An approach for seismic tomography is presented which allows the parameterization to be refined during the inversion. The objective is to use the data to refine the mesh and the velocity model together, and hence both are considered part of the solution. Some simple rules are used to identify the volumes of a three-dimensional model in need of refinement. The self-adaptive parameterization is applied to an initial mesh built from uniformly distributed spherical triangles and Delaunay tetrahedra. Application of the technique to a typical summary ray P-wave arrival time data set shows it to be both feasible and practical for large scale whole Earth tomography. A noticeable trend in the resulting models, as the parameterization is refined, is the thinning of the Farallon and Tethys subduction features imaged in the mid mantle, together with an increase in amplitude of the velocity perturbation.