Velocity-density systematics and its implications for the iron content of the mantle

Abstract

A unified relation among the hydrodynamic velocity Vϕ, the density ρ, the mean atomic weight m, and Poisson's ratio σ is proposed for oxides, silicates, and germanates as Vϕ = Vϕ+ ‐ 0.058(m ‐ m0) ‐ 2.62(ρ − ρ0), where Vϕ+ = −1.84 + 7.51 σ + 1.98ρ and ρ0 is the density of the crystallographically isostructural material of m = m0 = 20.2. The proposed relation can be considered as a linear form of the power law relation proposed by Shankland and Chung (1974). However, the incorporation of σ into the present relation would give a better correlation among the various parameters. It would also accommodate the velocity data of α quartz as well as those of materials undergoing various phase transformations. The value of the mean atomic weight calculated from this relation for various earth models implies that iron enrichment in the lower mantle with respect to the upper mantle is not necessary.

Elastic properties, chemical composition, and crystal structure of minerals

“…The change to mixed oxides appears to mimic the effect of an increase of rfi on a v-p plot. Only in the two-elastic-parameter systematics of Mao (1974) does this false Arfi appear to be negligible. Therefore, the petrofabric of rocks does have an influence.…”

“…Such jumps appear whenever systematics using only one elastic parameter are used. On the other hand Mao's (1974) systematics that use o-as a second parameter imply virtually no change of rfi at the places where it would be most expected. The simplest deduction from this inverse approach is that the mantle is chemically uniform with respect to iron content on the spherically averaged scale of present seismic profiles.…”

“…However, Mao (1974) pointed out that the materials of rfi-~ 20 having velocities above a line described by (31) had relatively high values of Poisson's ratio, and those below the line -most conspicuously or-quartz -had lower values of or. He defined a corrected velocity, vb* = 1.84+7.51o-+ 1.98p,…”

“…It is clear that the vb-o-systematics afford a more successful result; there is presently no way to reduce the scatter in the important region near n~ = 20 in Figure 11 a without including the Poisson ratio or a similar correction. Equation (34) a Ar~ = 0.1 (Mao, 1974). In applications to the Earth, where two elastic properties vp and vs commonly result from seismic profiles, the requirement for" both vb and o" makes full use of available information in a consistent way, and produces good results over a wide range of packing densities in oxides and silicates.…”

“…With this assumption it is possible to calculate the temperature at 400 km using laboratory petrological data on the transition. In a third example, the experimental verification (Ming and Bassett, 1975) of the decomposition of olivine into its component oxides as suggested for the lower mantle (Birch, 1952) makes it reasonable to calculate the velocities of the mixed oxides under mantle pressures-from the theories of elasticity of aggregates (Mao, 1974;andDavies, 1974a, 1974b).…”