A Project for an Atlas of Aftershocks Following Large Earthquakes

Abstract

The Omori law for repeated underground shocks after a large earthquake is written here in the form of a nonlinear differential equation. We define a coefficient of deactivation for the rupture zone after the main shock. Two advantages of the new formulation are pointed out. First, there is now an interesting possibility for a natural incorporation of exogenous and endogenous factors that affect the rupture zone. We highlight endogenous triggers in the form of a circumnavigating seismic echo and free oscillations of the Earth excited by the main shock. The other advantage consists in the fact that the differential equation for aftershocks enables us to formulate the inverse problem for the physics of the rupture zone. The inverse problem reduces to the determination of the coefficient of deactivation based on observed aftershock frequency. Examples are given to illustrate the solution of the inverse problem. We propose to develop an atlas of aftershocks based on the solution of the inverse problem for the rupture zone that is “cooling” after a large earthquake.