Modeling aftershocks as a stretched exponential relaxation

Abstract

AbstractThe decay rate of aftershocks has been modeled as a power law since the pioneering work of Omori in the late nineteenth century. Although other expressions have been proposed in recent decades to describe the temporal behavior of aftershocks, the number of model comparisons remains limited. After reviewing the aftershock models published from the late nineteenth century until today, I solely compare the power law, pure exponential and stretched exponential expressions defined in their simplest forms. By applying statistical methods recommended recently in applied mathematics, I show that all aftershock sequences tested in three regional earthquake catalogs (Southern and Northern California, Taiwan) and with three declustering techniques (nearest‐neighbor, second‐order moment, window methods) follow a stretched exponential instead of a power law. These results infer that aftershocks are due to a simple relaxation process, in accordance with most other relaxation processes observed in Nature.