The Calaveras fault lies within a low velocity zone (LVZ) 1-2 km wide near Gilroy, California. Accelerographs G06, located in the LVZ 1.2 km from the Calaveras fault, and G07, 4 km from G06, recorded both the M 6.2 1984 Morgan Hill and the M 6.9 1989 Loma Prieta earthquakes. Comparison of the ground motions shows that a large 0.6-1.0 Hz velocity pulse observed at G06 during the Morgan Hill event may be amplified by focussing caused by the LVZ. Such amplified waves might be a mappable seismic hazard, and the zone of increased hazard can extend as much as 1.2 km from the surface trace of the fault. Finite-difference simulations of ground motions in a simplified LVZ model show a zone of amplified motion similar to the observations.