A generalized Omori's law for earthquake aftershock decay

Earthquake aftershock sequences have been found to approximately satisfy three empirical scaling relations: i) the Gutenberg-Richter frequency-magnitude scaling, ii) Bath's law for the difference in the magnitude of a mainshock and its largest aftershock, and iii) the modified Omori's law for the temporal decay of aftershock rates. The three laws are incorporated to give a generalized Omori's law for aftershock decay rates that depend on several parameters specific for each given seismogenic region. It is shown that the characteristic time c, first introduced in the modified Omori's law, is no longer a constant but scales with a lower magnitude cutoff and a mainshock magnitude. The generalized Omori's law is tested against earthquake catalogs for the aftershock sequences of the Landers, Northridge, Hector Mine, and San Simeon earthquakes.