Quantifying seismic anisotropy induced by small-scale chemical heterogeneities

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, 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. 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 toymodels correspond to simple layeredmedia. 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.