Direct observations of the viscosity of the outer core and extrapolation of measurements of the viscosity of liquid iron

Estimates vary widely as to the viscosity of Earth's outer fluid core. Directly observed viscosity is usually orders of magnitude higher than the values extrapolated from high-pressure high-temperature laboratory experiments, which are close to those for liquid iron at atmospheric pressure. It turns out that this discrepancy can be removed by extrapolating via the widely known Arrhenius activation model modified by lifting the commonly used assumption of pressure-independent activation volume (which is possible due to the discovery that at high pressures the activation volume increases strongly with pressure, resulting in $10^2$ Pa s at the top of the fluid core and in $10^{11}$ Pa s at the bottom). There are of course many uncertainties affecting this extrapolation process. This paper reviews two viscosity determination methods, one for the top and the other for the bottom of the outer core, the former of which relies on the decay of free core nutations and yields $2.371\pm 1.530$ Pa s; and the other relies on the reduction in the rotational splitting of the two equatorial translational oscillation modes of the solid inner core and yields an average $1.247\pm 0.035\times 10^{11}$ Pa s. Encouraged by the good performance of the Arrhenius extrapolation, a differential form of the Arrhenius activation model is used to interpolate along the melting temperature curve and to find the viscosity profile across the entire outer core. The variation is found to be nearly log-linear between the measured boundary values.