S. Karato
Department of Geology and Geophysics, Yale University, New haven, CT, USA
Our current understanding of origin of inner core anisotropy will be reviewed. Any viable models for inner core anisotropy must be consistent with (microscopic and macroscopic) physics as well as (seismological) observations. I will assume the following as seismological observations: (1) the inner core has nearly axial anisotropy: fast (P-wave) velocity along the rotational axis (Song, 1997; Creager, 2000), (2) the shallow portions of the inner core is isotropic (song and Helmberger, 1998; Creager, 2000), and (3) the thickness of the isotropic layer has a hemi-spherical variation (thicker in the eastern hemisphere than in the western hemisphere; Tanaka and Hamaguchi, 1997; Song and Helmberger, 1998; Creager, 2000). I will also assume that the inner core is made (mostly) of hcp Fe and the elastic anisotropy calculated by Steinle-Neumann et al. (2001) (slowest along the c-axis) are applicable to the inner core. Given these assumptions, I will show that all models so far proposed have difficulties in explaining some of the seismological observations, particularly the depth variation (and hemispherical asymmetry) of anisotropy. [Solid-state versus partial melting mechanisms] The possible mechanisms for inner core anisotropy include (1) solid-state mechanisms (i.e., lattice preferred orientation) and (2) aligned melt pocket. Although the presence of a significant amount of partial melt has often been suggested (e.g., Fearn et a., 1981; Bergman and Fearn, 1994) and a model for anisotropy based on the aligned melt pocket has been proposed (Singh et al., 2000), theoretical considerations indicate that it is highly unlikely that the inner core contains a significant amount of melt (Sumita et al., 1996). Sumita et al. (1996) showed that the efficiency of compaction depends critically on the fluid permeability of the inner core which in turn depends on the grain-size. If we use plausible estimates of grain-size ({\ge}10 m; Bergman, 1998) and viscosity (Buffett, 1997; Karato, 1999), then the permeability is large and the compaction is so efficient that one expects negligible residual porosity. In fact, the recent results of theoretical calculation of elastic moduli of hcp Fe (Steinle-Neumann et al., 2001) and experimental work on attenuation in Fe (Jackson et al., 2000) show that partial melting is not required to explain the high Poisson’s ratio and high attenuation. I conclude that a model invoking aligned melt pocket is not a viable candidate of the mechanism for inner core anisotropy. [Solid-state mechanisms] Given the assumption that the inner core is made (mostly) of hcp Fe and using the elastic constants of Steinle-Neumann et al. (2001), models of anisotropy by solid-state mechanisms must explain (1) why c-axis of Fe crystals tends to be normal to the rotation axis and (2) why crystallographic orientation is nearly random in the shallow layers. (1) Growth anisotropy (Karato, 1993; Bergman, 1997) In these models, anisotropic crystallographic orientation of Fe crystals is assumed to be attained at solidification at ICB. Karato (1993) proposed that anisotropy in the paramagnetic susceptibility is a cause of selection of grains with particular orientation. Given the new results of crystal structure of Fe at the inner core conditions and using the results of Ducastelle and Cyrot-Lackmann (1971) on the relation between the orbital paramagnetic susceptibility and the c/a ratio of transition metals, one expects that the c-axis aligns along the magnetic field line. With a strong toroidal field at the ICB, this would predict that the seismic waves propagating along the rotation axis will be faster. Bergman (1997) and Bergman et al. (2000) conducted experimental work on crystallization of hcp metals and concluded that for hcp metal (such as Zn which has a large c/a ratio similar to hcp Fe in the inner core) containing some impurities, the a-axis tends to be parallel to the growth direction. If Zn containing a small amount of impurities is a good analog to the Earth’s core, this model predicts anisotropy that is inconsistent with the seismological observations. One of the major difficulties with these models is that they do not explain a (sharp) transition from isotropic to anisotropic structure at ~100-300 km depth (Song and Helmberger, 1998). If anisotropic structure is acquired at the ICB, the shallow portion of inner core would be anisotropic. One needs an ad hoc assumption to explain a sharp transition to anisotropic structure in the deep inner core. Also, in order to preserve anisotropic structure attained by solidification, deformation should not modify anisotropic structure. (2) Deformation-induced anisotropy (Jeanloz and Wenk, 1988; Yoshida et al., 1996; Buffett, 1997; Karato, 1999; Buffett and Wenk, 2001) Deformation-induced anisotropic structure is an obvious candidate for the origin of inner core anisotropy. But for deformation to cause anisotropic structures, several conditions must be met. First, deformation mechanism must be dislocation creep (or twinning) rather than diffusion creep. For this condition to be met, the grain-size (and stress) must be sufficiently high. Second, the magnitude of strain must be large (~1 or larger). Also, in order to explain the observed pattern of anisotropy, geometry of deformation must has rotational symmetry. Thermal convection models proposed by Jeanloz and Wenk (1988) does not meet this last requirement. Differential cooling (caused by the anisotropic flow pattern in the outer core; Yoshida et al. 1996) and the stress due to the magnetic field (Karato, 1999) are plausible driving forces that would result in anisotropic structures with rotational symmetry. Given plausible mechanisms of lattice preferred orientation (which depends on the dominant slip systems (Poirier and Price, 1999; Wenk et al., 2000; Solas et al., 2001) and elasticity, both models predict similar patterns of lattice preferred orientation: the c-axis of Fe tends to be normal to the rotational axis, leading to the anisotropy that is consistent with the seismological observations. However, one of the difficulties with these model is that if the inner core is thermally stratified, then the vertical motion is difficult to develop (Buffett and Bloxham, 2000). Buffett and Wenk (2001) proposed an alternative model in which flow is caused by the magnetic field but the flow pattern is zonal. This mode shares same type of difficulties as models of growth texture: one needs to invoke some ad hoc assumptions to explain the depth variation of anisotropy. In summary, one of the most challenging issues in the origin of inner core anisotropy is the explanation for the depth variation (and the hemi-spherical variation) of anisotropy. Some plausible models to explain the depth variation of anisotropy will be discussed including those dealing with the physical mechanisms of controlling the grain-size in the inner core. References Bergman, M.I., 1997. Measurement of elastic anisotropy due to solidification texturing and the implications for the Earth’s inner core, Nature, 389: 60-63. Bergman, M.I., 1998. Estimates of the Earth’s inner core grain size, Geophys. Res. Lett., 25: 1593-1596. Bergman, M.I. and Fearn, D.R., 1994. Chimneys on the Earth’s inner-outer core boundary? Geophys. Res. Lett., 21: 477-480. Bergman, M.I., Giersch, L., Hinczewski, M. and Izzo, V., 2000. 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