We investigate the validity of a proposed generalized Omori–Utsu law for the aftershock sequences for the Landers, Hector Mine, Northridge and Superstition Hills earthquakes, the four largest events in the southern California catalogue we analyse. This law unifies three of the most prominent empirical laws of statistical seismology—the Gutenberg–Richter law, the Omori–Utsu law, and a generalized version of B°ath’s law—in a formula casting the parameters in the Omori–Utsu law as a function of the lower magnitude cutoff mc for the aftershocks
considered. By applying a recently established general procedure for identifying aftershocks, we confirm that the generalized Omori–Utsu law provides a good approximation for the observed rates overall. In particular, we provide convincing evidence that the characteristic
time c is not constant but a genuine function of mc, which cannot be attributed to short-term aftershock incompleteness. However, the estimation of the specific parameters is somewhat sensitive to the aftershock selection method used. This includes c(mc), which has important implications for inferring the underlying stress field.