Читать книгу Mantle Convection and Surface Expressions - Группа авторов - Страница 67
3.8 EARTH’S LOWER MANTLE
ОглавлениеSeismic tomography shows lateral variations in P‐ and S‐wave velocities at all depths of the lower mantle and across length scales that are compatible with changes in temperature, chemical composition, and phase assemblage as well as combinations thereof (Durand et al., 2017; Hosseini et al., 2020; Koelemeijer et al., 2016). Scattering of seismic waves in the lower mantle, in contrast, points to changes in the elastic properties of the mantle over length scales that are commonly interpreted to be too short to arise from thermal gradients alone and require compositional heterogeneities or phase changes (Frost et al., 2017; Kaneshima & Helffrich, 2009; Waszek et al., 2018). Lateral and local variations are superimposed on the monotonous increase of seismic velocities that dominates global seismic reference models at depths between 800 km and 2400 km (Dziewonski & Anderson, 1981; Kennett et al., 1995; Kennett & Engdahl, 1991). The seismic structure of the upper mantle and transition zone can be compared with the results of mineral‐physical models (Cammarano et al., 2009; Cobden et al., 2008; Xu et al., 2008) that are based on internally consistent thermodynamic databases (Holland et al., 2013; Stixrude & Lithgow‐Bertelloni, 2011). For the lower mantle and depths in excess of 800 km, however, these databases are less reliable since both chemical compositions and elastic properties of relevant mantle minerals are less well constrained as discussed in Section 3.6 for bridgmanite. Moreover, existing thermodynamic databases do not include the effects of continuous phase transitions, such as the ferroelastic phase transition from stishovite to CaCl2‐type SiO2 and spin transitions, on elastic properties that are expected to affect seismic velocities in the lower mantle. This section focuses on seismic properties of relevant rock types in the depth interval from about 800 km to 2400 km. Chapter 8 of this volume addresses the lowermost mantle including the D" layer at depths in excess of 2400 km.
Experiments on peridotitic rock compositions found bridgmanite (bm), ferropericlase (fp), and calcium silicate perovskite (cp) as major phases with approximately constant volume fractions of bm:fp:cp ~ 70:20:10 at pressures and temperatures of the lower mantle (Irifune et al., 2010; Kesson et al., 1998; Murakami et al., 2005). Depending on composition and temperature, bridgmanite transforms to the post‐perovskite phase at pressures in excess of 100 GPa corresponding to an approximate depth of 2400 km (Murakami et al., 2005, 2004; Shim et al., 2004; Sun et al., 2018). Since the composition of calcium silicate perovskite remains close to pure CaSiO3 and bridgmanite incorporates virtually all available Al2O3, the main compositional variables are the Mg/(Fe+Mg) ratios of bridgmanite and ferropericlase that are coupled through Fe‐Mg exchange reactions. Fe‐Mg exchange between ferropericlase and bridgmanite is sensitive to a large number of thermodynamic parameters including pressure, temperature, composition, oxygen fugacity, and the spin states of Fe2+ and Fe3+ (Badro, 2014). Despite substantial progress in deciphering the effects of these parameters on the Fe‐Mg exchange between bridgmanite and ferropericlase, the variation of the Fe‐Mg exchange coefficient (Badro, 2014) through the lower mantle remains debated. While recent experimental studies found Fe‐Mg exchange coefficients of about 0.5 with no clear trend with increasing pressure between 40 GPa and 100 GPa (Piet et al., 2016; Prescher et al., 2014; Sinmyo & Hirose, 2013), DFT computations suggest generally smaller values that decrease with increasing pressure as a result of the progressing spin transition of Fe2+ in ferropericlase (Muir & Brodholt, 2016; Xu et al., 2017). The Fe‐Mg exchange coefficient for harzburgitic rocks seems to be closer to 0.2 and to decrease with increasing pressure (Auzende et al., 2008; Badro, 2014; Piet et al., 2016; Sakai et al., 2009; Sinmyo et al., 2008; Xu et al., 2017). Figure 3.6a summarizes experimental and computational findings on Fe‐Mg exchange between bridgmanite and ferropericlase.
For basaltic compositions that intend to represent recycled oceanic crust, experimental results suggest modal proportions of the major phases bridgmanite (bm), calcium silicate perovskite (cp), CF phase (cf), and stishovite (st) of bm:cp:cf:st ~ 45:30:15:10 throughout most of the lower mantle (Hirose et al., 2005, 1999; Ono et al., 2001; Perrillat et al., 2006; Ricolleau et al., 2010). At pressures between 25 GPa and 40 GPa, the NAL phase has been found to coexist with this assemblage but seems to become destabilized towards higher pressures (Perrillat et al., 2006; Ricolleau et al., 2010). Figure 3.6b shows exchange coefficients for Fe‐Mg and Al‐Mg exchange between bridgmanite and the CF phase as computed from experimentally observed mineral compositions for the assemblage bm‐cp‐cf‐st in basaltic bulk compositions. Although it appears difficult to assign robust trends of mineral compositions with changes in pressure or temperature, iron tends to be equally distributed between bridgmanite and the CF phase while aluminum seems to preferentially partition into the CF phase. The wide spread in experimentally observed mineral compositions is also reflected in the bridgmanite compositions shown in Figure 3.3. Clearly, more experiments are needed to better understand element partitioning and mineral compositions in peridotitic and metabasaltic rocks at conditions of the lower mantle.
Figure 3.6 Exchange coefficients for Fe‐Mg exchange between bridgmanite and ferropericlase in peridotitic bulk compositions (a) and for Fe‐Mg and Al‐Mg exchange between bridgmanite and the CF phase in basaltic bulk compositions (b). Color shading indicates the relevant parts of each diagram for different bulk compositions (a) or exchange coefficients (b). Note the reduction in the Fe‐Mg exchange coefficient between bridgmanite and ferropericlase with increasing pressure as predicted by thermodynamic modeling based on DFT computations.
To evaluate the impact of variations in rock composition and thermal state of the lower mantle on seismic properties, I computed P‐ and S‐wave velocities for pyrolite, harzburgite, and metabasalt over relevant pressure and temperature intervals. Recent experimental and computational results on the high‐pressure and high‐temperature elasticity of lower‐mantle phases are compiled in Table 3.1. This compilation aims at reflecting recent progress on individual mineral phases and does not represent an internally consistent data set in a thermodynamic sense. If not given in the original publication, finite‐strain and thermal parameters were determined by fitting experimental data to the finite‐strain formalism of Stixrude & Lithgow‐Bertelloni (2005). I included the effect of spin transitions of Fe2+ in ferropericlase and of Fe3+ in bridgmanite and in the CF phase using the parametrization introduced in Section 3.7 with parameters given in Figures 3.5a–c. The effect of the ferroelastic phase transition from stishovite to CaCl2‐type SiO2 was modeled based on the reanalysis of powder diffraction data (Andrault et al., 2003) using Landau theory as given by Buchen et al. (2018a). The experimentally determined phase boundary between stishovite and CaCl2‐type SiO2 with a Clapeyron slope of dP/dT = 15.5 MPa K–1 (Fischer et al., 2018) was used to constrain the temperature dependence of the Landau parameter A. Figure 3.7 shows P‐ and S‐wave velocities for each mineral composition in Table 3.1 along a typical adiabatic compression path.
Table 3.1 Finite‐strain parameters for mineral phases of the lower mantle.
References: [1] Fiquet et al. (2000), [2] Murakami et al. (2007), [3] Zhang et al. (2013), [4] Murakami et al. (2012), [5] Chantel et al. (2012), [6] Fu et al. (2018), [7] Jackson et al. (2005), [8] Kurnosov et al. (2017), [9] Sinogeikin & Bass (2000), [10] Murakami et al. (2009), [11] Yang et al. (2016), [12] Yang et al. (2015), [13] Thomson et al. (2019), [14] Mookherjee (2011), [15] Stixrude & Lithgow‐Bertelloni (2011), [16] Imada et al. (2012), [17] Dai et al. (2013), [18] Wu et al. (2017), [19] Andrault et al. (2003), [20] Jiang et al. (2009), [21] Gréaux et al. (2016), [22] Fischer et al. (2018), [23] Buchen et al. (2018a).
| Mineral/Phase | Formula | Volume | Bulk modulus | Shear modulus | Quasi‐harmonic parameters | References | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| V 0 (Å3) | K 0 (GPa) | K 0 ' | G 0 (GPa) | G 0 ' | θ 0 (K) | γ 0 | q 0 | η S0 | |||
| bridgmanite | MgSiO3 | 162.27(1) | 253(9) | 3.9(2) | 173(2) | 1.56(4) | 905.9 | 1.44 | 1.09 | 2.2(2) | [1,2,3,4] |
| (Mg0.95Fe0.05)SiO3 | 163.45(2) | 247(2)S | 3.6(1) | 168.3(9) | 2.02(3) | 905.9 | 1.44 | 1.09 | 2.2 | [3,4,5*,6*] | |
| (Mg0.96Al0.04)(Si0.96Al0.04)O3 | 163.21(1) | 252(5)S | 3.7(3) | 166(1) | 1.57(5) | 905.9 | 1.44 | 1.09 | 2.2 | [3,4,7] | |
| (Mg0.9Fe0.1)(Si0.9Al0.1)O3 | 162.96(2) | 250.8(4)S | 3.44(3) | 159.7(2) | 2.05(2) | 905.9 | 1.44 | 1.09 | 2.2 | [3,4,8] | |
| ferropericlase | MgO | 74.68(2) | 163(1)S | 3.8(1) | 131(1) | 1.92(2) | 770 | 1.5 | 2.8 | 3.0 | [9,10,11*] |
| (Mg0.92Fe0.08)O | 74.07(1) | 169(2)S | 4.01(7) | 126(2) | 2.08(3) | 770 | 1.5 | 2.8(6) | 3.0(3) | [11*,12*] | |
| Ca silicate perovskite | CaSiO3 | 45.57(2) | 248(3) | 3.6(1) | 107(1) | 1.66(22) | 771(90) | 1.67(4) | 1.1(2) | 3.3 | [13] |
| Ca ferrite‐type phase | MgAl2O4 | 236.07 | 217 | 3.7 | 133 | 1.7 | 840(20) | 1.3(3) | 1(1) | 2(1) | [14,15] |
| FeAl2O4 | 247.49 | 217 | 3.7 | 133 | 1.7 | 840 | 1.3 | 1 | 2 | [14,15] | |
| Na0.4Mg0.6Al1.6Si0.4O4 | 239.9(37) | 221(2) | 4 | 129.65(6) | 2.34(1) | 840 | 1.3 | 1 | 2 | [15,16,17] | |
| Na0.88Al0.99Fe0.13Si0.94O4 | 242.79(27) | 205(6) | 3.6(2) | 130 | 2 | 840 | 1.3 | 1 | 2 | [15,18*] | |
| stishovite | SiO2 | 46.51(2) | 320(2) | 4 | 264(2) | 1.90(1) | 1100 | 1.7 | 5.7(3) | 2.9(2) | [19,20,21*,22,23] |
| CaCl2‐type SiO2 | SiO2 | 47.54(18) | 238(6) | 4.82(2) | 264(2) | 2.23(1) | 1100 | 1.7 | 5.7 | 2.9 | [19,20,21*,22,23] |
Values in italics were estimated or adopted from other compositions/polymorphs of the same phase/compound.
S Isentropic bulk modulus.
* Original data were refit to the finite‐strain formalism of Stixrude & Lithgow‐Bertelloni (2005).
Figure 3.7 P-wave (a) and S-wave (b) velocities for different mineral phases and compositions along a typical adiabatic compression path starting at 1900 K and 25 GPa (see Figure 3.8). These mineral phases and compositions were mixed to model elastic wave speeds of rocks as shown in Figures 3.8 and 3.9. Dashed curves show P‐ and S‐wave velocities when the effect of relevant continuous phase transitions on elastic properties is ignored. See Table 3.1 for references.
Chemical bulk compositions for pyrolite and metabasalt were approximated by the depleted MORB mantle (DMM) and NMORB compositions of Workman and Hart (2005). In analogy to the approach of Xu et al. (2008), a hypothetical harzburgite composition was generated by assuming pyrolite to be an 80:20 mixture of harzburgite:basalt by mass. A basalt fraction of 20% in the mantle corresponds to the upper limit of estimates based on geochemical (Morgan & Morgan, 1999; Sobolev et al., 2007) and geodynamical arguments (Ballmer et al., 2015; Nakagawa et al., 2010). For pyrolite and harzburgite, mineral compositions were computed in the system CFMAS and for metabasalt in the system NCFMAS. Bulk compositions were partitioned into the phase assemblages bm‐fp‐cp for pyrolite and harzburgite and bm‐cp‐cf‐st for metabasalt resulting in approximate volume fractions of 77:16:7 (bm:fp:cp) in pyrolite, 74:24:2 (bm:fp:cp) in harzburgite, and 45:26:14:15 (bm:cp:cf:st) in metabasalt, respectively. For each phase, the compositions listed in Table 3.1 were mixed to match the computed mineral compositions as outlined in Section 3.6. For some mineral compositions, this approach required extrapolations beyond the compositional limits defined by the mineral compositions in Table 3.1. In these cases, the extrapolations of elastic moduli were restricted to not transcend compositional limits by more than 10% of the compositional range delimited by the mineral compositions of Table 3.1.
The exact mineral compositions and volume fractions for a given bulk rock composition depend critically on assumptions about element partitioning between minerals and the overall Fe3+/∑Fe ratio. To separate the effects of temperature and compositional parameters, I first computed P‐ and S‐wave velocities for each bulk rock composition setting Fe3+/∑Fe = 0.5 in bridgmanite for all rock compositions and requiring that (Fe/Mg)bm/(Fe/Mg)fp = 0.5 and 0.2 in pyrolite and harzburgite, respectively (Figure 3.6a), and that (Fe/Mg)bm/(Fe/Mg)cf = 1 and (Al/Mg)bm/(Al/Mg)cf = 0.2 in metabasalt (Figure 3.6b). For these reference scenarios, I computed adiabatic compression paths for each rock composition starting at 1900 K, 1400 K, and 2400 K at 25 GPa and mapped P‐ and S‐wave velocities between these compression paths based on the Voigt‐Reuss‐Hill average over all relevant mineral phases.
Figure 3.8 shows the modeling results for the reference scenario of each bulk rock composition in terms of deviations of the computed P‐ and S‐wave velocities from the seismic velocities of the preliminary reference Earth model (PREM; Dziewonski & Anderson, 1981):
Figure 3.8 Relative contrasts between modeled P-wave (upper row) and S-wave (lower row) velocities for pyrolitic (left column), harzburgitic (central column), and basaltic (right column) bulk rock compositions and PREM. Black curves show adiabatic compression paths for each rock composition and starting at 1400 K, 1900 K, and 2400 K at 25 GPa. For each rock composition, computed volume fractions of minerals and the choice of compositional space and parameters are given below the respective diagrams. See text for details of elastic wave speed modeling.
where vPREM stands for the P‐ or S‐wave velocity of PREM at the respective pressure and Δv = v − vPREM is the difference in velocity between the model and PREM. P‐wave velocities of pyrolite appear to systematically fall below those of PREM except for combinations of lowest pressures and temperatures. With magnitudes of less than 3%, these deviations are similar in magnitude to the combined uncertainties on computed P‐wave velocities that arise from propagating uncertainties on finite‐strain parameters, averaging over elastic anisotropy, and mixing mineral compositions with different elastic properties (Figures 3.1 and 3.3a). While affected by the same sources of uncertainties, computed S‐wave velocities appear to be more sensitive to temperature than P‐wave velocities and match S‐wave velocities of PREM, i.e., dlnvS = 0, within the considered temperature interval. The match with PREM would imply a temperature profile that deviates substantially from any of the computed adiabatic compression paths. Modeled S‐wave velocities match those of PREM for temperatures below the central adiabat down to a depth of around 1800 km where temperatures would need to rise above those of the central adiabat in order to follow PREM. Projecting the pyrolitic temperature profile for dlnvS = 0 onto the corresponding map for P‐wave velocities would lead to deviations of –1.5% < dlnvP < 0%. Maps of deviations dlnv for harzburgite are similar to those for pyrolite. However, S‐wave velocities of harzburgite seem to be systematically higher than those of pyrolite by about 0.5% to 1%, and P‐wave velocities show slightly steeper gradients with depths. Computed P-wave and in particular S‐wave velocities for metabasalt are significantly lower than those of PREM at most pressure–temperature combinations explored here. Despite the low volume fraction of free SiO2 phases that go through the phase transition from stishovite to CaCl2‐type SiO2, the related elastic softening of the shear modulus gives rise to a pronounced trough of amplified negative contrasts in P‐ and S‐wave velocities between metabasalt and PREM.
While the maps shown in Figure 3.8 illustrate the temperature dependence of P‐ and S‐wave velocity deviations from PREM, they heavily rely on assumptions about the Fe3+/∑Fe ratio in bridgmanite and about Fe‐Mg exchange between mineral phases. To explore the impact of these compositional parameters on computed P‐ and S‐wave velocities, I varied the Fe3+/∑Fe ratio of bridgmanite and the Fe‐Mg exchange coefficients between bridgmanite and ferropericlase in pyrolite and harzburgite and between bridgmanite and the CF phase in metabasalt within the ranges suggested by data plotted in Figures 3.6a and 3.6b. When varying one compositional parameter, all other parameters were fixed to their values in the references scenarios. Figure 3.9 shows the resulting deviations of P‐ and S‐wave velocities from PREM assuming a range of Fe3+/∑Fe ratios in bridgmanite or different Fe‐Mg exchange coefficients for each bulk rock composition along the central adiabats shown in Figure 3.8. Computed P‐ and S‐wave velocities of both pyrolite and harzburgite are more sensitive to changes in the Fe‐Mg exchange coefficient between bridgmanite and ferropericlase than to changes in the Fe3+/∑Fe ratio of bridgmanite. The sensitivity to Fe‐Mg exchange increases with depth, in particular for S waves. When combined with a reduction of the Fe‐Mg exchange coefficient with depth as suggested by recent computational studies (Muir & Brodholt, 2016; Xu et al., 2017), the strong sensitivity of P‐ and S‐wave velocities to Fe‐Mg exchange between bridgmanite and ferropericlase could result in substantial velocity reductions for peridotitic rocks towards the lowermost mantle, even along typical adiabatic temperature profiles.
Figure 3.9 Relative contrasts between modeled P-wave (upper row) and S-wave (lower row) velocities for pyrolitic (left column), harzburgitic (central column), and basaltic (right column) bulk rock compositions and PREM along adiabatic compression paths starting at 1900 K and 25 GPa (see Figure 3.8). Variations in the Fe3+/∑Fe ratio of bridgmanite and in the Fe‐Mg exchange coefficient have been explored for each bulk rock composition as indicated below the respective diagrams. Dashed curves show P‐ and S‐wave velocity contrasts when the effect of different continuous phase transitions on elastic properties is ignored or modified as specified. Red shaded bands indicate the differences in modeled P‐ 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 dlnvS = 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). First measurements on stishovite single crystals have captured the incipient elastic softening to pressures up to 12 GPa (Jiang et al., 2009) that has further been found to reduce the velocities of sound waves that propagate along selected crystallographic directions in aluminous SiO2 single crystals at higher pressures (Lakshtanov et al., 2007). For basaltic bulk rock compositions, stishovite was found to incorporate several weight percent Al2O3 (Hirose et al., 1999; Kesson et al., 1994; Ricolleau et al., 2010). Aluminum incorporation into stishovite has been shown to reduce the transition pressure to the CaCl2‐type polymorph (Bolfan‐Casanova et al., 2009; Lakshtanov et al., 2007). While the effect of aluminum incorporation into SiO2 phases has not been addressed in the modeling presented here, I illustrate the effect of changing the Clapeyron slope of the stishovite–CaCl2‐type SiO2 phase transition on the velocity profiles for metabasalt by using dP/dT = 11.1 MPa K–1 as reported by Nomura et al. (2010) instead of 15.5 MPa K–1 (Fischer et al., 2018) in an additional scenario shown in Figure 3.9.
While the modeling presented here primarily aims at providing examples for how elastic properties of rocks in Earth’s lower mantle can be assessed using mineral‐physical information on the elastic properties of mineral phases at high pressures and high temperatures, including the effects of continuous phase transitions, there are several sources of uncertainties that are difficult to evaluate quantitatively. For example, I combined computational with experimental results and used data from studies that used different types of samples, i.e., single crystals or polycrystals, and different methods to determine sound wave velocities, including Brillouin spectroscopy and ultrasonic interferometry. For none of the mineral phases do the available data cover the entire range of relevant pressures and temperatures. To illustrate uncertainties that result from averaging over the elastic properties of different mineral phases and compositions, Figure 3.9 shows the differences in P‐ and S‐wave velocities for the reference scenario of each bulk rock composition that result from the differences between the Voigt and Reuss bounds on the elastic moduli calculated based on the volume fractions that each mineral composition of Table 3.1 contributes to each of the rocks in Figure 3.9. It is further important to note that some compositions contribute with high volume fractions to all bulk rock compositions, in particular bridgmanite compositions, and revision of their finite‐strain parameters could substantially alter the computed velocity profiles.
Despite these uncertainties, some general and potentially more robust features can be observed and related to concepts of material transport in Earth’s mantle. P‐ and S‐wave velocities of metabasalt differ substantially from those of PREM throughout the lower mantle and for all compositional scenarios considered here. Deep recycling of oceanic lithosphere can therefore be expected to create strong contrasts in elastic properties between former basaltic crust and surrounding mantle rocks and to affect seismic wave propagation in the lower mantle. Since fragments of subducted oceanic crust can survive several hundred million years of convective stirring while retaining dimensions of several kilometers (Stixrude & Lithgow‐Bertelloni, 2012), they would create perturbations in elastic properties of sufficient magnitude and suitable size to efficiently scatter seismic energy. The interpretation of seismic scatterers in Earth’s lower mantle in terms of deep recycling of oceanic crust (Frost et al., 2017; Kaneshima and Helffrich, 2009; Rost et al., 2008; Waszek et al., 2018) is therefore compatible with mineral‐physical models and further supported by geodynamical simulations (Ballmer et al., 2015; Brandenburg & van Keken, 2007) and geochemical observations (Hofmann, 1997; Stracke, 2012). Modeled P‐ and S‐wave velocities of metabasalt are lower than those of PREM and, with few exceptions, lower than those of most scenarios of pyrolite and harzburgite (Figure 3.9). The low P‐ and S‐wave velocities of metabasalt reflect the low sound wave velocities of calcium silicate perovskite found in recent experimental studies (Gréaux et al., 2019; Thomson et al., 2019) and challenge earlier modeling results that predicted a fast seismic signature for recycled basaltic crust (Davies et al., 2012; Deschamps et al., 2012; Stixrude & Lithgow‐Bertelloni, 2012). As a consequence, the hypothesis that recycled oceanic crust might contribute to the velocity reductions of large low‐velocity provinces (LLVP) received new attention (Garnero et al., 2016; McNamara, 2019; Thomson et al., 2019). The example of calcium silicate perovskite demonstrates, however, how current mineral‐physical models for the lower mantle hinge on the elastic properties of individual mineral phases that, when revised, may exert a strong leverage on computed wave velocities.
For most of the compositional scenarios explored for pyrolite and harzburgite shown in Figure 3.9, S‐wave velocities show steeper gradients with depth than PREM while P‐wave velocity gradients are either similar to those of PREM or only slightly steeper than PREM. P‐ and S‐wave velocities are lower than those of PREM at 800 km depth for all scenarios, and only S‐wave velocities eventually rise above those of PREM for the majority of scenarios and at depths that depend on the combination of compositional parameters. P‐wave velocities remain below those of PREM for all pyrolite and harzburgite scenarios and at all depths considered here. Note that steep S‐wave velocity gradients and low P‐wave velocities remain characteristic signatures of pyrolite and harzburgite along hotter or colder adiabatic compression paths (Figure 3.8). P‐ and S‐wave velocity gradients that exceed those of seismic reference models have also been found by earlier mineral‐physical models for adiabatic compression paths of pyrolite (Cammarano et al., 2005b; Cobden et al., 2009; Matas et al., 2007) with the spin transition of ferropericlase bringing computed P‐wave velocity gradients closer to those of seismic reference models (Cammarano et al., 2010). Regions of the lower mantle that exhibit higher‐than‐average S‐wave velocity gradients have been found to coincide with the distribution of geoid lows and locations of former subduction (Richards & Engebretson, 1992; Spasojevic et al., 2010; Steinberger, 2000). In view of the mineral‐physical models shown in Figure 3.9, these observations are consistent with the storage of former slabs in the lower mantle that are dominated by peridotitic rocks from the upper mantle.
If we accept steeper‐than‐PREM S‐wave velocity gradients and lower‐than‐PREM P‐wave velocities as signatures of peridotitic rocks in the lower mantle, we find that a complementary lithology with higher‐than‐PREM P‐wave velocities and lower‐than‐PREM S‐wave velocity gradients would be required to match PREM as an average between these two lithologies. Based on the here‐used mineral‐physical data set (Table 3.1 and Figure 3.7), iron‐free bridgmanite compositions, i.e., MgSiO3 and (Mg0.96Al0.04)(Si0.96Al0.04)O3, would satisfy these criteria. Rocks that are dominated by iron-poor bridgmanite could therefore compensate for the steep S‐wave velocity gradients and low P‐wave velocities of former upper‐mantle rocks, such as pyrolite and harzburgite, that sink into the lower mantle as cold slabs imaged by seismic tomography (Fukao & Obayashi, 2013; Sigloch et al., 2008; Simmons et al., 2015; van der Hilst et al., 1997). The results of recent geodynamic simulations suggest that domains of bridgmanite‐rich rocks may remain isolated by channeling mantle flow around themselves when viscosity contrasts between such highly rigid domains and weaker pyrolitic rocks are high enough (Ballmer et al., 2017a). Mantle domains rich in bridgmanite but at the same time depleted in iron could have formed by fractional crystallization of a magma ocean, from which iron-poor bridgmanite would crystallize first as the liquidus phase (Andrault et al., 2012; Boukaré et al., 2015; Fiquet et al., 2010). Fe‐enriched fractionation products could have been separated from bridgmanite‐rich domains by accumulating at the base of the mantle (Ballmer et al., 2017b; Labrosse et al., 2015) and evolving to iron-rich mineral assemblages that have been invoked to explain geodynamic and seismic properties of LLVPs (Deschamps et al., 2012; Garnero et al., 2016) and ultra‐low velocity zones (ULVZ) (Bower et al., 2011; Muir and Brodholt, 2015b, 2015a; Wicks et al., 2017, 2010; Yu & Garnero, 2018).
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.
