Effective‐Medium Models of Inner‐Core Anisotropy

Abstract

AbstractBody‐wave and normal‐mode observations of Earth's inner core show cylindrical anisotropy consistent with an alignment of hexagonal close‐packed iron (hcp‐Fe) crystals along the rotation axis. We quantify the degree of alignment by comparing seismic observations longitudinally averaged over the outer 600 km of the inner core with stochastic rotation models based on ab initio calculations of hcp‐Fe stiffness tensors. Likelihood functions are constructed for the Woodhouse anisotropy ratios from an ensemble of normal‐mode models and for the Backus ray‐angle parameters from the Irving‐Deuss traveltime data set. The tensor at each inner‐core location is modeled as a random rotation of the hcp‐Fe stiffness tensor, and the rotations are assumed to have transversely isotropic statistics with correlation lengths that are small compared to the seismic wavelengths. Two stochastic rotation models are used, one based on Fisher statistics (F model) with concentration parameter κ and one by Jordan (J model) with orientation ratio ξ. The first‐order estimates, obtained by Voigt averaging, imply that hcp‐Fe tensors by Martorell and others considering premelting softening can account for the seismic data if the hcp‐Fe axes are moderately aligned with Earth's rotation axis ( , ). The J model is extended to include second‐order Born scattering, which in the low‐frequency limit depends on the aspect ratio η of the transversely isotropic correlation tensor. Although η is not usefully constrained by the existing data, we show that second‐order scattering acts to increase the required bipolar concentration of hcp‐Fe axes. Integrating over η yields the marginal estimate , corresponding to a 50% dispersion angle of .