Our information about the inner core comes primarily from
seismological observations. We have estimates for the P-wave velocity
and it's directional dependence in the inner core, S-wave velocity, and
P- and S-wave attenuation. The P-wave velocity appears to vary with
depth between 11.04 and 11.26 km/s, while the S-wave velocity is less well
constrained, but thought to be less than 3.65 km/s. The P-wave velocity
along the pole axis has been observed to be 3 - 4% higher than that in
the equatorial plane. Studies of seismic attenuation suggest that
at least the upper part of the inner core has high attenuation with quality
factors of 200 - 400 for P-waves, and 100 - 200 for S-waves. It is
hard to come up with models which simultaneously explain the seismic anisotropy,
very low shear wave velocity, and high attenuation.
Although the presence of fluid has been appealed to in a qualitative manner to explain individual observations, here, for the first time we make quantitative estimates of the geometry and amount of fluid that would be required to satisfy all of the above observations. We use an effective medium theory to calculate the stiffnesses and resulting seismic velocities and anisotropy of a composite material comprising a solid iron matrix with embedded spheroidal inclusions of melt between the iron crystals. A model of fluid flow between isolated inclusions driven by seismically induced pressure gradients is used to make estimates of the corresponding attenuation in such a medium. We show the effect of changing both the proportion of melt and the aspect ratio of the spheroidal inclusions. We find that a 5 - 10% volume fraction of elongated fluid inclusions, aligned in the equatorial plane, produce behaviour which is consistent with all of the seismic observations. Possible origins for such fluid include dendritic growth of iron, or a mixture of elements which exist in lesser proportion, but are liquid at inner core pressures and temperatures.