A Method for Processing and Analysis of Aftershocks Due to a Tectonic Earthquake: A New Look at an Old Problem

Abstract

This paper is devoted to the 130th anniversary of the discovery of the Omori law. This first law in earthquake physics was formulated in 1894, and has become widely known since that time as the Omori law. It was found that the frequency of aftershocks following an earthquake decays approximately obeying the hyperbolic law on average. This was an epoch-making discovery. It has governed the line of research in the study of aftershocks for many decades ahead. Attention is mainly focused in the present paper on one of the modern lines of research in the phenomenological theory of aftershocks. A new method has been developed within the framework of that theory for aftershock data processing and analysis. The theory is based on the differential equation governing the evolution of an earthquake source after the main rupture has been formed in rocks in that zone. The differential approach, unlike Omori’s algebraic approach, allows one to get a new insight into the experimental study, processing, and analysis of aftershock data. Proceeding as outlined above, we have discovered the existence of the so-called Omori epoch, which terminates by bifurcation. The basic simple nonlinear evolution equation whose solution is identical with the Omori law suggests natural extensions of the phenomenological theory. In particular, one such extension which has the form of the Kolmogorov–Petrovsky–Piskunov equation enables a hypothetical relationship to be developed connecting the propagation of aftershock activity to Umov’s energy flux at the source.