Complex Critical Exponents from Renormalization Group Theory of Earthquakes: Implications forEarthquake Predictions

Several authors have proposed discrete renormalization group models of earthquakes, viewing them as a kind of dynamical critical phenomena. Here, we propose that the assumed discrete scale invariance stems from the irreversible and intermittent nature of rupture which ensures a breakdown of translational invariance. As a consequence, we show that the renormalization group entails complex critical exponents, describing log-periodic corrections to the leading scaling behavior. We use the mathematical form of this solution to fit the time to failure dependence of the Benioff strain on the approach of large earthquakes. This might provide a new technique for earthquake prediction for which we present preliminary tests on the 1989 Loma Prieta earthquake in northern California and on a recent build-up of seismic activity on a segment of the Aleutian-Island seismic zone. The earthquake phenomenology of precursory phenomena such as the causal sequence of quiescence and foreshocks is captured by the general structure of the mathematical solution of the renormalization group.