On the Fundamental Laws of Earthquake Physics

This paper deals with the Omori and Bath laws describing the properties of aftershocks of strong earthquakes. We reformulated Omori’s law by presenting it as a differential equation for the evolution of aftershocks. This allowed us to introduce the idea of a deactivation coefficient for the earthquake source “cooling down” after the main shock. In the course of this work, we found a strong dependence of the deactivation coefficient on the magnitude of the main shock. In the case of Bath’s law, we determined the value of the difference between the main shock magnitude and the magnitude of the strongest aftershock at the initial stage of aftershock evolution. In addition, we modified the formulation of the problem by introducing the concept of so-called “mirror” foreshocks and established a law for them similar to Bath’s law.