Compositional and thermal state of the lower mantle from joint 3D inversion with seismic tomography and mineral elasticity

The compositional and thermal state of Earth's mantle provides critical constraints on the origin, evolution, and dynamics of Earth. However, the chemical composition and thermal structure of the lower mantle are still poorly understood. Particularly, the nature and origin of the two large low-shear-velocity provinces (LLSVPs) in the lowermost mantle observed from seismological studies are still debated. In this study, we inverted for the 3D chemical composition and thermal state of the lower mantle based on seismic tomography and mineral elasticity data by employing a Markov chain Monte Carlo framework. The results show a silica-enriched lower mantle with a Mg/Si ratio less than ~1.16, lower than that of the pyrolitic upper mantle (Mg/Si = 1.3). The lateral temperature distributions can be described by a Gaussian distribution with a standard deviation (SD) of 120 to 140 K at 800 to 1,600 km and the SD increases to 250 K at 2,200 km depth. However, the lateral distribution in the lowermost mantle does not follow the Gaussian distribution. We found that the velocity heterogeneities in the upper lower mantle mainly result from thermal anomalies, while those in the lowermost mantle mainly result from compositional or phase variations. The LLSVPs have higher density at the base and lower density above the depth of ~2,700 km than the ambient mantle, respectively. The LLSVPs are found to have ~500 K higher temperature, higher Bridgmanite and iron content than the ambient mantle, supporting the hypothesis that the LLSVPs may originate from an ancient basal magma ocean formed in Earth's early history.

The adjoint equations for thermochemical compressible mantle convection: derivation and verification by twin experiments

The adjoint method is an efficient way to obtain gradient information in a mantle convection model relative to past flow structure, allowing one to retrodict mantle flow from observations of the present-day mantle state. While adjoint equations for isochemical mantle flow have been derived for both incompressible and compressible flows, here we extend the method to thermochemical mantle flow models, and present thermochemical adjoint equations in the elastic-liquid approximation. We verify the method with twin experiments, and retrodict the flow history of a thermochemical reference model (reference twin) assuming for the final state, either a consistent thermochemical interpretation, using the thermochemical adjoint equations, or an inconsistent purely thermal interpretation, using the isochemical adjoint equations. The consistent simulation correctly retrodicts the flow evolution of the reference twin. The inconsistent case, instead, restores a false flow history whereby internal buoyancy forces and convectively maintained topography are overestimated. Because the cost function is reduced in either case, our results suggest that the adjoint method can be used to link assumptions on the role of chemical mantle heterogeneity to geologic inferences of dynamic topography, thus providing additional means to test hypotheses on mantle composition and dynamics.

Insights on Upper Mantle Melting, Rheology, and Anelastic Behavior From Seismic Shear Wave Tomography

In seismic tomography we map the wave speed structure inside the Earth, but we ultimately seek to interpret those images in terms of physical parameters. This is challenging because many parameters can trade-off with each other to produce a given wave speed. The problem is compounded by the convention of mapping seismic structures as perturbations relative to a 1-D reference model, rather than absolute wave speeds. Using a full waveform tomography model of Europe as a case study, we quantify the extent to which thermochemical and dynamic properties can be constrained using only S wave speed, expressed in absolute values. The wave speed distributions of this tomography model are compared with 4 million thermochemical models, whose seismic properties are computed via thermodynamic modeling. These models sample the full range of realistic mantle compositions, including variable water and melt contents, and mineral intrinsic anelasticity is taken into account. Intrinsic anelasticity causes waves to travel more slowly at higher temperatures, leading to seismic attenuation, but the sensitivity of the wave speed reduction to temperature is, in turn, controlled by the wave frequency. Global studies of surface waves indicate an anticorrelation between S wave speed and attenuation. We therefore only retain thermochemical models satisfying this anticorrelation. Our study indicates that the frequency dependence of anelasticity, α, depends on temperature or rheology, with α ≈ 0.1 being most appropriate in cold or lithospheric mantle and α ≈ 0.3 in warmer regions (i.e., the asthenosphere). Additionally, the slowest regions require specific compositions and/or a velocity-weakening mechanism, such as partial melting, elastically accommodated grain boundary sliding, or water.

The elastic solid solution model for minerals at high pressures and temperatures

Non-ideality in mineral solid solutions affects their elastic and thermodynamic properties, their thermobaric stability, and the equilibrium phase relations in multiphase assemblages. At a given composition and state of order, non-ideality in minerals is typically modelled via excesses in Gibbs free energy which are either constant or linear with respect to pressure and temperature. This approach has been extremely successful when modelling near-ideal solutions. However, when the lattice parameters of the solution endmembers differ significantly, extrapolations of thermodynamic properties to high pressures using these models may result in significant errors. In this paper, I investigate the effect of parameterising solution models in terms of the Helmholtz free energy, treating volume (or lattice parameters) rather than pressure as an independent variable. This approach has been previously applied to models of order-disorder, but the implications for the thermodynamics and elasticity of solid solutions have not been fully explored. Solid solution models based on the Helmholtz free energy are intuitive at a microscopic level, as they automatically include the energetic contribution from elastic deformation of the endmember lattices. A chemical contribution must also be included in such models, which arises from atomic exchange within the solution. Derivations are provided for the thermodynamic properties of n-endmember solutions. Examples of the use of the elastic model are presented for the alkali halides, pyroxene, garnet, and bridgmanite solid solutions. Elastic theory provides insights into the microscopic origins of non-ideality in a range of solutions, and can make accurate predictions of excess enthalpies, entropies, and volumes as a function of volume and temperature. In solutions where experimental data are sparse or contradictory, the Helmholtz free energy approach can be used to assess the magnitude of excess properties and their variation as a function of pressure and temperature. The formulation is expected to be useful for geochemical and geophysical studies of the Earth and other planetary bodies.

Density structure of Earth's lowermost mantle from Stoneley mode splitting observations

Advances in our understanding of Earth's thermal evolution and the style of mantle convection rely on robust seismological constraints on lateral variations of density. The large-low-shear-wave velocity provinces (LLSVPs) atop the core-mantle boundary beneath Africa and the Pacific are the largest structures in the lower mantle, and hence severely affect the convective flow. Here, we show that anomalous splitting of Stoneley modes, a unique class of free oscillations that are perturbed primarily by velocity and density variations at the core-mantle boundary, is explained best when the overall density of the LLSVPs is lower than the surrounding mantle. The resolved density variations can be explained by the presence of post-perovskite, chemical heterogeneity or a combination of the two. Although we cannot rule out the presence of a ∼100-km-thick denser-than-average basal structure, our results support the hypothesis that LLSVPs signify large-scale mantle upwelling in two antipodal regions of the mantle.

Visualizing the variability of gradients in uncertain 2D scalar fields

In uncertain scalar fields where data values vary with a certain probability, the strength of this variability indicates the confidence in the data. It does not, however, allow inferring on the effect of uncertainty on differential quantities such as the gradient, which depend on the variability of the rate of change of the data. Analyzing the variability of gradients is nonetheless more complicated, since, unlike scalars, gradients vary in both strength and direction. This requires initially the mathematical derivation of their respective value ranges, and then the development of effective analysis techniques for these ranges. This paper takes a first step into this direction: Based on the stochastic modeling of uncertainty via multivariate random variables, we start by deriving uncertainty parameters, such as the mean and the covariance matrix, for gradients in uncertain discrete scalar fields. We do not make any assumption about the distribution of the random variables. Then, for the first time to our best knowledge, we develop a mathematical framework for computing confidence intervals for both the gradient orientation and the strength of the derivative in any prescribed direction, for instance, the mean gradient direction. While this framework generalizes to 3D uncertain scalar fields, we concentrate on the visualization of the resulting intervals in 2D fields. We propose a novel color diffusion scheme to visualize both the absolute variability of the derivative strength and its magnitude relative to the mean values. A special family of circular glyphs is introduced to convey the uncertainty in gradient orientation. For a number of synthetic and real-world data sets, we demonstrate the use of our approach for analyzing the stability of certain features in uncertain 2D scalar fields, with respect to both local derivatives and feature orientation.