Philippe Cardin

Seismic studies indicate that the Earth's inner core has a complex structure and exhibits a strong elastic anisotropy with a cylindrical symmetry. Among the various models which have been proposed to explain this anisotropy, one class of models considers the effect of the Lorentz force associated with the magnetic field diffused within the inner core. In this paper, we extend previous studies and use analytical calculations and numerical simulations to predict the geometry and strength of the flow induced by the poloidal component of the Lorentz force in a neutrally or stably stratified growing inner core, exploring also the effect of different types of boundary conditions at the inner core boundary (ICB). Unlike previous studies, we show that the boundary condition that is most likely to produce a significant deformation and seismic anisotropy is impermeable, with negligible radial flow through the boundary. Exact analytical solutions are found in the case of a negligible effect of buoyancy forces in the inner core (neutral stratification), while numerical simulations are used to investigate the case of stable stratification. In this situation, the flow induced by the Lorentz force is found to be localized in a shear layer below the ICB, whose thickness depends on the strength of the stratification, but not on the magnetic field strength. We obtain scaling laws for the thickness of this layer, as well as for the flow velocity and strain rate in this shear layer as a function of the control parameters, which include the magnitude of the magnetic field, the strength of the density stratification, the viscosity of the inner core and the growth rate of the inner core. We find that the resulting strain rate is probably too small to produce significant texturing unless the inner core viscosity is smaller than about 10¹² Pa s.

This paper investigates whether observations of seismic anisotropy are compatible with a cubic structure of the inner core Fe alloy. We assume that anisotropy is the result of plastic deformation within a large scale flow induced by preferred growth at the inner core equator. Based on elastic moduli from the literature, bcc- or fcc-Fe produce seismic anisotropy well below seismic observations ($\textless{}0.4\%$). A Monte-Carlo approach allows us to generalize this result to any form of elastic anisotropy in a cubic system. Within our model, inner core global anisotropy is not compatible with a cubic structure of Fe alloy. Hence, if the inner core material is indeed cubic, large scale coherent anisotropic structures, incompatible with plastic deformation induced by large scale flow, must be present.

This paper investigates whether observations of seismic anisotropy are compatible with a cubic structure of the inner core Fe alloy. We assume that anisotropy is the result of plastic deformation within a large‐scale flow induced by preferred growth at the inner core equator. Based on elastic moduli from the literature, body‐centered cubic or face‐centered cubic Fe produces seismic anisotropy well below seismic observations (<0.4%). A Monte Carlo approach allows us to generalize this result to any form of elastic anisotropy in a cubic system. Within our model, inner core global anisotropy is not compatible with a cubic structure of Fe alloy. Hence, if the inner core material is indeed cubic, large‐scale coherent anisotropic structures, incompatible with plastic deformation induced by large‐scale flow, must be present.

We present a framework for simulating the measurement of seismic anisotropy in a model inner core by computing travel time residuals of synthetic seismic rays propagated through the model. The method is first tested on simple inner core structural models consisting of layers with distinct anisotropy, as often proposed in the literature. Those models are not consistent with geodynamics. Hence, we extend the method to a numerically grown inner core composed of ɛ -Fe with flow generated from an excess of crystallization in the equatorial belt, inducing polycrystalline textures. The global inner core anisotropy is seven times smaller than that of the single-crystal. Compositional stratification amplifies the global anisotropy by 15% while the addition of solidification textures reduces it by a factor of two. As such, and within the tested geodynamical models, no published elastic model of ɛ -Fe at inner core conditions allows one to reproduce the 3% cylindrical anisotropy reported in seismology publications. In addition, our models demonstrate that additional information, such as the depth dependence and the spread of the observed anisotropy is a key for revealing the dynamics and history of the inner core.

Inner core translation, with solidification on one hemisphere and melting on the other, provides a promising basis for understanding the hemispherical dichotomy of the inner core, as well as the anomalous stable layer observed at the base of the outer core—the so-called F-layer—which might be sustained by continuous melting of inner core material. In this paper, we study in details the dynamics of inner core thermal convection when dynamically induced melting and freezing of the inner core boundary (ICB) are taken into account. If the inner core is unstably stratified, linear stability analysis and numerical simulations consistently show that the translation mode dominates only if the viscosity η is large enough, with a critical viscosity value, of order ∼3 × 10¹⁸ Pa s, depending on the ability of outer core convection to supply or remove the latent heat of melting or solidification. If η is smaller, the dynamic effect of melting and freezing is small. Convection takes a more classical form, with a one-cell axisymmetric mode at the onset and chaotic plume convection at large Rayleigh number. η being poorly known, either mode seems equally possible. We derive analytical expressions for the rates of translation and melting for the translation mode, and a scaling theory for high Rayleigh number plume convection. Coupling our dynamic models with a model of inner core thermal evolution, we predict the convection mode and melting rate as functions of inner core age, thermal conductivity, and viscosity. If the inner core is indeed in the translation regime, the predicted melting rate is high enough, according to Alboussière et al.'s experiments, to allow the formation of a stratified layer above the ICB. In the plume convection regime, the melting rate, although smaller than in the translation regime, can still be significant if η is not too small. Thermal convection requires that a superadiabatic temperature profile is maintained in the inner core, which depends on a competition between extraction of the inner core internal heat by conduction and cooling at the ICB. Inner core thermal convection appears very likely with the low thermal conductivity value proposed by Stacey & Loper, but nearly impossible with the much higher thermal conductivity recently put forward by Sha & Cohen, de Koker et al. and Pozzo et al. We argue however that the formation of an iron-rich layer above the ICB may have a positive feedback on inner core convection: it implies that the inner core crystallized from an increasingly iron-rich liquid, resulting in an unstable compositional stratification which could drive inner core convection, perhaps even if the inner core is subadiabatic.

Metallic diapirs may have strongly contributed to core formations during the first million years of planetary evolutions. The aim of this study is to determine whether the dynamics induced by the diapir sinking can drive a dynamo and to characterize the required conditions on the size of the diapir, the mantle viscosity and the planetary latitude at which the diapir sinks. We impose a classical Hadamard flow solution for the motion at the interface between a spherical sinking diapir and a viscous mantle on dynamical simulations that account for rotational and inertial effects in order to model the flow within the diapir. The flows are confined to a velocity layer with a thickness that decreases with increasing rotation rate. These 3D flows are is then used as input for kinematic dynamo simulations to determine the critical magnetic Reynolds number for dynamo onset. Our results demonstrate that the flow pattern inside a diapir sinking into a rotating planet can generate a magnetic field. Large diapirs (R > 10 km) sinking in a mantle with a viscosity ranging from 10⁹ to 10¹⁴ Pa.s provide plausible conditions for a dynamo. Equatorial sinking diapirs are confined to a thicker velocity layer and are thus possibly more favorable for dynamo generation than polar sinking diapirs. In addition equatorial sinking diapirs produce stronger saturated magnetic fields. However, for the range of parameters studied here, estimation of the intensity of diapir‐driven magnetic fields suggests that they could not have contributed to the lunar or Martian crustal paleomagnetic fields.