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Keywords:

  • Instability analysis;
  • Seismic anisotropy

SUMMARY

Thermal convection is an effective mechanism for producing seismic anisotropy in many regions of the Earth. However, it is not known whether this mechanism is relevant for the anisotropy observed in the inner core. Here we establish the requirements for convection in the inner core by combining a simple model for inner-core growth with a solution for conductive cooling. Thermal convection is likely during the early stages of inner-core growth, but becomes less probable as the volume of the inner core increases. The transition to a non-convecting state is driven by changes in both the thermal and compositional stratification. A decrease in the vigour of convection near the transition to a non-convecting state isolates the pattern of flow with the lowest critical Rayleigh number Rac. We apply a perturbation method based on Rayleigh's principle to calculate Rac in a hydrostatically flattened inner core. We find that the final pattern of flow is characterized by a degree l= 1 mode in which the axis of upwelling aligns with the rotation axis. This pattern of flow has the symmetry required to explain the distribution of anisotropy at the largest scales. The extent of crystal alignment depends on the level of stress during this final convective state. One possible interpretation of the observed anisotropy is that the final convective state establishes the large scale crystal alignment without completely erasing a more complicated texture that developed when convection was more vigorous.