Linearized inverse techniques commonly are used to solve for velocity
models from traveltime data. The amount that a model may change withou
t producing large, nonlinear changes in the predicted traveltime data
is dependent on the surface topography and parameterization. Simple, o
ne-layer, laterally homogeneous, constant-gradient models are used to
study analytically and empirically the effect of topography and parame
terization on the linearity of the model-data relationship. If, in a w
eak-velocity-gradient model, rays turn beneath a valley with topograph
y similar to the radius of curvature of the raypaths, then large nonli
nearities will result from small model perturbations. Hills, conversel
y, create environments in which the data are more nearly linearly rela
ted to models with the same model perturbations.