A number of recent global tomographic studies have modeled three dimensional variations in the parameters of radial anisotropy. As yet there is limited agreement among such studies, suggesting significant uncertainties in the models, which could lead to divergent geodynamical interpretations. In this study we assess the robustness of lateral variations in radial anisotropy globally in the upper mantle and in the transition zone to determine the extent to which anisotropic parameters are constrained by a data set of over 10,000,000 fundamental and higher mode surface wave dispersion measurements. We carry out inversions for isotropic and radially anisotropic shear wave velocity, systematically changing regularization and using three different crustal models to remove the effects of the crust on the data. Using crustal corrections from different crustal models has an impact on the data fit comparable or larger than that obtained by including lateral variations of radial anisotropy in the modeling. Moreover, the use of crustal corrections from different a priori crustal models may lead to different images of radial anisotropy suggesting divergent geodynamical interpretations. This work suggests that the three-dimensional determination of global radial anisotropy in the Earth's mantle using surface wave dispersion data is still an ongoing experiment.