The second-order moment (cross-correlation function) of earthquakes in the U.S. Geological Survey central California catalog between 1969 and 1982 was calculated with respect to a magnitude threshold M≥4.0 over interevent distances up to 80 km and interevent times up to 320 days. The statistical procedure results in a representation of the spatial-temporal structure of the catalog associated with M≥4.0 earthquakes and is capable of revealing patterns too weak to be detected in the space-time distribution of seismicity for individual earthquake sequences. A method is introduced for identifying aftershocks based on a physical two-parameter model of the earthquake interaction process. The results show that the aftershock process dominates the second-order moment and may even obscure the statistical expression of a precursory process. A concentration of foreshocks within 15 km and 3 days of M≥4.0 main shocks exhibits an apparent migration toward the main shock loci with velocity 2.6--5.3 km/d. This concentration may be related to an observed tendency for M≥4.0 events to cluster (autocorrelate) over this interevent range. With the identified aftershocks removed, the residual catalog is Poissonion in space and time. When two M≥4.0 earthquakes occur within 80 km and 40 days of each other, aftershock productivity appears to be relatively enhanced in the earlier sequence. This suggests that aftershock populations are not solely dependent on their main shocks and that unusually productive aftershock sequences may be predictors of future moderate earthquakes.