The precise determination and interpretation of anisotropy are relatively difficult because the apparent anisotropy is usually a mixture of intrinsic and extrinsic anisotropy, which might partly hide the true properties of the medium investigated. The artificial anisotropy can be due to the fact that seismic waves do not ‘see’ the real details of a medium, but a ‘filtered’ (or ‘upscaled’) version of the Earth model. This can be due to a bad quality of the data coverage, to limited frequency band effects, or to errors in the approximate theory. With the limitation to layered Earth models, through comparisons of the results of the homogenization method with those of the periodic isotropic two-layered model as an analytical solution, we illustrate that the Backus theory for the long wavelength equivalent effect can be extended to calculate the extrinsic anisotropy, due to upscaling effects at discontinuities for the general isotropic layered model, when its spatial scale is much less than or equal to the seismic wavelength. We find that the extrinsic radial S-wave anisotropy produced by the vertical heterogeneities in the upper mantle of the Earth can be as large as 3% (about 30% extrinsic anisotropy of the 10% radial anisotropy). To better recover information from seismic data, we propose a surface wave phase velocity inversion method based on the first-order perturbation theory. We show that resolution at discontinuities can be improved by adding overtone modes of surface wave data. For more general layered models, the homogenization method could be considered, which can flexibly adapt the scale of the model to seismic wavelengths. However, the periodic isotropic two-layered model can also help to analytically quantify the amount of extrinsic radial, and possibly azimuthal anisotropy produced by the tilted fine layering.