All techniques that currently exist to invert arrival time data from earthquake sources for velocity structue rest on a local linearization of the nonlinear equations relating these data to the velocity model. We have studied the limitations imposed by this approximation using synthetic data in which a one dimensional velocity model is the only varible. We have found that this problem is sufficiently nonlinear that some iterative is generally required to obtain results that are quantitatively correct. On the other hand, convergence studies using the algorithm recently developed by Pavlis (1982) suggest that this problem is somewhat better behaved than one might think. Convergence to a solution linearly close to the truth is fairly readily achieved whenever the resolution of the data is sufficient to resolve the structure of the true velocity model. Convergence to solutions that are not linearly close where found to occur, however, when the true velocity model contained significant unresolvable structure.