Growth model of the inner core coupled with the outer core dynamics and the resulting elastic anisotropy

We present a growth tectonic model of Earth's inner core and the resulting model of the seismic anisotropy. The inner core grows anisotropically if the convection in the outer core is of Taylor column type. The anisotropic growth produces a flow field of the poloidal zonal order 2 type as a result of the isostatic adjustment of the viscous inner core. Crystals in the inner core align themselves under the stress field produced by the flow. We model the anisotropic structure of the inner core, using the theory of Kamb [1959] and elastic constants of Stixrude and Cohen [1995b]. We consider models for both hcp iron and fcc iron, which are the probable crystal structures for the inner core iron according to Stixrude and Cohen [1995a]. We have found that the c axis for hcp iron and [111] direction for fcc iron align in the polar direction. The alignment is consistent with seismic observations, which have revealed that the P wave velocity is faster in the polar direction. Our model predicts that the degree of the alignment decreases near the inner core boundary in accord with recent body wave observations. The radial dependence of the alignment would result from the following three effects: (1) crystals near the surface have not undergone stressed state long enough to acquire anisotropy after precipitation, (2) stress near the surface is different from that in the interior of the inner core due to shear stress free boundary condition, and (3) partially molten structure results in transversely isotropic stress condition near the inner core surface due to compaction. Thus the application of Kamb's theory successfully explains the seismic anisotropy in the inner core provided that the crystals have been subjected under the same stress condition for the timescale of the order of 10⁹ years.