While the idea of a lower mantle composed of complementary peridotitic and bridgmanite‐dominated rocks may seem consistent with a number of geophysical observations as discussed above and would also bring the Mg/Si ratio of the mantle as a whole closer to chondritic values (McDonough & Sun, 1995), this interpretation of the modeled P‐ and S‐wave velocity profiles is by no means unique. As mentioned above, S‐wave velocities for a pyrolitic bulk composition can in principle be reconciled with those of PREM when accepting deviations from an adiabatic temperature profile (Figure 3.8). The here‐modeled S‐wave velocity gradients for pyrolite and harzburgite would match PREM along superadiabatic temperature profiles. Superadiabatic thermal gradients have also been inferred from earlier comparisons of mineral‐physical models with seismic velocity profiles for the lower mantle and for a range of different compositions (Cammarano et al., 2010, 2005b; Cobden et al., 2009; Deschamps and Trampert, 2004; Khan et al., 2008; Matas et al., 2007). In contrast, an adiabatic pyrolitic lower mantle has been found to be consistent with PREM based on a data set for mineral elasticity derived exclusively from DFT computations (Wang et al., 2015). A recent attempt to reconcile existing data of Fe‐Mg exchange between bridgmanite and ferropericlase also found agreement between adiabatic compression of pyrolite and PREM based on S‐wave velocities (Hyung et al., 2016).
It is interesting to note that a significant reduction of the Fe‐Mg exchange coefficient between bridgmanite and ferropericlase with increasing pressure as indicated by recent thermodynamic models (Nakajima et al., 2012; Xu et al., 2017) could entail substantial reductions of P‐ and S‐wave velocities for peridotitic bulk rock compositions. The resulting low P‐ and S‐wave velocities could help to explain the uppermost protrusions of LLVPs that locally extend more than 1000 km upwards above the core–mantle boundary (Durand et al., 2017; Hosseini et al., 2020; Koelemeijer et al., 2016). Because P‐wave velocities of both bridgmanite and ferropericlase seem to be less sensitive to changes in the iron content than S‐wave velocities (Figure 3.7), a gradually decreasing Fe‐Mg exchange coefficient between these 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 dlnvS/dlnvP 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 dlnvS/dlnvP > 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 dlnvS/dlnP > 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