We consider the inverse problem of determining small variations in propagation speed from remote observations of signals which pass through an inhomogeneous medium. Under the conditions (1) that the variations can be written as a small perturbation from a known reference value and (2) that the medium of interest varies in one direction only, an integral equation has been developed for the variations which can be solved in closed form. Here, a technique is presented to obtain and process synthetic data from a scattering profile of arbitrary shape. The results of numerical testing show that, as long as a velocity variation is indeed ’’small,’’ both its size and its shape can be reproduced with negligible error by this method.