The resolution operator ${cal{R}}$ is a critical accompaniment to tomographic models of the mantle. ${cal{R}}$ facilitates the comparison between conceptual three-dimensional velocity models and tomographic models because it can filter these theoretical models to the spatial resolution of the tomographic model. We compute ${cal{R}}$ for the tomographic model S20RTS (Ritsema et al., 1999, 2004) and two companion models that are based on the same data but derived with different norm damping values. The three models explain (within measurement uncertainty) S-SKS and S-SKKS travel times equally well. To demonstrate how artifacts distort tomographic images and complicate model interpretation, we apply ${cal{R}}$ to (1) a thermochemical and (2) an isochemical model of convection in the mantle that feature different patterns of shear velocity heterogeneity in the deep mantle if we assume that shear velocity heterogeneity is caused by temperature variations only. ${cal{R}}$ suppresses short-wavelength structures, removes strong velocity gradients, and introduces artificial stretching and tilting of velocity anomalies. Temperature anomalies in the thermochemical model resemble the spatial extent of low seismic velocity anomalies and the shear velocity spectrum in the D" region better than the isochemical model. However, the thermochemical model overpredicts the amplitude of shear velocity variation and places the African and Pacific anomalies imperfectly. We suspect that inaccurate velocity scaling laws and uncertain initial conditions control these mismatches. Extensive hypothesis testing is required to identify successful models.