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Seismic observations indicate that the lowermost mantle above the core–mantle boundary (CMB) is strongly heterogeneous. Body waves reveal a variety of ultra-low velocity zones (ULVZs), which extend not more than 100 km above the CMB and have shear velocity reductions of up to 30 per cent. While the nature and origin of these ULVZs remain uncertain, some have suggested they are evidence of partial melting at the base of mantle plumes. Here we use coupled geodynamic/thermodynamic modelling to explore the hypothesis that present-day deep mantle melting creates ULVZs and introduces compositional heterogeneity in the mantle. Our models explore the generation and migration of melt in a deforming and compacting host rock at the base of a plume in the lowermost mantle. We test whether the balance of gravitational and viscous forces can generate partially molten zones that are consistent with the seismic observations. We find that for a wide range of plausible melt densities, permeabilities and viscosities, lower mantle melt is too dense to be stirred into convective flow and instead sinks down to form a completely molten layer, which is inconsistent with observations of ULVZs. Only if melt is less dense or at most ca. 1 per cent more dense than the solid, or if melt pockets are trapped within the solid, can melt remain suspended in the partial melt zone. In these cases, seismic velocities would be reduced in a cone at the base of the plume. Generally, we find partial melt alone does not explain the observed ULVZ morphologies and solid-state compositional variation is required to explain the anomalies. Our findings provide a framework for testing whether seismically observed ULVZ shapes are consistent with a partial melt origin, which is an important step towards constraining the nature of the heterogeneities in the lowermost mantle and their influence on the thermal, compositional and dynamic evolution of the Earth. [ABSTRACT FROM AUTHOR]

A large class of solid solution models are formulated on the premise that exchange of chemical species takes place on a finite number of unique crystallographic sites, and that the thermodynamic properties of the solution are a function of the proportions of species occupying each of the sites. These models are broadly classified as being of Bragg–Williams-type. They form an excellent first order approximation of non-ideal mixing and long-range order. In this article we present the mathematical framework common to all Bragg–Williams models, introducing necessary concepts from geometry, set theory and linear algebra. We combine this with a set of mathematical tools which we have found useful in building and using such models. We include several worked examples to illustrate key concepts and provide general expressions which can be used for all models. This paper is split into two parts. In the first part, we show how the valences of the species occupying each site and the total charge of the species involved in site exchange are sufficient to define the space of valid site occupancies of a solid solution, and to compute the endmembers bounding that space. We show that this space can be visualised as a polytope, i.e, an n-dimensional polyhedron, and we describe the relationship between site-occupancy space and compositional space. In the second part of the paper, we present the linear algebra required to transform descriptions of modified van Laar and subregular solution models from one independent endmember basis to another. The same algebra can also be used to derive macroscopic endmember interactions from microscopic site interactions. This algebra is useful both in the initial design of solution models, and when performing thermodynamic calculations in restricted chemical subsystems. A polytope description of solid solutions is used in the thermodynamic software packages Perple_X and burnman. The algorithms described in this paper are made available as python code. [ABSTRACT FROM AUTHOR]

The high-pressure phases Fe4O5 and Fe5O6 have recently been added to the list of known iron oxides. As mixed-valence phases, it has been suggested that they could form in the Earth’s mantle once the dominant minerals become saturated in ferric iron. The possibility that Fe4O5 could exist in the mantle is also supported by the fact that it forms extensive solid solutions with both Mg2+ and Cr3+. In this study, we present the results of high-pressure and high-temperature multi-anvil experiments performed between 5 and 24 GPa at 1000–1400 °C aimed at constraining the stability field of the Fe4O5 phase. We combine these results with published phase equilibria, equation of state and Fe–Mg partitioning data to estimate the thermodynamic properties of Fe4O5, Fe5O6 and the (Mg,Fe)2Fe2O5 solid solution. Using our thermodynamic model, the oxygen fugacity at which the high-pressure iron oxides become stable is calculated and the redox stability of (Mg,Fe)2Fe2O5 in an assemblage of olivine and pyroxene is calculated as a function of the bulk Fe/(Fe + Mg) ratio. Fe4O5 and (Mg,Fe)2Fe2O5 are stable at oxygen fugacities higher than the diamond stability field and are, therefore, unlikely to be found as inclusions in diamonds. The stability field of Fe5O6, on the other hand, extends to oxygen fugacities compatible with diamond formation. Using the Mg–Fe solid solution model, we show that Fe4O5-structured phases would be restricted to aluminium-poor environments in the mantle such as dunites or silica–iron oxide-rich sediments transported into the mantle via subduction. [ABSTRACT FROM AUTHOR]

The source rocks for basaltic lavas that form ocean islands are often inferred to have risen as part of a thermal plume from the lower mantle. These rocks are water-rich compared with average upper-mantle rocks. However, experiments indicate that the solubility of water in the dominant lower-mantle phases is very low, prompting suggestions that plumes may be sourced from as-yet unidentified reservoirs of water-rich primordial material in the deep mantle. Here we perform high-pressure experiments to show that Al2SiO4(OH)2-the aluminium-rich endmember of dense, hydrous magnesium silicate phase D-is stable at temperatures extending to over 2,000 °C at 26 GPa. We find that under these conditions, Al-rich phase D is stable within mafic rocks, which implies that subducted oceanic crust could be a significant long-term water reservoir in the convecting lower mantle. We suggest that melts formed in the lower mantle by the dehydration of hydrous minerals in dense ultramafic rocks will migrate into mafic lithologies and crystallize to form Al-rich phase D. When mantle rocks upwell, water will be locally redistributed into nominally anhydrous minerals. This upwelling material provides a potential source for ocean-island basalts without requiring reservoirs of water-rich primordial material in the deep mantle. [ABSTRACT FROM AUTHOR]

The large low‐shear‐velocity provinces (LLSVPs) are thought to be thermo‐chemical in nature, with recycled oceanic crust (OC) being a contender for the source of the chemical heterogeneity. The melting process which forms OC concentrates heat producing elements (HPEs) within it which, over time, may cause any collected piles of OC to destabilize, limiting their suitability to explain LLSVPs. Despite this, most geodynamic studies which include recycling of OC consider only homogeneous heating rates. We perform a suite of spherical, three‐dimensional mantle convection simulations to investigate how buoyancy number, geochemical model and heating model affects the ability of recycled OC to accumulate at the core‐mantle boundary. Our results agree with others that only a narrow range of buoyancy numbers allow OC to form piles in the lower mantle which remain stable to present day. We demonstrate that heterogeneous radiogenic heating causes piles to destabilize more readily, reducing present day CMB coverage from 63% to 47%. Consequently, the choice of geochemical model can influence pile formation. Geochemical models which lead to high internal heating rates can cause more rapid replenishment of piles, increasing their longevity. Where piles do remain to present day, first order comparisons suggest that old (hot) OC material can produce seismic characteristics, such as Vs anomalies, similar to those of LLSVPs. Given the range of current density estimates for lower mantle mineral phases, subducted OC remains a contender for the chemical component of thermo‐chemical LLSVPs. Plain Language Summary: Large, pile‐like structures at the base of Earth's mantle may be partially composed of accumulations of recycled oceanic crust. When oceanic crust is formed, heat producing elements are concentrated within it. This causes oceanic crust to experience relatively high heating rates compared to surrounding material when it is recycled into the mantle. A consequence of the high heating rates is that piles of oceanic crust may become unstable and so may not survive to present day. We conduct three‐dimensional numerical mantle simulations to investigate how the excess chemical density of recycled oceanic crust affects the survival of piles. In line with previous work, we find only a narrow range of excess chemical densities allow the survival of piles to the present day. Piles are more readily destroyed when internal heating is controlled by the concentration of heat producing elements compared to when internal heating is distributed evenly through the mantle. Consequently, assumptions made in the geochemical model, which controls the distribution of heat producing elements, can affect the long‐term stability of piles. Key Points: Heterogenous heating rates cause piles to destabilize more rapidly than homogeneous heating ratesA narrow range of buoyancy numbers allows piles to persist to present day without being destroyed or forming a layerFaster mantle processing rates can replenish piles more efficiently, increasing their longevity [ABSTRACT FROM AUTHOR]

• The volume change of olivine to wadsleyite reverses the disproportionation of iron. • Ferric iron in majorites peaks in the upper transition zone. • The lowermost upper mantle is a zone of partial resorption for reduced phases. • Majorite inclusions are a powerful probe to characterize the diamond forming fluid. The Earth's mantle hosts a variety of reduced and oxidized phases, including iron-bearing alloys, diamond, and sulfide and carbonate melts. In the upper mantle, increasing pressure favors the stabilization of reduced iron-bearing phases via disproportionation of ferrous iron into ferric and metallic iron. Pressure-driven disproportionation is thought to continue into the transition zone, based on the extrapolation of experiments conducted at lower pressures. To test this hypothesis, we performed high-temperature and high-pressure experiments on basaltic and peridotitic compositions at pressures of 10 to 20 GPa, buffered at different oxygen fugacities. Under these conditions, majoritic garnet is the dominant ferric-iron bearing phase. We analyze our experimental run products for their ferric iron concentrations with EELS and Mössbauer spectroscopy. Contrary to expectations, results show that at iron saturation, ferric iron content of majorite peaks in the upper transition zone and then decreases between 500 and 650 km depth, destabilizing and resorbing reduced phases. This peak can be explained by decreases in the effective volume of ferrous minerals in transition zone assemblages. We also show that natural diamond-hosted majorite inclusions that equilibrated in the sublithospheric mantle grew from variably reduced fluids. These results are consistent with the idea that these diamonds formed during progressive reduction of an originally carbonatitic melt. [ABSTRACT FROM AUTHOR]

Abstract: Earthquakes beneath the southwest Pacific occur from the surface down to 700km depth. Teleseismic waveforms created by some of these earthquakes are almost identical. We investigate Tonga–Kermadec and Vanuatu subduction zone earthquake P-coda waveforms using a cross-correlation technique and hierarchical clustering algorithm in order to determine the origin of waveform similarity and the distribution of earthquakes producing similar waveforms. We show that scatterers forming the majority of power in the P-wave coda are localised around the receiver. As a result, waveform similarity provides a much weaker constraint on source separation than in local studies. Waveform similarity can provide stronger constraints on focal mechanism. Most earthquake multiplets within the Tonga–Fiji–Kermadec Wadati–Benioff zone are found at depths between 0–60km and 520–620km. A significant proportion of all deep-focus events in south Pacific subduction zones have waveforms similar to those of at least one other event. Relative relocation of events within the largest identified multiplet reveals a planar zone of seismicity sub-parallel to the nodal plane of a related centroid moment tensor solution. Groups of earthquakes with similar waveforms remain active on at least the 14-year recording timescale. We equate this to repeated rupture on single or closely related shear systems within the subducting slabs. [Copyright &y& Elsevier]

There were regrettably a few typos that appeared in the published version of Myhill et al. (2016). [ABSTRACT FROM AUTHOR]

We have performed an experimental cross calibration of a suite of mineral equilibria within mantle rock bulk compositions that are commonly used in geobarometry to determine the equilibration depths of upper mantle assemblages. Multiple barometers were compared simultaneously in experimental runs, where the pressure was determined using in-situ measurements of the unit cell volumes of MgO, NaCl, Re and h-BN between 3.6 and 10.4 GPa, and 1250 and 1500 °C. The experiments were performed in a large volume press (LVPs) in combination with synchrotron X-ray diffraction. Noble metal capsules drilled with multiple sample chambers were loaded with a range of bulk compositions representative of peridotite, eclogite and pyroxenite lithologies. By this approach, we simultaneously calibrated the geobarometers applicable to different mantle lithologies under identical and well determined pressure and temperature conditions. We identified discrepancies between the calculated and experimental pressures for which we propose simple linear or constant correction factors to some of the previously published barometric equations. As a result, we establish internally-consistent cross-calibrations for a number of garnet-orthopyroxene, garnet-clinopyroxene, Ca-Tschermaks-in-clinopyroxene and majorite geobarometers. [ABSTRACT FROM AUTHOR]

Eutectic melting curves in the system MgO–SiO 2 have been experimentally determined at lower mantle pressures using laser-heated diamond anvil cell (LH-DAC) techniques. We investigated eutectic melting of bridgmanite plus periclase in the MgO–MgSiO 3 binary, and melting of bridgmanite plus stishovite in the MgSiO 3 –SiO 2 binary, as analogues for natural peridotite and basalt, respectively. The melting curve of model basalt occurs at lower temperatures, has a shallower d T / d P slope and slightly less curvature than the model peridotitic melting curve. Overall, melting temperatures detected in this study are in good agreement with previous experiments and ab initio simulations at ∼25 GPa ( Liebske and Frost, 2012 ; de Koker et al., 2013 ). However, at higher pressures the measured eutectic melting curves are systematically lower in temperature than curves extrapolated on the basis of thermodynamic modelling of low-pressure experimental data, and those calculated from atomistic simulations. We find that our data are inconsistent with previously computed melting temperatures and melt thermodynamic properties of the SiO 2 endmember, and indicate a maximum in short-range ordering in MgO–SiO 2 melts close to Mg 2 SiO 4 composition. The curvature of the model peridotite eutectic relative to an MgSiO 3 melt adiabat indicates that crystallization in a global magma ocean would begin at ∼100 GPa rather than at the bottom of the mantle, allowing for an early basal melt layer. The model peridotite melting curve lies ∼ 500 K above the mantle geotherm at the core–mantle boundary, indicating that it will not be molten unless the addition of other components reduces the solidus sufficiently. The model basalt melting curve intersects the geotherm at the base of the mantle, and partial melting of subducted oceanic crust is expected. [ABSTRACT FROM AUTHOR]

High-pressure and high-temperature melting experiments were conducted in the systems Mg 2 SiO 4 –H 2 O and MgSiO 3 –H 2 O at 6 and 13 GPa and between 1150 and 1900 °C in order to investigate the effect of H 2 O on melting relations of forsterite and enstatite. The liquidus curves in both binary systems were constrained and the experimental results were interpreted using a thermodynamic model based on the homogeneous melt speciation equilibrium, H 2 O + O 2− = 2OH − , where water in the melt is present as both molecular H 2 O and OH − groups bonded to silicate polyhedra. The liquidus depression as a function of melt H 2 O concentration is predicted using a cryoscopic equation with the experimental data being reproduced by adjusting the water speciation equilibrium constant. Application of this model reveals that in hydrous MgSiO 3 melts at 6 and 13 GPa and in hydrous Mg 2 SiO 4 melts at 6 GPa, water mainly dissociates into OH − groups in the melt structure. A temperature dependent equilibrium constant is necessary to reproduce the data, however, implying that molecular H 2 O becomes more important in the melt with decreasing temperature. The data for hydrous forsterite melting at 13 GPa are inconclusive due to uncertainties in the anhydrous melting temperature at these conditions. When applied to results on natural peridotite melt systems at similar conditions, the same model infers the presence mainly of molecular H 2 O, implying a significant difference in physicochemical behaviour between simple and complex hydrous melt systems. As pressures increase along a typical adiabat towards the base of the upper mantle, both simple and complex melting results imply that a hydrous melt fraction would decrease, given a fixed mantle H 2 O content. Consequently, the effect of pressure on the depression of melting due to H 2 O could not cause an increase in the proportion, and hence seismic visibility, of melts towards the base of the upper mantle. [ABSTRACT FROM AUTHOR]

Constraining the thermal and compositional state of the mantle is crucial for deciphering the formation and evolution of Mars. Mineral physics predicts that Mars’ deep mantle is demarcated by a seismic discontinuity arising from the pressureinduced phase transformation of the mineral olivine to its higher-pressure polymorphs, making the depth of this boundary sensitive to both mantle temperature and composition. Here, we report on the seismic detection of a midmantle discontinuity using the data collected by NASA’s InSight Mission to Mars that matches the expected depth and sharpness of the postolivine transition. In five teleseismic events, we observed triplicated P and S waves and constrained the depth of this discontinuity to be 1,006 ± 40 km by modeling the triplicated waveforms. From this depth range, we infer a mantle potential temperature of 1,605 ± 100 K, a result consistent with a crust that is 10 to 15 times more enriched in heat-producing elements than the underlying mantle. Our waveform fits to the data indicate a broad gradient across the boundary, implying that the Martian mantle is more enriched in iron compared to Earth. Through modeling of thermochemical evolution of Mars, we observe that only two out of the five proposed composition models are compatible with the observed boundary depth. Our geodynamic simulations suggest that the Martian mantle was relatively cold 4.5 Gyr ago (1,720 to 1,860 K) and are consistent with a present-day surface heat flow of 21 to 24 mW/m². [ABSTRACT FROM AUTHOR]

Mantle convection and long-term lithosphere dynamics in the Earth and other planets can be treated as the slow deformation of a highly viscous fluid, and as such can be described using the compressible Navier–Stokes equations. Since on Earth-sized planets the influence of compressibility is not a dominant effect, density deviations from a reference profile are at most on the order of a few percent and using the full governing equations poses numerical challenges, most modelling studies have simplified the governing equations. Common approximations assume a temporally constant, but depth-dependent reference profile for the density (the anelastic liquid approximation), or drop compressibility altogether and use a constant reference density (the Boussinesq approximation). In most previous studies of mantle convection and crustal dynamics, one can assume that the error introduced by these approximations was small compared to the errors that resulted from poorly constrained material behaviour and limited numerical accuracy. However, as model parametrizations have become more realistic, and model resolution has improved, this may no longer be the case and the error due to using simplified conservation equations might no longer be negligible: while such approximations may be reasonable for models of mantle plumes or slabs traversing the whole mantle, they may be unsatisfactory for layered materials experiencing phase transitions or materials undergoing significant heating or cooling. For example, at boundary layers or close to dynamically changing density gradients, the error arising from the use of the aforementioned compressibility approximations can be the dominant error source, and common approximations may fail to capture the physical behaviour of interest. In this paper, we discuss new formulations of the continuity equation that include dynamic density variations due to temperature, pressure and composition without using a reference profile for the density. We quantify the improvement in accuracy relative to existing formulations in a number of benchmark models and evaluate for which practical applications these effects are important. Finally, we consider numerical aspects of the new formulations. We implement and test these formulations in the freely available community software aspect , and use this code for our numerical experiments. [ABSTRACT FROM AUTHOR]

Recent studies have revealed that Earth's deep mantle may have a wider range of oxygen fugacities than previously thought. Such a large heterogeneity might be caused by material subducted into the deep mantle. However, high‐pressure phase relations are poorly known in systems including Fe3+ at the top of the lower mantle, where the subducted slab may be stagnant. We therefore conducted high‐pressure and high‐temperature experiments using a multi‐anvil apparatus to study the phase relations in a Fe3+‐bearing system at 26 GPa and 1573–2073 K, at conditions prevailing at the top of the lower mantle. At temperatures below 1923 K, MgSiO3‐rich bridgmanite, an Fe3+‐rich oxide phase, and SiO2 coexist in the recovered sample. Quenched partial melt was observed above 1973 K, which is significantly lower than the solidus temperature of an equivalent Fe3+‐free bulk composition. The partial melt obtained from the Fe3+‐rich bulk composition has a higher iron content than coexisting bridgmanite, similar to the Fe2+‐dominant system. The results suggest that strong mantle oxygen fugacity anomalies might alter the subsolidus and melting phase relations under lower mantle conditions. We conclude that (1) a small amount of melt may be generated from an Al‐depleted region of a stagnant slab, such as subducted former banded‐iron‐formation, and (2) Fe3+ is not transported into the deep part of the lower mantle because of its incompatibility during melting. Key Points: We determined phase relationships of Fe3+‐rich system at top of the lower mantleMelting temperature of Fe3+‐rich system is lower than Fe2+‐dominant systemFe3+ may not be transported into the deep lower mantle because of its incompatibility [ABSTRACT FROM AUTHOR]

Mars atmospheric pressure variations induce ground deformations that are the main source of environmental noise on the InSight SEIS instrument. Phenomena generating pressure variations, such as meteorological wavefronts, gravity waves, convective vortices and small-scale turbulence are covering the whole frequency range of SEIS broadband seismometers. These signals impact the capability of SEIS sensors to detect seismic waves propagating in Mars interior. However, the relation between pressure variations measured by the InSight pressure sensor and ground movements measured by SEIS being essentially linear, it is possible to invert both signals to find the transfer function between pressure and ground motion. Then, pressure generated ground movements can be substracted from SEIS records in order to improve their sensitivity to seismic waves. The transfer function, usually called compliance, depends on the ground properties. Thus, the decorrelation of SEIS records from pressure effects will also allow us to constrain the subsurface properties at the InSight landing site.Our study compares two different pressure decorrelation methods applied to Mars synthetic data, and records by both short period and very broadband SEIS sensors. The pressure-decorrelation methods are presented and their differences in terms of underlying assumptions and implementations are explained. Their performances and drawbacks, analyzed on realistic synthetic datasets, are discussed. We plan to apply these methods to real Mars data and use them to retrieve the ground compliance at the InSight landing site over a broad frequency range. Accordingly, we expect to extract elastic properties of the subsurface through the compliance measurements. Wind measurements by the TWINS wind sensor will be integrated in order to separate the effects of various atmospheric phenomena. This sensor is almost identical to the Rover Environmental Monitoring Station sent to Mars as part of the Mars Science Laboratory (MSL), which operated even after the damage suffered during the MSL landing for more than two Martian years. Thus, wind measured by TWINS will provide valuable inputs to the decorrelation on the InSight SEIS instrument. Finally, the variations of decorrelation performances and compliance measurements with the diurnal Mars cycle will be analyzed. [ABSTRACT FROM AUTHOR]