Apparent triggering function of aftershocks resulting from rate-dependent incompleteness of earthquake catalogs

Abstract

The onset of the aftershock decay after main shocks is controversial. Physical models predict that the onset time is stress dependent, and catalog analysis shows a clear increase of the c value of the Omori-Utsu law with increasing main shock magnitude. However, earthquake catalogs are known to have variable quality and completeness levels; in particular, they miss events directly after main shocks. Thus, it has been also argued that the delayed onset of recorded aftershock activity triggered by large earthquakes is simply an artifact of the time-varying completeness. Here I utilize a recent approach describing the detection probability of earthquakes as function of the actual earthquake rate. I derive an analytical relation between apparent and true earthquake rate which only depends on the blind time of detection algorithms after the occurrence of an earthquake. This relation is tested and verified for synthetic simulations of Omori-type aftershock sequences. For a comparison, I analyze earthquake sequences occurred in Southern California and Taiwan, finding that the derived analytical decay function consistently explains the empirical aftershock activity in the catalogs. This indicates that the observed scaling of the Omori c value is mainly related to catalog incompleteness and not to any underlying physical process.