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
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