S U M M A R YLarge-scale chemical lateral heterogeneities are inferred in the Earth's lowermost mantle by seismological studies. We explore the model space of thermochemical convection that can maintain reservoirs of dense material for a long period of time, by using similar analysis in 3-D spherical geometry. In this study, we focus on the parameters thought to be important in controlling the stability and structure of primordial dense reservoirs in the lower mantle, including the chemical density contrast between the primordial dense material and the regular mantle material (buoyancy ratio), thermal and chemical viscosity contrasts, volume fraction of primordial dense material and the Clapeyron slope of the phase transition at 660 km depth. We find that most of the findings from the 3-D Cartesian study still apply to 3-D spherical cases after slight modifications. Varying buoyancy ratio leads to different flow patterns, from rapid upwelling to stable layering; and large thermal viscosity contrasts are required to generate long wavelength chemical structures in the lower mantle. Chemical viscosity contrasts in a reasonable range have a second-order role in modifying the stability of the dense anomalies. The volume fraction of the initial primordial dense material does not effect the results with large thermal viscosity contrasts, but has significant effects on calculations with intermediate and small thermal viscosity contrasts. The volume fraction of dense material at which the flow pattern changes from unstable to stable depends on buoyancy ratio and thermal viscosity contrast. An endothermic phase transition at 660 km depth acts as a 'filter' allowing cold slabs to penetrate while blocking most of the dense material from penetrating to the upper mantle.

Basalts and mantle peridotites of mid-ocean ridges are thought to sample Earth’s upper mantle. Osmium isotopes of abyssal peridotites uniquely preserve melt extraction events throughout Earth history, but existing records only indicate ages up to ~2 billion years (Ga) ago. Thus, the memory of the suspected large volumes of mantle lithosphere that existed in Archean time (>2.5 Ga) has apparently been lost somehow. We report abyssal peridotites with melt-depletion ages up to 2.8 Ga, documented by extremely unradiogenic 187 Os/ 188 Os ratios (to as low as 0.1095) and refractory major elements that compositionally resemble the deep keels of Archean cratons. These oceanic rocks were thus derived from the once-extensive Archean continental keels that have been dislodged and recycled back into the mantle, the feasibility of which we confirm with numerical modeling. This unexpected connection between young oceanic and ancient continental lithosphere indicates an underappreciated degree of compositional recycling over time.

We performed numerical experiments of thermochemical convection in 3‐D spherical geometry to investigate the effects of a low viscosity of post‐perovskite (pPv) on the stability and structure of primordial reservoirs of dense material in the lower mantle of the Earth. Our results show that weak pPv (1000× viscosity reduction in regions containing pPv) strongly increases the core‐mantle boundary (CMB) heat flux. The volume‐averaged mantle temperature with weak pPv is slightly higher than that with regular pPv, except in the lowermost mantle. This is because weak pPv weakens the base of the cold downwellings, allowing cold slabs to spread more easily and broadly along the CMB. The stability and size of the dense reservoirs is not substantially altered by weak pPv. In the weak pPv case, slabs spreading along the CMB slightly decreases the stability of dense reservoirs, i.e., the amount of dense material entrained upward is slightly larger than in the regular pPv case (i.e., viscosity of pPv identical to that of perovskite). Furthermore, the topography and steepness of these reservoirs slightly increase. However, as in the regular pPv case, the dense reservoirs are maintained over periods of time comparable to the age of the Earth.

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Core‐mantle boundary (CMB) topography may provide useful hints on the deep mantle thermochemical structure, as clusters of thermal plumes and piles of chemically differentiated material, which are usually proposed as end‐member explanations for the large low shear‐wave velocity regions observed in the deep mantle, have different actions on this topography. CMB topography is further sensitive to several parameters, including mantle viscosity and its variations with thermal and compositional changes. Here we assess the influence of the postperovskite (pPv) phase viscosity on deep mantle dynamics and on CMB topography. We perform numerical simulations of thermal and thermochemical convection in spherical geometry, varying the ratio between pPv and bridgmanite viscosities, ΔηpPv, between 1 (regular pPv) and 10−3 (weak pPv). Thermochemical structures are dominated by smaller‐scale wavelengths (spherical harmonic degrees 3 to 6) and are more stable in weak than in regular pPv models. The amplitude of CMB topography is reduced by about a factor of 2 as ΔηpPv changes from 1 to 10−3, mostly due to a sharp drop in the depressions induced by downwellings reaching the CMB. By contrast, the topographies induced by plumes clusters and thermochemical piles are mostly unaffected. For all the values of ΔηpPv we tested, long‐wavelength CMB topography and reconstructed shear‐wave tomography are anticorrelated in purely thermal models, and correlated in thermochemical models with strong chemical density contrast (ΔρC = 140 kg/m3). In models with smaller density contrast (ΔρC = 90 kg/m3), topography and tomography are anticorrelated at ΔηpPv = 1, but correlated at ΔηpPv = 10−3.

During the last 20 years, geophysicists have developed great interest in using gravity gradient tensor signals to study bodies of anomalous density in the Earth. Deriving exact solutions of the gravity gradient tensor signals has become a dominating task in exploration geophysics or geodetic fields. In this study, we developed a compact and simple framework to derive exact solutions of gravity gradient tensor measurements for polyhedral bodies, in which the density contrast is represented by a general polynomial function. The polynomial mass contrast can continuously vary in both horizontal and vertical directions. In our framework, the original three-dimensional volume integral of gravity gradient tensor signals is transformed into a set of one-dimensional line integrals along edges of the polyhedral body by sequentially invoking the volume and surface gradient (divergence) theorems. In terms of an orthogonal local coordinate system defined on these edges, exact solutions are derived for these line integrals. We successfully derived a set of unified exact solutions of gravity gradient tensors for constant, linear, quadratic and cubic polynomial orders. The exact solutions for constant and linear cases cover all previously published vertex-type exact solutions of the gravity gradient tensor for a polygonal body, though the associated algorithms may differ in numerical stability. In addition, to our best knowledge, it is the first time that exact solutions of gravity gradient tensor signals are * Jingtian Tang

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We perform numerical experiments of thermochemical mantle convection in 2‐D spherical annulus geometry to investigate the distribution of post‐perovskite (pPv) with respect to the location of primordial reservoirs of dense material in the lowermost mantle. High core‐mantle boundary temperatures lead to strong anticorrelation between the locations of pPv and large primordial reservoirs, while low values lead to a pPv layer fully covering the outer core. Intermediate values avoid a full pPv layer but allow pPv phase change to occur within the primordial reservoirs. Through interactions between cold downwellings and primordial reservoirs, low viscosity (weak) pPv leads to the formation of long‐lived, thin tails of primordial materials extending laterally at the edges of these reservoirs. Small patches of pPv also form within the primordial reservoir but are short‐lived. If primordial reservoirs are enriched in iron, these patches may provide an explanation for the ultralow‐velocity zones.