The Omori Law: The 150-Year Birthday Jubilee of Fusakichi Omori

Abstract

The outstanding Japanese seismologist Fusakichi Omori was born 150 years ago, on October 30, 1868. He discovered his first law in earthquake physics that now bears his name when he was 26. Essentially, Omori’s law tells us that the decay of aftershock rate follows a hyperbolic law. This paper provides a brief account of how that discovery was made. Attention is focused on two approaches in an attempt at generalizing Omori’s law. One of these has been known for many years and to many researchers. It is based on the concept that the aftershock rate depends on time as a power law. The other approach was discovered recently by using a formal analogy between the decay of aftershock activity in the lithosphere and the recombination of charged particles in the ionosphere. A differential equation for aftershocks has been proposed. The general solution to the equation retains the hyperbolic structure of Omori’s law, but also enables a flexible simulation of rock instability at the earthquake source that is “cooling down” after the main shock. The general solution also incorporates the non-monotonic function that describes the time-dependent decay of aftershock rate, which occurs when an earthquake source is acted on by endogenous and exogenous triggers. The aftershock equation is used to formulate the inverse problem in earthquake source physics.