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) Båth'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.