About the aftershocks, the Omori law, and the Utsu formula

Abstract

After the main shock of an earthquake, a stream of aftershocks that does not subside for a long time is usually observed. Fusakichi Omori found that the frequency of aftershocks decreases hyperbolically with time. It has recently been observed that Omori's law can be viewed as a solution to a differential equation describing the evolution of aftershocks. An alternative way of describing is based on Utsu law, which states that the frequency of aftershocks decreases with time according to a power law. The presented paper is polemical. We discuss the issue of the applicability of each of the three alternative ways of describing aftershocks. The Omori law has a limited scope. The law is valid only in the so-called Omori epoch, after which the earthquake source undergoes a bifurcation. In the Omori epoch, the Utsu law is also valid, but it does not differ in this epoch from the Omori law. The general conclusion is that the existence of the Omori epoch and the phenomenon of bifurcation exclude the possibility of describing by a continuous smooth function. At the same time, the differential evolution equation is applicable both before and after the bifurcation point. Key words: earthquake, main shock, evolution equation, deactivation factor, Omori epoch, bifurcation.Comment: 7 pages, 1 figur