent structural and chemical evolution. According to our models, the evolution of partially molten planetesimal interiors falls into two categories. In the magma ocean scenario, the whole interior of a planetesimal experiences nearly complete melting, which would result in turbulent convection and core-mantle differentiation by the rainfall mechanism. In the magma sill scenario, segregating melts gradually deplete the deep interior of the radiogenic heat source. In this case, magma may form melt-rich layers beneath a cool and stable lid, while core formation would proceed by percolation. Our findings suggest that grain sizes prevalent during the internal heating stage governed magma ascent in planetesimals. Regardless of whether evolution progresses toward a magma ocean or magma sill structure, our models predict that temperature inversions due to rapid Al-26 redistribution are limited to bodies formed earlier than $\approx$ 1 Myr after CAIs. We find that if grain size was smaller than $\approx$ 1 mm during peak internal melting, only elevated solid-melt density contrasts (such as found for enstatite chondrite compositions) would allow substantial melt segregation to occur., Comment: 15 pages, 6 figures, 1 table; associated video file at http://goo.gl/V1UK1i; associated blog post at http://bit.ly/2GZZ0e9

Certain geological features have been interpreted as evidence of channelized magma flow in the mantle, which is a compacting porous medium. Aharonov et al. (1995) developed a simple model of reactive porous flow and numerically analysed its instability to channels. The instability relies on magma advection against a chemical solubility gradient and the porosity-dependent permeability of the porous host rock. We extend the previous analysis by systematically mapping out the parameter space. Crucially, we augment numerical solutions with asymptotic analysis to better understand the physical controls on the instability. We derive scalings for critical conditions of the instability and analyse the associated bifurcation structure. We also determine scalings for the wavelength and growth rate of the channel structures that emerge. We obtain quantitative theories for and a physical understanding of: first, how advection or diffusion over the reactive time scale set the horizontal length scale of channels; second, the role of viscous compaction of the host rock, which also affects the vertical extent of channelized flow. These scalings allow us to derive estimates of the dimensions of emergent channels that are consistent with the geologic record., Comment: 30 pages, 10 figures. Revised manuscript accepted for publication in the Journal of Fluid Mechanics

Following the mid-Pleistocene transition, the dominant period of glacial cycles changed from 40 ka to ~100 ka. It is broadly accepted that the 40 ka glacial cycles were driven by cyclical changes in obliquity. However, this forcing does not explain the ~100 ka glacial cycles. Mechanisms have been proposed for ~100 ka cycles, but none are universally accepted. Any proposed mechanism for ~100 ka glacial cycles must give the Earth's climate system a memory of tens-of-thousands-of-years. This timescale is difficult to achieve for surface processes, however it is possible for the solid Earth. Recent work suggests volcanic CO2 emissions change in response to glacial cycles and that there could be a ~50 ka delay in that response. Such a lagged response could drive glacial cycles from 40 ka cycles to an integer multiple of the forcing period. Under what conditions could the climate system admit such a response? We investigate this using a reduced-complexity model to establish the threshold volcanic variations required to induce 100 ka glacial cycles. This threshold is compared to the probable range of volcanic activity over glacial cycles. Our model is composed of three component models for energy balance, ice sheet growth and atmospheric CO2. The model is driven by insolation alone, with other components varying according to a system of coupled, differential equations. The model replicates modern climate conditions and seasonality, CO2-doubling experiments, and - when forced with ice core CO2 - the late-Pleistocene sea level record. We obtain a switch from 40 ka to ~100 ka cycles as the mid-ocean ridge CO2 response to glacial cycles is increased. These ~100 ka cycles are phase-locked to obliquity, lasting 80 or 120 ka. The mid-ocean ridge response required is, at best, just within a 95% confidence interval of MOR CO2 emissions.

Melting beneath mid-ocean ridges occurs over a region that is much broader than the zone of magmatic emplacement to form the oceanic crust. Magma is focused into this zone by lateral transport. This focusing has typically been explained by dynamic pressure gradients associated with corner flow, or by a sub-lithospheric channel sloping upward toward the ridge axis. Here we discuss a novel mechanism for magmatic focusing: lateral transport driven by gradients in compaction pressure within the asthenosphere. These gradients arise from the co-variation of melting rate and compaction viscosity. The compaction viscosity, in previous models, was given as a function of melt fraction and temperature. In contrast, we show that the viscosity variations relevant to melt focusing arise from grain-size variability and non-Newtonian creep. The asthenospheric distribution of melt fraction predicted by our models provides an improved ex- planation of the electrical resistivity structure beneath one location on the East Pacific Rise. More generally, although grain size and non-Newtonian viscosity are properties of the solid phase, we find that in the context of mid-ocean ridges, their effect on melt transport is more profound than their effect on the mantle corner-flow., Comment: 20 pages, 4 figures, 1 table

Magmatism in subduction zones builds continental crust and causes most of Earth's subaerial volcanism. The production rate and composition of magmas are controlled by the thermal structure of subduction zones. A range of geochemical and heat flow evidence has recently converged to indicate that subduction zones are hotter at lithospheric depths beneath the arc than predicted by canonical thermomechanical models, which neglect magmatism. We show that this discrepancy can be resolved by consideration of the heat transported by magma. In our one- and two-dimensional numerical models and scaling analysis, magmatic transport of sensible and latent heat locally alters the thermal structure of canonical models by $\sim$300 K, increasing predicted surface heat flow and mid-lithospheric temperatures to observed values. We find the advection of sensible heat to be larger than the deposition of latent heat. Based on these results we conclude that thermal transport by magma migration affects the chemistry and the location of arc volcanoes., Comment: Revised version. 10 pages, 9 figures (plus Supplementary Material: 5 pages, 4 figures). Changes: slightly expanded description of model and discussion of results

Deep-Earth volatile cycles couple the mantle with near-surface reservoirs. Volatiles are emitted by volcanism and, in particular, from mid-ocean ridges, which are the most prolific source of basaltic volcanism. Estimates of volatile extraction from the asthenosphere beneath ridges typically rely on measurements of undegassed lavas combined with simple petrogenetic models of the mean degree of melting. Estimated volatile fluxes have large uncertainties; this is partly due to a poor understanding of how volatiles are transported by magma in the asthenosphere. Here, we assess the fate of mantle volatiles through numerical simulations of melting and melt transport at mid-ocean ridges. Our simulations are based on two-phase, magma/mantle dynamics theory coupled to idealised thermodynamic model of mantle melting in the presence of water and carbon dioxide. We combine simulation results with catalogued observations of all ridge segments to estimate a range of likely volatile output from the global mid-ocean ridge system. We thus predict global MOR crust production of 66-73 Gt/yr (22-24 km3/yr) and global volatile output of 52-110 Mt/yr, corresponding to mantle volatile contents of 100--200~ppm. We find that volatile extraction is limited: up to half of deep, volatile-rich melt is not focused to the axis but is rather deposited along the LAB. As these distal melts crystallise and fractionate, they metasomatise the base of the lithosphere, creating rheological heterogeneity that could contribute to the seismic signature of the LAB., Comment: 42 pages; 8 figures; 2 appendices (incl 1 table); 7 suppl. figures; 1 suppl. table

Experimental studies of mantle petrology find that small concentrations of water and carbon dioxide have a large effect on the solidus temperature and distribution of melting in the upper mantle. However, it has remained unclear what effect small fractions of deep, volatile-rich melts have on melt transport and reactive melting in the shallow asthenosphere. Here we present theory and computations indicating that low-degree, reactive, volatile-rich melts cause channelisation of magmatic flow at depths approximately corresponding to the anhydrous solidus temperature. These results are obtained with a novel method to simulate the thermochemical evolution of the upper mantle in the presence of volatiles. The method uses a thermodynamically consistent framework for reactive, disequilibrium, multi-component melting. It is coupled with a system of equations representing conservation of mass, momentum, and energy for a partially molten grain aggregate. Application of this method in two-phase, three-component upwelling-column models demonstrates that it reproduces leading-order features of hydrated and carbonated peridotite melting; in particular, it captures the production of low-degree, volatile-rich melt at depths far below the volatile-free solidus. The models predict that segregation of volatile-rich, deep melts promotes a reactive channeling instability that creates fast and chemically isolated pathways of melt extraction. Reactive channeling occurs where volatile-rich melts flux the base of the silicate melting region, enhancing dissolution of fusible components from the ambient mantle. We find this effect to be similarly expressed for models of both hydrated and carbonated mantle melting. These findings indicate that despite their small concentrations, water and carbon dioxide have an important control on the extent and style of magma genesis, as well as on the dynamics of melt transport., Comment: Revised version of original manuscript titled "Effects of volatiles on melt production and reactive flow in the mantle"

Recent insights to melt migration beneath ridges suggest that channelized flow is a consequence of melting of a heterogeneous mantle, and that spreading rate modulates the dynamics of the localized flow. A corollary of this finding is that both mantle het- erogeneity and spreading rate have implications for the speed and time scale of melt migration. Here, we investigate these implications using numerical models of magma flow in heterogeneous mantle beneath spreading plates. The models predict that a broad distribution of magma flow speeds is characteristic of the sub-ridge mantle. Within the melting region, magmatic flow is fastest in regions of average fusibility; surprisingly, magmas from sources of above-average fusibility travel to the ridge in a longer time. Spreading rate has comparatively simple consequences, mainly resulting in faster segregation speeds at higher spreading rates. The computed time scales are short enough to preserve deep origin 230Th disequilibria and, under favourable parameter regimes, also 226Ra excesses. An important prediction from the models is that mantle heterogeneity induces significant natural variability into U-series disequilibria, complicating the identification of relationships between disequilibria and ridge properties or chemical signatures of heterogeneity., Comment: 42 pages, 10 figures, in press at Geochimica Cosmochimica Acta

The processes that are involved in migration and extraction of melt from the mantle are not yet fully understood. Gaining a better understanding of material properties of partially molten rock could help shed light on the behavior of melt on larger scales in the mantle. In this study, we simulate three-dimensional torsional deformation of a partially molten rock that contains a rigid, spherical inclusion. We compare the computed porosity patterns to those found in recent laboratory experiments. The laboratory experiments show emergence of melt-rich bands throughout the rock sample, and pressure shadows around the inclusion. The numerical model displays similar melt-rich bands only for a small bulk-to-shear-viscosity ratio (five or less). The results are consistent with earlier two-dimensional numerical simulations; however, we show that it is easier to form melt-rich bands in three dimensions compared to two. The addition of strain-rate dependence of the viscosity causes a distinct change in the shape of pressure shadows around the inclusion. This change in shape presents an opportunity for experimentalists to identify the strain-rate dependence and therefore the dominant deformation mechanism in torsion experiments with inclusions.

In laboratory experiments that impose shear deformation on partially molten aggregates of initially uniform porosity, melt segregates into high-porosity sheets (bands in cross-section). The bands emerge at 15-20 degrees to the shear plane. A model of viscous anisotropy can explain these low angles whereas previous, simpler models have failed to do so. The anisotropic model is complex, however, and the reason that it produces low-angle bands has not been understood. Here we show that there are two mechanisms: (i) suppression of the well-known tensile instability, and (ii) creation of a new, shear-driven instability. We elucidate these mechanisms using linearised stability analysis in a coordinate system that is aligned with the perturbations. We consider the general case of anisotropy that varies dynamically with deviatoric stress, but approach it by first considering uniform anisotropy that is imposed a priori and showing the difference between static and dynamic cases. We extend the model of viscous anisotropy to include a strengthening in the direction of maximum compressive stress. Our results support the hypothesis that viscous anisotropy is the cause of low band-angles in experiments., Comment: 32 pages, 8 figures. Accepted for publication in the Journal of Fluid Mechanics on 4 October 2015

Shear deformation of partially molten rock in laboratory experiments causes the emergence of melt-enriched sheets (bands in cross-section) that are aligned at about 15-20 degrees to the shear plane. Deformation and deviatoric stress also cause the coherent alignment of pores at the grain scale. This leads to a melt-preferred orientation that may, in turn, give rise to an anisotropic permeability. Here we develop a simple, general model of anisotropic permeability in partially molten rocks. We use linearised analysis and nonlinear numerical solutions to investigate its behaviour under simple-shear deformation. In particular, we consider implications of the model for the emergence and angle of melt-rich bands. Anisotropic permeability affects the angle of bands and, in a certain parameter regime, it can give rise to low angles consistent with experiments. However, the conditions required for this regime have a narrow range and seem unlikely to be entirely met by experiments. Anisotropic permeability may nonetheless affect melt transport and the behaviour of partially molten rocks in Earth's mantle., Comment: 19 pages, 7 figures, accepted for publication in Geophysical Journal International on 3 September 2015

The geological record shows links between glacial cycles and volcanic productivity, both subaerially and at mid-ocean ridges. Sea-level-driven pressure changes could also affect chemical properties of mid-ocean ridge volcanism. We consider how changing sea-level could alter the CO2 emissions rate from mid-ocean ridges, on both the segment and global scale. We develop a simplified transport model for a highly incompatible element through a homogenous mantle; variations in the melt concentration the emission rate of the element are created by changes in the depth of first silicate melting. The model predicts an average global mid-ocean ridge CO2 emissions-rate of 53 Mt/yr, in line with other estimates. We show that falling sea level would cause an increase in ridge CO2 emissions with a lag of about 100 kyrs after the causative sea level change. The lag and amplitude of the response are sensitive to mantle permeability and plate spreading rate. For a reconstructed sea-level time series of the past million years, we predict variations of up to 12% (7 Mt/yr) in global mid-ocean ridge CO2 emissions. The magnitude and timing of the predicted variations in CO2 emissions suggests a potential role for ridge carbon emissions in glacial cycles.

The superheating that usually occurs when a solid is melted by volumetric heating can produce irregular solid-liquid interfaces. Such interfaces can be visualised in ice, where they are sometimes known as Tyndall stars. This paper describes some of the experimental observations of Tyndall stars and a mathematical model for the early stages of their evolution. The modelling is complicated by the strong crystalline anisotropy, which results in an anisotropic kinetic undercooling at the interface; it leads to an interesting class of free boundary problems that treat the melt region as infinitesimally thin.

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 modelled 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 piezometric 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 mean grain-size field in the context of permeability. 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 forms a boundary that is steeply sloped toward the ridge axis. We hypothesise that such a permeability structure generated from the variability of the mean grain size may be able to focus melt towards the ridge axis, analogous to a 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 [Baba et al., 2006, Key et al., 2013]., Comment: 26 pages, 3 tables, 10 figures

Chemical differentiation of rocky planets occurs by melt segregation away from the region of melting. The mechanics of this process, however, are complex and incompletely understood. In partially molten rocks undergoing shear deformation, melt pockets between grains align coherently in the stress field; it has been hypothesized that this anisotropy in microstructure creates an anisotropy in the viscosity of the aggregate. With the inclusion of anisotropic viscosity, continuum, two-phase-flow models reproduce the emergence and angle of melt-enriched bands that form in laboratory experiments. In the same theoretical context, these models also predict sample-scale melt migration due to a gradient in shear stress. Under torsional deformation, melt is expected to segregate radially inward. Here we present new torsional deformation experiments on partially molten rocks that test this prediction. Microstructural analyses of the distribution of melt and solid reveal a radial gradient in melt fraction, with more melt toward the centre of the cylinder. The extent of this radial melt segregation grows with progressive strain, consistent with theory. The agreement between theoretical prediction and experimental observation provides a validation of this theory, which is critical to understanding the large-scale geodynamic and geochemical evolution of Earth., Comment: 21 pages, 4 figures, 1 table, supplementary info

For a prescribed porosity, the coupled magma/mantle flow equations can be formulated as a two-field system of equations with velocity and pressure as unknowns. Previous work has shown that while optimal preconditioners for the two-field formulation can be obtained, the construction of preconditioners that are uniform with respect to model parameters is difficult. This limits the applicability of two-field preconditioners in certain regimes of practical interest. We address this issue by reformulating the governing equations as a three-field problem, which removes a term that was problematic in the two-field formulation in favour of an additional equation for a pressure-like field. For the three-field problem, we develop and analyse new preconditioners and we show numerically that they are optimal in terms of problem size and less sensitive to model parameters, compared to the two-field preconditioner. This extends the applicability of optimal preconditioners for coupled mantle/magma dynamics into parameter regimes of physical interest., Comment: To appear in SIAM Journal on Scientific Computing

Glacial cycles redistribute water between oceans and continents causing pressure changes in the upper mantle, with consequences for melting of Earth's interior. Using Plio-Pleistocene sea-level variations as a forcing function, theoretical models of mid-ocean ridge dynamics that include melt transport predict temporal variations in crustal thickness of hundreds of meters. New bathymetry from the Australian-Antarctic ridge shows significant spectral energy near the Milankovitch periods of 23, 41, and 100 ky, consistent with model predictions. These results suggest that abyssal hills, one of the most common bathymetric features on Earth, record the magmatic response to changes in sea level. The models and data support a link between glacial cycles at the surface and mantle melting at depth, recorded in the bathymetric fabric of the sea floor., Comment: 30 pages, 6 figures (including supplementary information). Resubmitted to Science on 12 December 2014

Laboratory experiments in which synthetic, partially molten rock is subjected to forced deformation provide a context for testing hypotheses about the dynamics and rheology of the mantle. Here our hypothesis is that the aggregate viscosity of partially molten mantle is anisotropic, and that this anisotropy arises from deviatoric stresses in the rock matrix. We formulate a model of pipe Poiseuille flow based on theory by Takei and Holtzman [2009a] and Takei and Katz [2013]. Pipe Poiseuille is a configuration that is accessible to laboratory experimentation but for which there are no published results. We analyse the model system through linearised analysis and numerical simulations. This analysis predicts two modes of melt segregation: migration of melt from the centre of the pipe toward the wall and localisation of melt into high-porosity bands that emerge near the wall, at a low angle to the shear plane. We compare our results to those of Takei and Katz [2013] for plane Poiseuille flow; we also describe a new approximation of radially varying anisotropy that improves the self-consistency of models over those of Takei and Katz [2013]. This study provides a set of baseline, quantitative predictions to compare with future laboratory experiments on forced pipe Poiseuille flow of partially molten mantle., Comment: 23 pages, 7 figures. Submitted to Geophysical Journal International on 25 April 2014. Revised after reviewer comments and resubmitted on 20 August 2014

This article considers the iterative solution of a finite element discretisation of the magma dynamics equations. In simplified form, the magma dynamics equations share some features of the Stokes equations. We therefore formulate, analyse and numerically test a Elman, Silvester and Wathen-type block preconditioner for magma dynamics. We prove analytically and demonstrate numerically the optimality of the preconditioner. The presented analysis highlights the dependence of the preconditioner on parameters in the magma dynamics equations that can affect convergence of iterative linear solvers. The analysis is verified through a range of two- and three-dimensional numerical examples on unstructured grids, from simple illustrative problems through to large problems on subduction zone-like geometries. The computer code to reproduce all numerical examples is freely available as supporting material.

In this fluid dyanmics video, we show experimental images and simulations of chimney formation in mushy layers. A directional solidification apparatus was used to freeze 25 wt % aqueous ammonium chloride solutions at controlled rates in a narrow Hele-Shaw cell (1mm gap). The convective motion is imaged with schlieren. We demonstrate the ability to numerically simulate mushy layer growth for direct comparison with experiments.