Precursors, aftershocks, criticality and self-organized criticality

¹ Department of Physics, University of Southern California, Los Angeles, CA 90089-0484, USA
² Department of Earth Sciences, University of Southern California, Los Angeles, CA 90089-0484, USA
³ Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095-1567, USA
⁴ Laboratoire de Physique de la Matière Condensée, CNRS and Université de Nice-Sophia Antipolis, Parc Valrose, 06108 Nice, France

Received: 18 April 1997
Accepted: 19 November 1997

Abstract

We present a simple model of earthquakes on a pre-existing hierarchical fault structure. The system self-organizes at large times in a stationary state with a power law Gutenberg-Richter distribution of earthquake sizes. The largest fault carries irregular great earthquakes preceded by precursors developing over long time scales and followed by aftershocks obeying an Omori's law. The cumulative energy released by precursors follows a time-to-failure power law with log-periodic structures, qualifying a large event as an effective dynamical (depinning) critical point. Down the hierarchy, smaller earthquakes exhibit the same phenomenology, albeit with increasing irregularities.