Here we present the thermoelastic properties of the postperovskite phase at relevant conditions obtained by first-principles computations within the quasiharmonic approximation. We compute shear, longitudinal, and bulk velocities of the postperovskite phase, compare with those of the perovskite phase (11), and, by invoking our previous thermodynamic phase boundary (2), we predict the seismic signature of its presence in the LM, i.e., density and velocity jumps across this transformation. We also predict in a continuum P,T space various ratios of relative changes in velocities and density caused by temperature and phase change in pure aggregates. They prove to be fundamental for interpreting the unexplained origin of lateral heterogeneities in D″.

The elastic constants of MgSiO₃ postperovskite are remarkably different from those of perovskite (11). Postperovskite is a layered structure, expands anisotropically, and has complex pressure- and temperature-dependent elastic behavior (see ref. 8 and Fig. 4, which is published as supporting information on the PNAS web site). However, its aggregate moduli do not differ dramatically from those of perovskite. The adiabatic bulk moduli of both phases, B_S(P, T) (Fig. 1A), are very similar at >80 GPa. The shear modulus of postperovskite, G(P, T) (Fig. 1 A), is larger and has larger pressure and temperature gradients. This result and the fact that postperovskite is ≈1.5% denser than perovskite at deep LM conditions determine the velocity contrasts between these phases. The shear velocity, V_S(P, T), of postperovskite and its gradients are larger than those of perovskite (see Fig. 1 legend and ref. 11). Because of G(P, T), postperovskite's V_S(P, T) is also larger and has larger gradients. The longitudinal velocity, V_P(P, T), is a little larger and has slightly larger gradients because of G(P, T) as well (see Fig. 1B). In contrast, the bulk velocity, V(P, T), is smaller than that of perovskite because of their similar B_S(P, T) values and the larger density (ρ) of postperovskite. Something similar is observed across the phase transition in postperovskite synthesized from natural samples of (Mg,Fe)SiO₃ orthopyroxene (14). Fig. 1C shows the velocity jumps across the calculated phase boundary (2) (see Fig. 1 legend). These results are consistent with the increase in seismic velocities observed ≈200–300 km above the core–mantle boundary in certain places (15) but most easily detected beneath regions of past subduction, presumably cold places, such as beneath Central America (15). There, ΔV_S > ΔV_P and ΔV_S ≈ 2–3% is observed, but this observation is clearly a regional property of a notably heterogeneous layer (refs. 16–18 and references therein).

Fig. 1. Elastic properties as functions of pressure and temperature. (A) Pressure dependence of aggregate adiabatic bulk (BS) and shear (G) moduli and density (ρ) of postperovskite along the 300 K (red), 1,000 K (orange), 2,000 K (green), 3,000 K (blue), (more ...)

Another baffling property of D″ revealed by global tomographic models (19) is the anticorrelation between lateral (isobaric) heterogeneities in V and V_S. The likely causes are usually addressed by comparing the seismic parameters, R_S/P = (lnV_S/lnV_P)_P and R_/S = (lnV/lnV_S)_P, to theoretical or experimental predictions of these ratios at relevant conditions (20). It is known that in the shallow LM R_S/P ~ 2.3 and R_/S ~ 0.0, whereas in D″ R_S/P ~ 3.4 and R_/S ~ –0.2 (19). Velocity anomaly ratios produced by isobaric temperature changes in pure postperovskite and perovskite aggregates are displayed in Fig. 2 A and B along with the seismic parameters extracted from ref. 19 and reported in ref. 20. In pure perovskite aggregates, R_S/P increases with pressure and temperature but reaches at most ≈2.3 at 135 GPa and 4,000 K, whereas R_/S is approximately pressure independent and slightly decreases with temperature to reach ≈0.16 at similar P, T values (see Fig. 2 A). In postperovskite R_S/P decreases with pressure, but because of its larger (G/T)_P, it increases more rapidly with temperature to reach ≈ 2.8 at the same P, T values. R_/S is smaller than that of perovskite, 0.1, at these conditions (see Fig. 2B). It has been argued that anelasticity, anisotropy effects, and lateral variations in calcium content in the deepest mantle might be necessary to produce large values for R_S/P and negative ones for R_/S, unless there is a phase transformation (20).

Fig. 2. Ratios of velocities and/or density anomalies. Seismic parameters RS/P = (lnVS/lnVP)P, R/S = (lnV/lnVP)P, and Rρ/S = (lnρ/lnVS)P at several temperatures for postperovskite (more ...)

Fig. 2C compares the seismic parameters with the computed ratios of velocity anomalies caused by the postperovskite transition along our phase boundary (2). Very large values for R_S/P (>6) and negative values for R_/S (<–0.5) result from this phase change. Therefore, lateral variation in phase abundances enhances the seismic parameters in the correct directions. This effect was approximately estimated in ref. 3 assuming the temperature dependence of perovskite and postperovskite's velocities were the same. The presence of secondary phases, such as magnesiowüstite and CaSiO₃, will decrease these anomaly ratios. In addition, the phase boundary and the velocities of minor element bearing perovskite and postperovskite should produce a P, T domain for perovskite/postperovskite coexistence also with unknown properties. Nevertheless, the effect of lateral variations of phase abundances on these parameters seems very robust.

As pointed out from the outset, the topography of D″ is consistent with a phase transition with positive Clapeyron slope (≈4–10 MPa·K^–1) induced by lateral temperature variations (7). Interestingly, the correlation between geographic location and nature of V and V_S anomalies is also consistent with this assumption if postperovskite is abundant in D″. Beneath the Central Pacific V is faster and V_S is slower than their spherical mantle averages, whereas beneath the Circum-Pacific the opposite holds. These regions are generally considered to be respectively hotter and colder than average. The positive Clapeyron slope of this transition implies that hotter regions should contain less postperovskite and therefore have faster V and slower V_S, whereas colder regions should be enriched in the latter and have slower V and faster V_S, as observed. Lateral variations in phase abundances alone do not account for the complex structure and properties of D″. However, this perspective should be useful as a reference model from which deviations should be interpreted. Obviously the effect of secondary phases and minor element partitioning on the postperovskite phase boundary and on aggregate elasticity, particularly the important effect of iron (21), must be determined before a more quantitative reference mineralogical model for D″ is developed.

The origin of the negative values of R_/S above D″ indicated in Fig. 2B is also unclear. It could originate in the degree of resolution of tomographic models. However, if this effect is real, it could have several origins, including anelasticity. A possible mineralogical origin and an argument against anelasticity alone will be discussed at the end of the text in connection with the elasticity of postperovskite-free aggregates (11) and the stability of iron-rich postperovskite (21).

These results and inferences imply that a third seismic parameter, R_ρ/S = (lnρ/lnV_S)_P, the average ratio between ρ and V_S anomalies caused by the postperovskite transition, should be positive and perhaps increase with depth in the lowermost mantle (see lowest portion of Fig. 2C), unless other effects such as change in anelastic effects or chemical heterogeneities (18, 20, 22)§ occur simultaneously. Some 3D density models do not support this prediction (24), whereas others do (25). Estimates of this parameter obtained by joint inversions of seismic and geodynamic data also tend to offer a positive ratio (26). It appears that until a clear consensus on the 3D structure of ρ is reached, this issue will remain an open point. Recently, it has been pointed out that an average excess density of 0.4% in the lowermost mantle is possible (27), in agreement with our expectations.

Another pressing issue is the anisotropy of D″, a case of boundary layer anisotropy possibly enhanced by the bias of seismic detection techniques toward these regions. Despite the lack of global seismic coverage of D″, the observed diversity of anisotropy styles (16, 28), and the numerous possible sources of anisotropy (29), evidence has been accumulating suggesting that anisotropy in certain places of D″ could result from lattice preferred orientation in largely strained aggregates produced by mantle circulation (ref. 30 and references therein). The analogy between the D″ region and the topmost upper mantle, where anisotropy is also strong, is very compelling. Beneath regions of past and present subduction, such as the Caribbean, where colder than average and largely deformed paleo-plates are expected to reside, and horizontal flow presumably happens, transverse isotropy with V_SH > V_SV is generally observed [V_SH(SV) being the velocity of horizontally (vertically) polarized shear waves propagating horizontally]. It is plausible that in postperovskite the primary slip system involves (010). Lateral material displacement should then align mainly the silica layers parallel to the horizontal plane. However, this simple picture does not provide a satisfactory explanation for the anisotropy in D″ (8). Static elasticity calculations have shown that (V_SH – V_SV) in transversely isotropic aggregates with this preferred orientation is positive but small (2, 3, 8). The largest V_S splitting is produced by aligning [001] vertically, not [010] (8).

Fig. 3 shows the calculated shear wave splittings along the thermodynamic phase boundary (2) for various vertical alignments of the crystalline axes of these phases and of periclase (MgO) (31),¶ the presumably most abundant secondary phase in the LM. It can be seen that at relevant P, T conditions that (i) vertical alignment of postperovskite's [001] produces the largest positive (V_SH – V_SV) but considerably smaller than that predicted at T = 0 K (8); (ii) the shear wave splittings in perovskite and postperovskite have similar magnitudes regardless of orientation; (iii) similarly to the static results (32), only vertical alignment of perovskite's [100] produces positive (V_SH – V_SV); and (iv) horizontal alignment of MgO's {100}, its primary slip plane at high Ps (33), produces considerably larger (V_SH – V_SV). Despite our lack of direct information on the slip systems of these phases at D″ conditions, it appears that unless a significant alteration in plastic deformation mechanism from diffusion to dislocation creep accompanies the postperovskite transition, it is unlikely that postperovskite can be a more significant source of anisotropy in D″ than perovskite. Despite being less abundant (≈20 vol%) magnesiowüstite (33) is the most anisotropic (31, 34) and weaker phase present. It is therefore likely to undergo more extensive deformation (33) and be a more important source of lattice preferred orientation-derived anisotropy (30), particularly in D″. Across the postperovskite transition, the contrast in strength between MgSiO₃ and MgO should increase because the strength of a material usually increases with the shear modulus (see Table 1). MgO therefore could undergo greater deformation next to postperovskite.

Fig. 3. Shear wave splittings (VSH – VSV) (see text) in MgSiO3 postperovskite and perovskite, along the thermodynamic phase boundary with respective uncertainties, for horizontally propagating waves in transversely isotropic aggregates with three possible (more ...)

Table 1. Elastic properties in GPa, km/s, and K of MgSiO3 perovskite (1) and postperovskite (2, 4, 6) at 125 GPa and 2,500 K and (3) 140 GPa and 4,000 K

Finally, it has been pointed out (11) that G in the shallow LM, as extracted from the Preliminary Reference Earth Model (PREM; G^PREM) (12), agrees well with that of an aggregate of (Mg,Fe)SiO₃-perovskite and (Mg,Fe)O with approximately pyrolitic composition at Ts predicted by a standard adiabatic geotherm (G^calc) (35). However, in the deep LM G^PREM exceeds G^calc by ≈10–15 GPa, i.e., differs by more than estimated uncertainties (11). The nonthermal nature of this phenomenon was indicated by the reasonably good agreement between and , or possibly a slightly smaller . Presently, the larger G^PREM is an argument against anelasticity in the LM. PREM, being a 1D model with a narrow D″ layer only 150-km thick without discontinuities in this region, smoothes the effect of a discontinuous increase in V_S and G throughout the lower-most mantle (ref. 16 and references therein). Therefore, the existence of postperovskite with larger G (≈20 GPa; see Table 1) in the D″ layer could contribute to the type of inconsistency between G^PREM and G^calc observed in ref. 11.

Another enticing origin for this inconsistency could be of mineralogical nature. With respect to a homogeneous and postperovskite free LM, the existence of a nonhomogeneous distribution of postperovskite introduces positive shear and negative bulk velocity heterogeneities. Their spherical averages increase and decrease as well. The spherically averaged shear and bulk moduli increase and remain approximately unchanged (or decrease slightly depending on the average geotherm), respectively. Ref. 11 pointed to this type of deviation starting at pressures as low as ≈75 GPa. This finding and the simultaneous observation of anticorrelations above ≈80 GPa indicated in Fig. 2 could be pointing to the existence of postperovskite already at these pressures, perhaps in regions with substantially greater iron content (20), or of another phase introducing the same type of elastic anomaly. In short, the origin of negative R_/S values above D″ could be the same as of those discrepancies observed in ref. 11.

This discussion is speculative, but it is essential to recognize this relationship. Until we have more information about equilibrium high P, T properties of (low and high spin) iron bearing aggregates this issue will not be simply tackled, including the role of anelasticity.

The methodology used here has been used in several previous investigations and reported in detail in other publications (2, 9, 11, 36) and is described in Supporting Methods, which is published as supporting information on the PNAS web site, with individual elastic constants of postperovskite and perovskite. It proved very successful when applied to the perovskite phase (11) at these conditions, producing results in excellent agreement with those obtained in molecular dynamics calculations (37). A recent investigation of the thermodynamic properties of the postperovskite phase (36) indicates that the quasiharmonic approximation is also valid for this phase at relevant conditions. Both phases are mechanically and vibrationally very stable well beyond their thermodynamic stability fields, and, at D″ conditions, their thermodynamic properties are very similar (36). This characteristic is reflected in the nature of the postperovskite transformation: it is kinetically slow displaying large hysteresis in pressure (1, 4, 5).

We thank Koichiro Umemoto for assistance with earlier calculations and Don Weidner and participants of the Cooperative Institute for Deep Earth Research workshop (National Science Foundation Grants PHY99-0794 and EAR-0215587) where these results were first presented for helpful discussions. This work was supported by National Science Foundation Grants EAR-0135533, EAR-0230319, and ITR-0428774. J.T. and T.T. were supported in part by the Japan Society for the Promotion of Science (JSPS).