Constraints on grain size and stable iron phases in the uppermost inner core from multiple scattering modeling of seismic velocity and attenuation

We propose to model the uppermost inner core as an aggregate of randomly oriented anisotropic “patches”. A patch is defined as an assemblage of a possibly large number of crystals with identically oriented crystallographic axes. This simple model accounts for the observed velocity isotropy of short period body waves, and offers a reasonable physical interpretation for the scatterers detected at the top of the inner core. From rigorous multiple scattering modeling of seismic wave propagation through the aggregate, we obtain strong constraints on both the size and the elastic constants of iron patches. In a first step, we study the phase velocity and scattering attenuation of aggregates composed of hexagonal and cubic crystals, whose elastic constants have been published in the mineral physics literature. The predicted attenuations for P waves vary over two orders of magnitude. Our calculations demonstrate that scattering attenuation is extremely sensitive to the anisotropic properties of single crystals and offers an attractive way to discriminate among iron models with e.g. identical Voigt average speeds. When anisotropy of elastic patches is pronounced, we find that the S wavespeed in the aggregate can be as much as 15% lower than the Voigt average shear velocity of a single crystal. In a second step, we perform a systematic search for iron models compatible with measured seismic velocities and attenuations. An iron model is characterized by its symmetry (cubic or hexagonal), elastic constants, and patch size. Independent of the crystal symmetry, we infer a most likely size of patch of the order of 400 m. Recent bcc iron models from the literature are in very good agreement with the most probable elastic constants of cubic crystals found in our inversion. Our study (1) suggests that the presence of melt may not be required to explain the low shear wavespeeds in the inner core and (2) supports the recent experimental results on the stability of cubic iron in the inner core, at least in its upper part.