The energetics of melting fertile heterogeneities within the depleted mantle

To explore the consequences of mantle heterogeneity for primary melt production, we develop a mathematical model of energy conservation for an upwelling, melting body of recycled oceanic crust embedded in the depleted upper mantle. We consider the end‐member geometric cases of spherical blobs and tabular veins. The model predicts that thermal diffusion into the heterogeneity can cause a factor‐of‐ two increase in the degree of melting for bodies with minimum dimension smaller than ∼1 km, yielding melt fractions between 50 and 80%. The role of diffusion is quantified by an appropriately defined Peclet number, which represents the balance of diffusion‐driven and adiabatic melting. At intermediate Peclet number, we show that melting a heterogeneity can cool the ambient mantle by up to ∼20 K (spherical) or ∼60 K (tabular) within a distance of two times the characteristic size of the body. At small Peclet number, where heterogeneities are expected to be in thermal equilibrium with the ambient mantle, we calculate the energetic effect of pyroxenite melting on the surrounding peridotite; we find that each 5% of recycled oceanic crust diminishes the peridotite degree of melting by 1–2%. Injection of the magma from highly molten bodies of recycled oceanic crust into a melting region of depleted upper mantle may nucleate reactive‐dissolution channels that remain chemically isolated from the surrounding peridotite

Textural equilibrium melt geometries around tetrakaidecahedral grains.

In textural equilibrium, partially molten materials minimize the total surface energy bound up in grain boundaries and grain-melt interfaces. Here, numerical calculations of such textural equilibrium geometries are presented for a space-filling tessellation of grains with a tetrakaidecahedral (truncated octahedral) unit cell. Two parameters determine the nature of the geometries: the porosity and the dihedral angle. A variety of distinct melt topologies occur for different combinations of these two parameters, and the boundaries between different topologies have been determined. For small dihedral angles, wetting of grain boundaries occurs once the porosity has exceeded 11%. An exhaustive account is given of the main properties of the geometries: their energy, pressure, mean curvature, contiguity and areas on cross sections and faces. Their effective permeabilities have been calculated, and demonstrate a transition between a quadratic variation with porosity at low porosities to a cubic variation at high porosities

A crystallographic approach to symmetry-breaking in fluid layers

Symmetry-breaking bifurcations, where a flow state with a certain symmetry undergoes a transition to state with a different symmetry, are ubiquitous in fluid mechanics. Much can be understood about the nature of these transitions from symmetry alone, using the theory of groups and their representations. Here we show how the extensive databases on groups in crystallography can be exploited to yield insights into fluid-dynamical problems. In particular, we demonstrate the application of the crystallographic layer groups to problems in fluid layers, using thermal convection as an example. Crystallographic notation provides a concise and unambiguous description of the symmetries involved, and we advocate its broader use by the fluid dynamics community.Comment: 27 pages, 9 figures, 3 supplementary table

Rate of Melt Ascent beneath Iceland from the Magmatic Response to Deglaciation

Observations of the time lag between the last deglaciation and a surge in volcanic activity in Iceland constrain the average melt ascent velocity to be $\geq50$ $\mathrm{m/yr}$. Although existing theoretical work has explained why the surge in eruption rates increased $5$-$30$ fold from the steady-state rates during the last deglaciation, they cannot account for large variations of Rare Earth Element (REE) concentrations in the Icelandic lavas. Lavas erupted during the last deglaciation are depleted in REEs by up to $70\%$; whereas, existing models, which assume instantaneous melt transport, can only produce at most $20\%$ depletion. Here, we develop a numerical model with finite melt ascent velocity and show that the variations of REEs are strongly dependent on the melt ascent velocity. When the average melt ascent velocity is $100$ $\mathrm{m/yr}$, the variation of $\mathrm{La}$ calculated by our model is comparable to that of the observations. In contrast, when the melt ascent velocity is $1,000$ $\mathrm{m/yr}$ or above, the model variation of $\mathrm{La}$ becomes significantly lower than observed, which explains why previous models with instantaneous melt transport did not reproduce the large variations. We provide the first model that takes account of the diachronous response of volcanism to deglaciation. We show by comparing our model calculations of the relative volumes of different eruption types (subglacial, finiglacial and postglacial) and the timing of the bursts in volcanic eruptions with the observations across different volcanic zones that the Icelandic average melt ascent velocity during the last deglaciation is likely to be $\sim100$ $\mathrm{m/yr}$

A mechanism for mode selection in melt band instabilities

The deformation of partially molten mantle in tectonic environments can lead to exotic structures, which potentially affect both melt and plate-boundary focussing. Examples of such structures are found in laboratory deformation experiments on partially molten rocks. Simple-shear and torsion experiments demonstrate the formation of concentrated melt bands at angles of around 20° to the shear plane. The melt bands form in the experiments with widths of a few to tens of microns, and a band spacing roughly an order of magnitude larger. Existing compaction theories, however, cannot predict this band width structure, let alone any mode selection, since they infer the fastest growing instability to occur for wavelengths or bands of vanishing width. Here, we propose that surface tension in the mixture, especially on a diffuse interface in the limit of sharp melt-fraction gradients, can mitigate the instability at vanishing wavelength and thus permit mode selection for finite-width bands. Indeed, the expected weak capillary forces on the diffuse interface lead to predicted mode selection at the melt-band widths observed in the experiments

Melt-band instabilities with two-phase damage

Deformation experiments on partially molten rocks in simple shear form melt bands at 20° to the shear plane instead of at the expected 45° principal compressive stress direction. These melt bands may play an important role in melt focusing in mid-ocean ridges. Such shallow bands are known to form for two-phase media under shear if strongly non-Newtonian power-law creep is employed for the solid phase, or anisotropy imposed. However laboratory experiments show that shallow bands occur regardless of creep mechanism, even in diffusion creep, which is nominally Newtonian. Here we propose that a couple of forms of two-phase damage allow for shallow melt bands even in diffusion creep

A Statistical description of concurrent mixing and crystallisation during MORB differentiation: Implications for trace element enrichment

The pattern of trace element enrichment and variability found in differentiated suites of basalts is a sim- ple observable, which nonetheless records a wealth of information on processes occurring from the mantle to crustal magma chambers. The incompatible element contents of some mid-ocean ridge basalt (MORB) sample suites show progressive enrichment beyond the predictions of simple models of fractional crystalli- sation of a single primary melt. Explanations for this over-enrichment have focused on the differentiation processes in crustal magma chambers. In this paper we consider an additional mechanism, and focus instead on the deviation from simple fractionation trends that is possible by mixing of diverse mantle-derived melts supplied to magma chambers. A primary observation motivating this strategy is that there is significant chemical diversity in primitive high MgO basalts, which single liquid parent models cannot match. Models were developed to simulate the compositional effects of concurrent mixing and crystallisation (CMC): diverse parental melts were allowed to mix, with a likelihood that is proportional to the extent of fractional crys- tallisation. Using a simple statistical model to explore the effects of concurrent mixing and crystallisation on apparent liquid lines of descent, we show how significant departure from Rayleigh fractionation is possible as a function of the diversity of trace elements in the incoming melts, their primary MgO, and the relative proportion of enriched to depleted melts. The model was used to make predictions of gradients of trace element enrichment in log[trace element]– MgO space. These predictions were compared with observations from a compilation of global MORB and provide a test of the applicability of CMC to natural systems. We find that by considering the trace element variability of primitive MORB, its MgO content and degree of enrichment, CMC accurately predicts the pattern of trace element over-enrichment seen in global MORB. Importantly, this model shows that the relationship between over-enrichment and incompatibility can derive from mantle processes: the fact that during mantle melting maximum variability is generated in those elements with the smallest bulk K d . Magma chamber processes are therefore filtering the signal of mantle-derived chemical diversity to produce trace element over-enrichment during differentiation. Finally, we interrogate the global MORB dataset for evidence that trace element over-enrichment varies as a function of melt supply. There is no correlation between over-enrichment and melt supply in the global dataset. Trace element over-enrichment occurs at slow-spreading ridges where extensive steady-state axial magma chambers, the most likely environment for repeated episodes of replenishment, tapping and crystallisation, are very rarely detected. This supports a model whereby trace element over-enrichment is an inevitable consequence of chemically heterogeneous melts delivered from the mantle, a process that may operate across all rates of melt supply

Physics of melt extraction from the mantle : speed and style

Funding: This research received funding from the European Research Council under Horizon 2020 research and innovation program grant agreement number 772255. The authors thank the Isaac Newton Institute for Mathematical Sciences for its hospitality during the programme Melt in the Mantle which was supported by EPSRC Grant Number EP/K032208/1.Melt extraction from the partially molten mantle is among the fundamental processes shaping the solid Earth today and over geological time. A diversity of properties and mechanisms contribute to the physics of melt extraction. We review progress of the past ∼25 years of research in this area, with a focus on understanding the speed and style of buoyancy-driven melt extraction. Observations of U-series disequilibria in young lavas and the surge of deglacial volcanism in Iceland suggest this speed is rapid compared to that predicted by the null hypothesis of diffuse porous flow. The discrepancy indicates that the style of extraction is channelized. We discuss how channelization is sensitive to mechanical and thermochemical properties and feedbacks, and to asthenospheric heterogeneity. We review the grain-scale physics that underpins these properties and hence determines the physical behavior at much larger scales. We then discuss how the speed of melt extraction is crucial to predicting the magmatic response to glacial and sea-level variations. Finally, we assess the frontier of current research and identify areas where significant advances are expected over the next 25 years. In particular, we highlight the coupling of melt extraction with more realistic models of mantle thermochemistry and rheological properties. This coupling will be crucial in understanding complex settings such as subduction zones. ▪ Mantle melt extraction shapes Earth today and over geological time. ▪ Observations, lab experiments, and theory indicate that melt ascends through the mantle at speeds ∼30 m/year by reactively channelized porous flow. ▪ Variations in sea level and glacial ice loading can cause significant changes in melt supply to submarine and subaerial volcanoes. ▪ Fluid-driven fracture is important in the lithosphere and, perhaps, in the mantle wedge of subduction zones, but remains a challenge to model.PreprintPeer reviewe

Torsion of a cylinder of partially molten rock with a spherical inclusion: Theory and simulation

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