We investigate the problem of retrieving anisotropy as a function of depth in the mantle, from the observed azimuthal variations of Love and Rayleigh wave velocities. Following the approach of Smith and Dahlen, this azimuthal dependence is expressed in terms of a Fourier series of the azimuth θ. For the most general case of anisotropy (provided it is small enough), some simple linear combinations of the elastic tensor coefficients are shown to describe the total effect of anisotropy (both polarization anisotropy and azimuthal anisotropy) on the propagation of surface Waves. For the terms that do not depend on the azimuth the combinations are related to the elastic coefficients of a transversely isotropic mantle. For the azimuthal terms the relevant combinations are explicited. It is found that the partial derivatives of the azimuthal terms with respect to these combinations are easy to compute for they are proportional to the partial derivatives of a transversely isotropic model in the case of a plane‐layered model. In a first approximation the same property holds true for a spherical earth and we calculate from PREM all the partial derivatives needed for performing the inversion of the azimuthal anisotropy of surface waves in the period range 50–300 s. It is observed that very shallow anisotropy can be responsible for substantial azimuthal variations up to the longest periods. With this approach it is also easy to compute the azimuthal variations of surface wave velocities produced by any anisotropic model. When a Ci j elastic tensor is chosen for the upper mantle, azimuthal variations up to 2% are obtained for Rayleigh waves. The azimuthal variations of Love wave velocities are very small. The 2 θ term of the azimuthal variations of Rayleigh wave velocities is the dominant term. Its fast axis corresponds to the fast axis of P waves.

We present an attempt to reach realistic turbulent regime in direct numerical simulations of the geodynamo. We rely on a sequence of three convection-driven simulations in a rapidly rotating spherical shell. The most extreme case reaches towards the Earth's core regime by lowering viscosity (magnetic Prandtl number P m = 0.1) while maintaining vigorous convection (magnetic Reynolds number Rm > 500) and rapid rotation (Ekman number E = 10 −7 ), at the limit of what is feasible on today's supercomputers. A detailed and comprehensive analysis highlights several key features matching geomagnetic observations or dynamo theory predictions -all present together in the same simulation -but it also unveils interesting insights relevant for Earth's core dynamics.In this strong-field, dipole-dominated dynamo simulation, the magnetic energy is one order of magnitude larger than the kinetic energy. The spatial distribution of magnetic intensity is highly heterogeneous, and a stark dynamical contrast exists between the interior and the exterior of the tangent cylinder (the cylinder parallel to the axis of rotation that circumscribes the inner core).In the interior, the magnetic field is strongest, and is associated with a vigorous twisted polar vortex, whose dynamics may occasionally lead to the formation of a reverse polar flux patch at the surface of the shell. Furthermore, the strong magnetic field also allows accumulation of light material within the tangent cylinder, leading to stable stratification there. Torsional Alfvén waves are frequently triggered in the vicinity of the tangent cylinder and propagate towards the equator.Outside the tangent cylinder, the magnetic field inhibits the growth of zonal winds and the kinetic energy is mostly non-zonal. Spatio-temporal analysis indicates that the low-frequency, non-zonal flow is quite geostrophic (columnar) and predominantly large-scale: an m=1 eddy spontaneously emerges in our most extreme simulations, without any heterogeneous boundary forcing.Our spatio-temporal analysis further reveals that (i) the low-frequency, largescale flow is governed by a balance between Coriolis and buoyancy forces -magnetic field and flow tend to align, minimizing the Lorentz force; (ii) the high-frequency flow obeys a balance between magnetic and Coriolis forces; (iii) the convective plumes mostly live at an intermediate scale, whose dynamics is driven by a 3-term 1 arXiv:1701.01299v3 [physics.geo-ph] 15 Jun 2017 MAC balance -involving Coriolis, Lorentz and buoyancy forces. However, smallscale ( E 1/3 ) quasi-geostrophic convection is still observed in the regions of low magnetic intensity.

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