Linearized inverse techniques commonly are used to solve for velocity models from traveltime data. The amount that a model may change without producing large, nonlinear changes in the predicted traveltime data is dependent on the surface topography and parameterization. Simple, one-layer, laterally homogeneous, constant-gradient models are used to study analytically and empirically the effect of topography and parameterization on the linearity of the model-data relationship. If, in a weak-velocity-gradient model, rays turn beneath a valley with topography similar to the radius of curvature of the raypaths, then large nonlinearities will result from small model perturbations. Hills, conversely, create environments in which the data are more nearly linearly related to models with the same model perturbations.