## 1. Introduction

[2] The rotational dynamics of the inner core depend on the viscosity [*Buffett*, 1997; *Greff-Lefftz et al.*, 2000; *Dumberry and Bloxham*, 2002], as do the various mechanisms proposed for generating seismically anisotropic structures in the inner core [e.g., *Jeanloz and Wenk*, 1988; *Yoshida et al.*, 1996; *Bergman*, 1997; *Karato*, 1999]. Unfortunately, few observational constraints on inner core viscosity exist. Based on seismic inferences of ∼1 degree per year super-rotation of the inner core with respect to the mantle, *Buffett* [1997] constrained the viscosity to be less than 3 × 10^{16} Pa s, or greater than 1.5 × 10^{20} Pa s in a less likely dynamic regime. These constraints must be relaxed if the rate of super-rotation is less than one degree per year, as recent body-wave and normal-mode studies indicate [*Tromp*, 2001, and references therein]. In principle, the viscosity of the inner core can be inferred from seismic attenuation data, since attenuation of seismic waves is due in part to non-elastic (anelastic and/or viscous) deformation. However, such estimates must be treated with caution since deformation mechanisms at seismic frequencies may differ from those at longer timescales. *Collier and Helffrich* [2001] inferred a viscosity of ∼3.9 × 10^{19} Pa s from the attenuation of a low-frequency (1.3/yr) oscillation in inner core rotation; however the oscillatory signal is not firmly established.

[3] Here I take a mineral physics approach to estimate the viscosity of the inner core. Previous materials-based estimates of inner core viscosity [*Jeanloz and Wenk*, 1988; *Yoshida et al.*, 1996] have not fully considered the creep mechanisms likely to operate under inner core conditions. These estimates have covered a wide range, from ∼10^{13}–10^{21} Pa s. Experimental studies of creep in a broad range of crystalline materials have shown that at low and intermediate stress levels and absolute temperatures *T* > 0.4 *T*_{m}, (where *T*_{m} is the melting temperature) the creep rate can be represented generally by

where *D* is the diffusion coefficient, *G* is the shear modulus, *b* is the Burgers vector, *k* is Boltzmann's constant, *d* is the grain size, σ is shear stress, and *p*, *n*, and *A* are dimensionless constants. Because the inner core has a high homologous temperature (greater than ∼0.85*T*_{m}) and non-hydrostatic stresses must be small, the essential task in establishing a mineral physics constraint on inner core viscosity is to obtain reliable estimates of the parameters in equation (1).