Evidence for a Significant Level of Extrinsic Anisotropy Due to Heterogeneities in the Mantle.

Observations of seismic anisotropy are used as a proxy for lattice-preferred orientation (LPO) of anisotropic minerals in the Earth's mantle. In this way, it provides important constraints on the geometry of mantle deformation. However, in addition to LPO, small-scale 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. Here, 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 1D and 2D isotropic models that exhibit a power spectrum of heterogeneities as what is expected for the Earth's mantle, i.e. varying as 1/k, with k the wavenumber of these heterogeneities. The 1D toy models correspond to simple layered media. In the 2D case, our models depict marble-cake patterns in which an anomaly in S-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, i.e. 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 1D 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 1D and 2D media. In addition, we predict that 10 % of chemical heterogeneities in 2D marble-cake models can induce more than 3.9 % 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.