Pressure Dependence of Elastic Wave Velocity for β-Mg 2 SiO 4 and the Composition of the Earth's Mantle

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Abstract
The pressure dependence of the elastic wave velocities for hot-pressed, elastically isotropic polycrystals of the β (modified spinel) phase of magnesium orthosilicate (Mg2SiO4) has been determined at room temperature to 3 gigapascals (GPa) by ultrasonic pulse interferometry. Pressure derivatives of the bulk (dK/dP = 4.8) and shear (dG/dP = 1.7) moduli derived from the travel times of the compressional (P) and shear (S) waves clearly demonstrate that the velocity contrast between the olivine and β phases of Mg2SiO4 decreases with increasing pressure. When combined with plausible values for the (as yet unmeasured) temperature derivatives, these new data can be used to calculate the contrast in P and S wave velocities across an olivine-β phase transformation occuaring at pressure-temperature conditions corresponding to about 400 kilometers depth in the earth. The seismologically observed contrasts ΔV in both P and S wave velocities constrain the percentage of orthosilicate in a model mantle of uniform chemical composition for appropriate relative magnitudes of the temperature (T) derivatives of the bulk and shear moduli for the β phase. Allowed combinations of orthosilicate content (percent), dK/dT, and dG/dT (both in gigapascals per Kelvin) for a pair of recent seismological models with ΔVp = ΔVs 4.6% include (65, -0.018, -0.020), (55, -0.015, -0.018), and (45, -0.012, -0.016).