Mantle Convection and Surface Expressions. Группа авторов

and S‐wave velocity contrasts that result from combining the elastic properties of mineral phases and compositions according to either the Voigt or the Reuss bound.

      The Fe³⁺/∑Fe ratio of bridgmanite dictates the whole‐rock Fe³⁺/∑Fe ratio and, for pyrolite and harzburgite, appears to affect velocity gradients dv/dz with higher Fe³⁺/∑Fe ratios leading to steeper gradients dv/dz. Again, the effect seems to be strongest for S waves. Based on a comparison of computed P‐ and S‐wave velocity gradients of pyrolite with PREM, Kurnosov et al. (2017) argued for a reduction of the ferric iron content in bridgmanite with depth. While a steepening of velocity gradients with higher Fe³⁺/∑Fe ratios of bridgmanite is consistent with the modeling results presented here, an actual match of a pyrolitic bulk composition with PREM seems only possible for S‐wave velocities and at depths in excess of 1500 km. Assuming a Fe‐Mg exchange coefficient of , modeled S‐wave velocities match those of PREM at about 1600 km depth for Fe³⁺/∑Fe = 1 in bridgmanite. To maintain dlnv_S = 0 at depths greater than 1600 km, the Fe³⁺/∑Fe ratio of bridgmanite would then need to gradually decrease with increasing depth. For harzburgite, the impact of the Fe³⁺/∑Fe ratio of bridgmanite on P‐ and S‐wave velocity profiles is complicated by the stabilization of a Fe₂O₃ component for high Fe³⁺/Al ratios in bridgmanite due to the lower overall Al₂O₃ content of harzburgite. As long as sufficient aluminum is available, ferric iron is preferentially incorporated into bridgmanite as the component FeAlO₃ (Frost & Langenhorst, 2002; Richmond & Brodholt, 1998; Zhang & Oganov, 2006). While iron cations of the FeSiO₃ and FeAlO₃ components of bridgmanite replace magnesium on the dodecahedral A site and remain in high‐spin states at pressures of the lower mantle (Catalli et al., 2010; Jackson et al., 2005a; Lin et al., 2016), one Fe³⁺ cation of the Fe₂O₃ component is located on the octahedral B site and goes through a spin transition at pressures above 40 GPa (Catalli et al., 2010; Liu et al., 2018). For the modeling results shown in Figure 3.9, Fe³⁺/Al ratios in bridgmanite become high enough to stabilize the Fe₂O₃ component only for harzburgite models with Fe³⁺/∑Fe > 0.5 or . The elastic softening of the bulk modulus due to the spin transition of Fe³⁺ on the B site of bridgmanite (Fu et al., 2018) significantly reduces P‐wave velocities for the respective harzburgite models at pressures between 40 and 100 GPa. The low overall Al₂O₃ content affects both P‐ and S‐wave velocities.

While dominated by the elastic softening due to the ferroelastic phase transition between stishovite and CaCl₂‐type SiO₂, modeled P‐ and S‐wave velocity profiles of metabasalt are sensitive to both the Fe³⁺/∑Fe ratio of bridgmanite and Fe‐Mg exchange between bridgmanite and the CF phase. In contrast to pyrolite and harzburgite, higher Fe³⁺/∑Fe ratios appear to reduce velocity gradients with depths. Varying the Fe‐Mg exchange coefficient between bridgmanite and the CF phase has the opposing effect and results in higher P‐ and S‐wave velocities for higher values of the Fe‐Mg exchange coefficient. For all three bulk rock compositions addressed here, the sensitivity of P‐ and S‐wave velocities to variations in Fe‐Mg exchange coefficients demonstrates the need for better constraining equilibrium mineral compositions at relevant pressures and temperatures. While Fe‐Mg exchange coefficients and Fe³⁺/∑Fe ratios were treated here as independent parameters, they are coupled through the preferred incorporation of ferric iron into bridgmanite (Frost et al., 2004; Irifune et al., 2010). As shown in Figure 3.6, however, available data on element partitioning cannot unambiguously constrain mineral compositions. More experiments and thermodynamic data are required to improve forward models of the petrology and elastic properties of lower‐mantle rocks.

To depict the effect of continuous phase transitions on modeled P‐ and S‐wave velocities, I computed additional velocity profiles by ignoring changes in spin states of iron cations and by suppressing the phase transition from stishovite to CaCl₂‐type SiO₂. The results are included in Figure 3.9 for each reference scenario and for selected combinations of compositional parameters that are expected to be particularly susceptible to the effects of spin transitions. All pyrolite models as well as the reference scenario for harzburgite are only affected by the spin transition of ferrous iron in ferropericlase as no ferric iron is expected to enter the B site of bridgmanite for the respective combinations of Fe‐Mg exchange coefficients and Fe³⁺/∑Fe ratios of bridgmanite. Along an adiabatic compression path, the spin transition of Fe²⁺ in ferropericlase broadens substantially for reasons discussed in Section 3.7 and mainly reduces P‐wave velocities. As mentioned earlier, Fe³⁺ is found to enter the crystallographic B site of bridgmanite only for harzburgite models with Fe³⁺/∑Fe > 0.5 or . For these scenarios, the spin transition of Fe³⁺ on the B site of bridgmanite gives rise to an additional P‐wave velocity reduction over a pressure interval from 40 to 100 GPa. Despite substantial broadening of the Fe²⁺ spin transition in ferropericlase and the Fe³⁺ spin transition in bridgmanite at high temperatures, both spin transitions can significantly reduce P‐wave velocities of pyrolite and harzburgite and need to be taken into account when modeling elastic properties. In addition, the spin transition in ferropericlase is further expected to affect Fe‐Mg exchange between ferropericlase and bridgmanite (Badro, 2014; Badro et al., 2005, 2003; Lin et al., 2013). Given the strong sensitivity of both P‐ and S‐wave velocities to changes in the Fe‐Mg exchange coefficient, the spin transition in ferropericlase could have a compositional effect on seismic properties that surpasses the elastic effect. Increasing the iron content of ferropericlase will also shift the spin transition to higher pressures (Fei et al., 2007; Persson et al., 2006; Solomatova et al., 2016; Speziale et al., 2005). Since S‐wave velocities are more sensitive to Fe‐Mg exchange than P‐wave velocities, the compositional contribution would strongly affect S‐wave velocities as opposed to the elastic contribution that mostly affects P‐wave velocities via elastic softening of the bulk modulus.

      The spin transition of ferric iron in the CF phase does not seem to strongly affect P‐ or S‐wave velocities of metabasalt. In contrast, suppressing the effect of the ferroelastic phase transition from stishovite to CaCl₂‐type SiO₂ results in very different velocity profiles for metabasalt. While the softening of the shear modulus was modeled here based on a Landau theory prediction (Buchen et al., 2018a; Carpenter et al., 2000), the full extent of elastic softening remained uncertain until the very recent determination of complete elastic stiffness tensors of SiO₂ single crystals across the ferroelastic phase transition (Zhang et al., 2021). Zhang et al. (2021) combined Brillouin spectroscopy, ISS, and X‐ray diffraction to track the evolution of the elastic stiffness tensor with increasing pressure and across the stishovite–CaCl₂‐type SiO₂ phase transition. In terms of the magnitude of the S‐wave velocity reduction, the predictions of Landau theory analyses seem to be consistent with the experimental results by Zhang et al. (2021). The elastic properties of stishovite and CaCl₂‐type SiO₂ had previously been computed for relevant pressures and temperatures using DFT and DFPT (Karki et al., 1997a; Yang and Wu, 2014). While indicating substantial elastic softening in the vicinity of the phase transition, the computations addressed both polymorphs independently and suggested discontinuous changes in the elastic properties at the phase transition, contradicting recent experimental results (Zhang et al., 2021) and earlier predictions based on Landau theory (Buchen et al., 2018a; Carpenter, 2006; Carpenter et al., 2000).