Observations of seismic anisotropy are usually used as a proxy for lattice-preferred orientation (LPO) of anisotropic minerals in the Earth's mantle. In this way, seismic anisotropy observed in tomographic models provides important constraints on the geometry of mantle deformation associated with thermal convection and plate tectonics. However, in addition to LPO, smallscale heterogeneities that cannot be resolved by long-period seismic waves may also produce anisotropy. The observed (i.e. apparent) anisotropy is then a combination of an intrinsic and an extrinsic component. Assuming the Earth's mantle exhibits petrological inhomogeneities at all scales, tomographic models built from long-period seismic waves may thus display extrinsic anisotropy. In this paper, we investigate the relation between the amplitude of seismic heterogeneities and the level of induced S-wave radial anisotropy as seen by long-period seismic waves. We generate some simple 1-D and 2-D isotropic models that exhibit a power spectrum of heterogeneities as what is expected for the Earth's mantle, that is, varying as 1/k, with k the wavenumber of these heterogeneities. The 1-D toy models correspond to simple layered media. In the 2-D case, our models depict marble-cake patterns in which an anomaly in shear wave velocity has been advected within convective cells. The long-wavelength equivalents of these models are computed using upscaling relations that link properties of a rapidly varying elastic medium to properties of the effective, that is, apparent, medium as seen by long-period waves. The resulting homogenized media exhibit extrinsic anisotropy and represent what would be observed in tomography. In the 1-D case, we analytically show that the level of anisotropy increases with the square of the amplitude of heterogeneities. This relation is numerically verified for both 1-D and 2-D media. In addition, we predict that 10 per cent of chemical heterogeneities in 2-D marble-cake models can induce more than 3.9 per cent of extrinsic radial S-wave anisotropy. We thus predict that a non-negligible part of the observed anisotropy in tomographic models may be the result of unmapped small-scale heterogeneities in the mantle, mainly in the form of fine layering, and that caution should be taken when interpreting observed anisotropy in terms of LPO and mantle deformation. This effect may be particularly strong in the lithosphere where chemical heterogeneities are assumed to be the strongest.

Summary Probing seismic anisotropy of the lithosphere provides valuable clues on the fabric of rocks. We present a 3-D probabilistic model of shear wave velocity and radial anisotropy of the crust and uppermost mantle of Europe, focusing on the mountain belts of the Alps and Apennines. The model is built from Love and Rayleigh dispersion curves in the period range 5 to 149 s. Data are extracted from seismic ambient noise recorded at 1521 broadband stations, including the AlpArray network. The dispersion curves are first combined in a linearised least squares inversion to obtain 2-D maps of group velocity at each period. Love and Rayleigh maps are then jointly inverted at depth for shear wave velocity and radial anisotropy using a Bayesian Monte-Carlo scheme that accounts for the trade-off between radial anisotropy and horizontal layering. The isotropic part of our model is consistent with previous studies. However, our anisotropy maps differ from previous large scale studies that suggested the presence of significant radial anisotropy everywhere in the European crust and shallow upper mantle. We observe instead that radial anisotropy is mostly localized beneath the Apennines while most of the remaining European crust and shallow upper mantle is isotropic. We attribute this difference to trade-offs between radial anisotropy and thin (hectometric) layering in previous studies based on least-squares inversions and long period data (>30 s). In contrast, our approach involves a massive dataset of short period measurements and a Bayesian inversion that accounts for thin layering. The positive radial anisotropy (VSH > VSV) observed in the lower crust of the Apennines cannot result from thin layering. We rather attribute it to ductile horizontal flow in response to the recent and present-day extension in the region.

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