We assume that a dilatant zone which develops as a precursor to an earthquake may be modeled by a zone of low-velocity rock having the shape of a triaxial ellipsoid. For varying ellipsoid dimensions, velocity contrasts, and hypocenter distributions, we generate a synthetic data set of arrival times at surface stations. The artifical events are relocated using a constant-velocity model to test for systematic hypocenter biasing. For all cases tested, the depth change for the distribution as a whole was not significant although individual events may move substantially. A downward migration of the ensemble of hypocenters was produced by a long, narrow ellipsoidal zone, however, the magnitude of migration for this case was only two percent.