Voigt and Reuss prediction of anisotropic elasticity of dunite

Abstract

Aggregate anisotropic elastic constants were calculated for two nearly mono‐minerallic dunites by both the Voigt and the Reuss averaging schemes. The average constants were obtained rigorously from petrofabric data, which provided precise orientation of a sample of 100 grains in each specimen, by using published values of olivine single‐crystal constants. The resultant elastic constants were used to calculate P‐ and S‐wave phase velocities in various directions for comparison with actual measurements made in the same specimens. Agreement between the predicted and observed velocities was within the observational error for compressional (pseudo‐compressional) waves when using the Voigt scheme, with best agreement at pressures above 2 kb. The Reuss scheme also predicts the variation in velocity with direction quite well. Agreement of shear wave velocities is not so good, probably because of larger uncertainties in the measured data. The data suggest that the anisotropy of crystalline aggregates at hydrostatic pressures above a few kilobars is governed almost exclusively by crystal orientation.