Renormalization group theory of earthquakes

• Main Authors: H. Saleur, C. G. Sammis, D. Sornette
• Format: Article
• Language: English
• Published: Copernicus Publications 1996-01-01
• Series: Nonlinear Processes in Geophysics
• Online Access: http://www.nonlin-processes-geophys.net/3/102/1996/npg-3-102-1996.pdf

We study theoretically the physical origin of the proposed <I>discrete</I> scale invariance of earthquake processes, at the origin of the <I>universal</I> 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<B> </B>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<B> </B>mechanism for discrete scale invariance, based on the<B> </B>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.