  A new non-parametric statistic is introduced for the characterization of
deviations from power laws. It is tested on the distribution of seismic
energies given by 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
g=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.
