We propose a spherical surface-spline method that parametrizes a two-dimensional model on a sphere in terms of a local cubic B-spline basis on a triangular grid of knots with approximately equal interknot spacing. Numerical results show that such a parameterization can represent a model on a sphere with an accuracy equal to that of the spherical-harmonic parameterization of the corresponding nominal degree. Furthermore, it significantly reduces the computational time needed to calculate surface-wave synthetic seismograms on a laterally heterogeneous Earth, and makes it feasible to apply JWKB theory to surface-wave inversion studies. ¿ American Geophysical Union 1995