The Phenomenology of Aftershocks

TL;DR

This paper explores a mathematical framework based on nonlinear diffusion equations to model aftershock sequences, successfully capturing key empirical laws such as Omori's law and the slow spatial propagation of aftershocks.

Contribution

It introduces a novel approach using a nonlinear diffusion master equation to describe aftershock evolution, linking experimental observations with mathematical modeling.

Findings

The model reproduces Omori's law for aftershock decay.

It explains the slow spatial propagation of aftershocks.

The approach provides a basis for inverse problem analysis in seismology.

Abstract

The presented paper is devoted to the search for mathematical basis for describing the aftershock evolution of strong earthquakes. We consider the experimental facts and heuristic arguments that allow to make a choice and to focus on the nonlinear diffusion equation as the master equation. Analysis of the master equation indicates that, apparently, the selected mathematical basis makes it possible to simulate two important properties of the aftershock evolution known from the experiment. We are talking about the Omori law and the slow propagation of aftershocks from the epicenter of the main shock. Keywords: earthquakes, propagation of aftershocks, Omori law, deactivation coefficient, nonlinear diffusion, master equation, inverse problem