Deviations of the distributions of seismic energies from theGutenberg-Richter law

Vladilen Pisarenko, Didier Sornette, & M. Rodkin

Published 2004, SCEC Contribution #751

A new non-parametric statistic is introduced for the characterization of deviations of the distribution of seismic energies from the Gutenberg-Richter law. Based on the two first
statistical log-moments, it evaluates quantitatively the deviations of the distribution of scalar seismic moments from a power-like (Pareto) law. This statistic is close to zero for the Pareto law with arbitrary power index, and deviates from zero for any non-Pareto distribution. A
version of this statistic for discrete distribution of quantified magnitudes is also given. A methodology based on this statistics consisting in scanning the lower threshold for earthquake
energies provides an explicit visualization of deviations from the Pareto law, surpassing in sensitivity the standard Hill estimator or other known techniques. This new statistical
technique has been applied to shallow earthquakes (h ≤ 70 km) both in subduction zones and in mid-ocean ridge zones (using the Harvard catalog of seismic moments, 1977-2000), and to
several regional catalogs of magnitudes (California, Japan, Italy, Greece). We discover evidence for log-periodicity and thus for a discrete hierarchy of scales for low-angle dipping, low-strain subduction zones with a preferred scaling ratio γ=7±1 for seismic moments, compatible with a preferred scaling ratio of 2 for linear rupture sizes, and consistent with previous reports. We propose a possible mechanism in terms of cascades of fault competitions.

Key Words
Gutenberg-Richter law, non-parametric statistics, deviation of distribution from standard law, discrete scale invariance, log-periodicity

Citation
Pisarenko, V., Sornette, D., & Rodkin, M. (2004). Deviations of the distributions of seismic energies from theGutenberg-Richter law. Computational Seismology, 35, 138-159. http://arxiv.org/ftp/physics/papers/0312/0312020.pdf