Building a regime diagram for the Earth's inner core

Abstract:

A number of geodynamical mechanisms have been proposed to explain the origin of the observed structure of the inner core, using either solidification texturing or deformation texturing to produce anisotropy. Our goal here is to compare quantitatively mechanisms involving deformation of the inner core and build a regime diagram giving the dominant mechanism as a function of the values of key control parameters.

We focus on deformation mechanisms, which can be further subdivided between natural convection (arising from unstable thermal or compositional gradients, the relevant mode being here Rayleigh-Benard type convection) and externally forced convection, with possible forcing including the effect of the core magnetic field, which can force a flow either through the direct effect of the Lorentz force (Karato, 1999; Buffett and Bloxham, 2000; Buffett and Wenk, 2001) or through heterogeneous Joule heating of the inner core (Takehiro, 2010), and viscous relaxation of a topography at the inner core boundary (ICB) associated with spatially heterogeneous inner core growth (Yoshida et al., 1996).

Two key parameters emerge for the inner core dynamics. The first one is the sign and strength of the density stratification, separating convective and non-convective inner core, either from a thermal or compositional point of view. The second one is the viscosity of the inner core, with published estimates ranging from $10^{11}$ to $10^{22}$ Pa.s. A meaningful comparison between the different mechanisms requires the definition of a measure of the strength of the flow, and we choose here to compare this mechanisms in terms of the instantaneous strain rate, and consider that the dominant mechanism is the one which induces the highest strain rates at a given time. Using scaling laws for all proposed mechanisms, we build regime diagrams giving the dominant mechanism as a function of control parameters and compute the predicted geometry of the flows in the different domains. Whereas the computed strain is of the order of one over the life of the inner core, most of the predicted dynamics do not induce the expected geometry.