Renormalization group theory of earthquakes
- 1Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-0740, USA
- *Packard Fellow
- 2Department of Earth Sciences, University of Southern California, Los Angeles, CA 90089-0740, USA
- 3Laboratoire de Physique de la Matière Condensée, CNRS URA 190, Université des Sciences, B. P. 70, Parc Valrose, 06108 Nice Cedex 2, France
Abstract. We study theoretically the physical origin of the proposed discrete scale invariance of earthquake processes, at the origin of the universal log-periodic corrections to scaling, recently discovered in regional seismic activity (Sornette and Sammis (1995)). The discrete scaling symmetries which may be present at smaller scales are shown to be robust on a global scale with respect to disorder. Furthermore, a single complex exponent is sufficient in practice to capture the essential properties of the leading correction to scaling, whose real part may be renormalized by disorder, and thus be specific to the system. We then propose a new mechanism for discrete scale invariance, based on the interplay between dynamics and disorder. The existence of non-linear corrections to the renormalization group flow implies that an earthquake is not an isolated "critical point", but is accompanied by an embedded set of "critical points", its foreshocks and any subsequent shocks for which it may be a foreshock.