Alternatively the elastic wave velocities

Alternatively, the elastic wave velocities (Vs and Vp in km/s) of the Rw at certain P-T condition can be readily calculated by using its corresponding shear modulus (G; GPa), adiabatic bulk modulus (KS; GPa) and density (ρ; g/cm3), according to the following equations:and With its G0, KS0 and ρ0 (G, KS and ρ at ambient P and T, respectively), әG/әT and әG/әP, әKS/әT and әKS/әP, and KT0, әKT/әP (or KT′) and α well determined, one can probe the influence of P and T on the Vs and Vp. If these parameters are measured for the Rw in a large range of compositions, further, one can simultaneously characterize the effects of P, T and composition, which all are variables in the real Earth. The effects of the Rw composition on the Vs in the system Mg2SiO4–Fe2SiO4 at ambient P-T condition, calculated with equation (6), are compared in Fig. 4(a) (Sinogeikin et al., 1998; Higo et al., 2006; Liu et al., 2008a). In general, the result from Liu et al. (2008a) is in good agreement with Higo et al. (2006), which is completely expected from equation (6) and the data listed in Table 4. The absolute (relative) difference in the Vs values between these two studies is very small, from ∼0.13 km/s (2%; Mg2SiO4-Rw) to 0.04 km/s (1%; Fe2SiO4-Rw). The most important point shown in Fig. 4(a) is that lp-pla2 the effect of the Rw composition on the Vs is very pronounced, as found in all these studies: when the Rw changes its composition from XFe = 0 to XFe = 1, the overall Vs decrease is ∼24% (the thin broken curve), or ∼31% (the solid curves). This large composition effect is almost equally contributed by the large variations in the density and shear modulus of the Rw along the join Mg2SiO4–Fe2SiO4: as the XFe increases from 0 to 1, the density increases by ∼36% whereas the shear modulus decreases by ∼21% (Sinogeikin et al., 1998) to 35% (Liu et al., 2008a). Finally, substantial uncertainty still exists in the composition effect on the Vs, due to the difference in the equations describing the Rw composition effect on the shear modulus (Table 4): as the two extreme cases (the thick solid curve versus thin broken curve), the equations from Liu et al. (2008a) and Sinogeikin et al. (1998) result in a relative difference of ∼0% in the Vs for the Mg2SiO4-Rw, but a relative difference of ∼11% for the Fe2SiO4-Rw. Considering the similarity of the equations from Weidner et al. (1984), Higo et al. (2006) and Liu et al. (2008a), and the relatively large effect of the Rw composition on the shear modulus (Table 4) which should facilitate an experimental determination with high accuracy, anyhow, we will adopt the latest equation from Liu et al. (2008a) in our later relevant calculations. The effects of the Rw composition on the Vp in the system Mg2SiO4–Fe2SiO4 at ambient P-T condition, calculated with equation (7), are shown in Fig. 4(b) (Sinogeikin et al., 1998; Higo et al., 2006; RNA transcript study). In general, the result from this study is in good agreement with Higo et al. (2006): the absolute (relative) difference in the Vp values between these two studies is very small, from ∼0.01 km/s (0%; Mg2SiO4-Rw) to 0.11 km/s (1%; Fe2SiO4-Rw). Furthermore, the composition effect is very pronounced: when the Rw changes its composition from XFe = 0 to XFe = 1, its Vp decreases by ∼17% (the thin broken curve), or by ∼21% (the solid curves). This large composition effect is generally prescribed by the variations of the density and shear modulus of the Rw along the join Mg2SiO4–Fe2SiO4, similar to the Vs case. The increase of the bulk modulus for the entire composition range, varying from ∼20% (Sinogeikin et al., 1998), to 10% (Liu et al., 2008a), or to ∼4% (this study), also makes its contribution by partially counteracting the effects of the density and shear modulus of the Rw: according to equation (7), a smaller composition effect on the bulk modulus leads to a larger composition effect on the Vp. Consequently, small uncertainty in the composition effect on the Vp still exists due to the difference in the equations describing the correlation between the Rw composition and the bulk modulus from different studies: as the two extreme cases (the thick solid curve versus thin broken curve), the equations from this study and Sinogeikin et al. (1998) result in a difference of ∼0% in the Vp for the Mg2SiO4-Rw, but a difference of ∼5% for the Fe2SiO4-Rw. Additionally, the potential influence of those different equations describing the correlation between the Rw composition and shear modulus (Table 4) has been assessed: with the effects of the Rw composition on the bulk modulus and density from this study, we have found that the difference in Vp is ∼0% for the Mg2SiO4-Rw, but gradually increases to ∼4% for the Fe2SiO4-Rw.