A precise model for relocation of earthquakes of a region or the multiple ruptures of a large earthquake, using P-wave arrival-time difference data, is given by the equation of condition of the standard single-event location model (Geiger model). The use of P-wave arrival-time differences provides ray path redundancies from earthquakes in a limited source region to a given station set. Thus, this relocation model implicitly compensates certain time anomalies caused by lateral velocity heterogeneities, leading to good relative locations without the requirement of a set of master residuals. Because the solution vector of the arrival-time difference model may be significantly nonzero at convergence, the second-order terms of the Geiger model are derived and used to determine the size of the neighborhood in which this arrival-time difference formulation will give acceptable location resolution. Evaluation of these second-order terms shows that accurate, teleseismically-determined relative locations are possible with the arrival-time difference method for events within distance of a reference earthquake's epicenter. The use of this relocation method with teleseismic data requires independent depth information. The cosine term relative location model, often used with arrival-time difference data to graphically locate multiple ruptures, is an approximation to the Geiger model as it is used here.