Mantle Convection and Surface Expressions. Группа авторов

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СКАЧАТЬ minerals could further contribute to the negative correlation between S-wave and bulk sound velocities that has been detected by seismology and appears to become more pronounced towards the lowermost mantle (Ishii & Tromp, 1999; Koelemeijer et al., 2016; Masters et al., 2000; Trampert et al., 2004).

      If we explore, as an alternative, the effect of thermal anomalies and keep mineral compositions constant throughout the lower mantle, we find from Figure 3.8 that for pyrolite and harzburgite the ratio dlnv_S/dlnv_P would increase with temperature at a given depth but would require extremely high temperatures at depths in excess of about 1800 km to attain seismically observed values of dlnv_S/dlnv_P > 1 (Davies et al., 2012; Koelemeijer et al., 2016). By allowing for temperature variations on the order of 1000 K and taking into account the limited resolution of seismic tomography, a pyrolitic lower mantle may still be reconciled with seismic observations (Davies et al., 2012; Schuberth et al., 2009b, 2009a). A reduction of the Fe‐Mg exchange coefficient between bridgmanite and ferropericlase with increasing depth, in contrast, would allow for dlnv_S/dln_P > 1 along a typical adiabatic compression path (Figure 3.9). The variety of potential thermochemical structures that comply with seismic constraints on lower‐mantle structure highlights the need both for improved forward models of seismic properties for relevant rock compositions and for integrating mineral‐physical models with several types of geophysical and geochemical observations.

3.9 CONCLUSIONS

Finite‐strain theory provides a compact yet flexible framework for the computation of elastic properties of minerals and rocks at pressures and temperatures of Earth’s mantle (Birch, 1947; Davies, 1974; Stixrude & Lithgow‐Bertelloni, 2005). This framework is constantly being filled with new elasticity data on mantle minerals as obtained from high‐pressure experiments and quantum‐mechanical computations. Experimental measurements of elastic properties at simultaneously high pressures and high temperatures, however, remain challenging. Propagation velocities of ultrasonic waves can now be determined for samples being compressed and heated in multi‐anvil presses to pressures and temperatures corresponding to conditions of the uppermost lower mantle (Chantel et al., 2012; Gréaux et al., 2019, 2016), and laser‐heated diamond anvil cells (DAC) are capable of creating pressures and temperatures as they prevail throughout the entire mantle. Thermal gradients across samples heated in DACs by infrared lasers, however, are not necessarily compatible with requirements imposed by common light or X‐ray scattering techniques used to measure sound wave velocities. First successful measurements of sound wave velocities on samples being simultaneously laser‐heated and compressed in DACs promise future progress in this direction (Murakami et al., 2012; Zhang & Bass, 2016). Full elastic stiffness tensors are needed to assess elastic anisotropy and to constrain rigorous bounds on average elastic moduli. For lower‐mantle minerals, measurements of full elastic stiffness tensors at relevant pressures are limited to ferropericlase (Antonangeli et al., 2011; Crowhurst et al., 2008; Finkelstein et al., 2018; Marquardt et al., 2009b, 2009c; Yang et al., 2016, 2015), bridgmanite (Fu et al., 2019; Kurnosov et al., 2017), and SiO₂ polymorphs (Zhang et al., 2021).

      While density functional theory (DFT) computations are more flexible than experiments in terms of addressing extreme pressure–temperature combinations, they can only be as accurate as their underlying approximations such as the local density approximation (LDA) and generalized gradient approximations (GGA) for the electron density distribution and the quasi‐harmonic approximation (QHA) for the vibrational structure. Discrepancies with experimental results have been observed for Fe‐bearing compositions and reflect challenges in treating the localized d electrons of transition metal cations with LDA and GGA. Important developments in the study of mantle minerals with DFT computations include accounting for d electron interactions in terms of the Hubbard parameter U (Stackhouse et al., 2010; Tsuchiya et al., 2006) and bypassing the QHA with ab initio molecular dynamics (Oganov et al., 2001; Stackhouse et al., 2005b) or density functional perturbation theory (Giura et al., 2019; Oganov & Dorogokupets, 2004). As the full potential of these and other improvements is being explored, future progress in reducing discrepancies between the results of experiments and DFT computations can be expected.

      A systematic analysis of the sensitivity of computed elastic wave velocities to individual finite‐strain parameters reveals uncertainties on parameters that capture the quasi‐harmonic contribution to elastic properties as a main source of uncertainty. Reported uncertainties on Grüneisen parameters and their strain derivatives propagate to relative uncertainties of several percent on elastic wave velocities for realistic pressures and temperatures of Earth’s mantle. While measurements and computations of elastic properties at combined high pressures and high temperatures will certainly help to reduce this source of uncertainty, consequent and systematic analyses of cross‐correlations between finite‐strain and quasi‐harmonic parameters can avoid overestimating uncertainties by accounting for these correlations when propagating uncertainties. The analysis of parameter correlations, however, requires consistent data sets that include data both at high pressures and at high temperatures and ideally at combinations of both, again pointing out the need to perform experiments at combinations of high pressures and high temperatures. P‐ and S‐wave velocities computed for isotropic polycrystalline aggregates of anisotropic minerals can differ by several percent when using either the Voigt or the Reuss bound. These bounds provide the extreme values for the elastic response of a polycrystalline aggregate of randomly oriented grains and can only be evaluated when full elastic stiffness tensors are available for the respective minerals and at the pressures and temperatures of interest.

Computing elastic wave velocities for realistic bulk rock compositions requires accurate descriptions of elastic properties across solid solutions of mantle minerals. In contrast to the elastic properties of mantle minerals with compositions spanned by binary solid solutions, i.e., olivine and ferropericlase, the change of elastic properties with chemical composition is not well constrained for mantle minerals that form complex solid solutions between several end member compositions, such as pyroxenes, garnets, bridgmanite, and the calcium ferrite‐type aluminous (CF) phase. High‐pressure experimental data on bridgmanite, for example, barely span bridgmanite compositions observed in experiments on peridotitic bulk rock compositions. While DFT computations have addressed wider compositional ranges (Shukla et al., 2016, 2015; Zhang et al., 2016), the results are not always consistent with those of direct measurements or are limited to specific combinations of pressure and temperature, making it difficult to derive finite‐strain parameters. Inter‐ and extrapolations of elastic properties between different mineral compositions and beyond compositional limits imposed by available elasticity data are subject to uncertainties that arise from averaging over elastic properties of different mineral compositions and from assumptions about how elastic properties vary across solid solutions. Experiments on peridotitic and basaltic bulk rock compositions at pressures and temperatures of the lower mantle show substantial spread in observed mineral compositions and, as a consequence, in derived element exchange or partition coefficients. Despite progress in deriving trends for element partitioning with pressure, temperature, and compositional parameters for specific bulk compositions (Hyung et al., 2016; Irifune et al., 2010; Nakajima et al., 2012; Piet et al., 2016; Xu et al., 2017), it remains difficult to assess to which extent experimentally observed mineral compositions are representative of chemical equilibrium. While capable of reproducing pressures and temperatures of the lower mantle, laser‐heating experiments in diamond anvil cells often give rise to strong thermal gradients across the sample that can drive disparate diffusion of chemical elements and bias mineral compositions (Andrault and Fiquet, 2001; Sinmyo and Hirose, 2010). In comparison to typical sample sizes, thermal gradients tend to be less pronounced for experiments in multi‐anvil presses. Recent progress in multi‐anvil press technology has extended achievable pressures to those of the lowermost mantle (Ishii et al., 2019; Yamazaki et al., 2019) and promises to facilitate experiments that better constrain equilibrium mineral compositions at pressures and temperatures of the lower СКАЧАТЬ