This research program considers the spatial variation and correlation of strong earthquake ground motion. It is common in earthquake engineering to focus on the time history of ground acceleration at a given location. However, the spatial variation of ground motion is potentially just as important as the time variation, and is the focus of this study. This research program includes analytical modeling of ground motions, and statistical analysis of closely spaced accelerograms, principally from strong motion instrument arrays, and especially the accelerograms recorded during the September 19, 1985 earthquake. It also involves a study of patterns of building damage and variations in local geology, all to obtain insight into the spatial variation of strong ground motion.