P waves from 13 teleseismic events, well distributed in azimuth and recorded on a large short-period network in southern California, show a positive correlation between travel time residuals and relative amplitudes. Slower arrivals are consistently larger than faster arrivals. Although there is a large amount of scatter, the data show an amplitude increase of about a factor of 2 for a 1-s increase in travel time. The correlation can be seen in various subsets of the data: individual earthquakes, single stations recording 10 or more earthquakes and data averaged over all recorded events at each station. Because the variations in amplitude and travel time can be associated with surface geology, much of the data recorded at non bedrock sites can be explained in terms of a near-surface layer of varying velocity. The travel time residual would then be directly proportional to the velocity in the layer and the amplitude proportional to the square root of the velocity contrast at the base of the layer. However, some stations show azimuthally varying travel time residuals that are attributed to upper mantel velocity structures. We use a two-dimensional finite difference calculation to show that velocity anomalies in the upper mantle can also contribute to the observed correlation of travel time and amplitude. ¿ American Geophysical Union 1992