We present a practical method of locating earthquakes in laterally varying media. The procedure has two distinct phases: an estimation phase, and an application phase. In the estimation phase, all existing araival time residuals relative to some reference, one-dimensional velocity model for a region are used to estimate a set of path anomalies (station corrections) that vary as a function of source position. This is done by sorting earthquakes into groups localized in space and applying a novel multiple event location algorithm. This algorithm uses a pair of complementary projection operators to combine a priori information about the lateral structure that is indeterminate from the available data with the information that can be determined uniquely from the available data. Having estimated path anomalies as a function of source location, we can generate a table of path anomalous that can be accessed and interpolated for future earthquake location. This is the application phase of the method. We have tested the method on synthetic data designed to study how well earthquakes can be located in the vicinity of the rupture zone of the 1984 Morgan Hill, California, earthquake. We found precise absolute locations could be obtained, provided the a priori information was specified appropriately. Distortion of relative locations occurred near large lateral velocity gradients and for groups of events spread over large areas because of the inadequacy of fitting a single set of path anomalies to the whole group.