Statistical Tests for the Tail of the Seismic-Moment Distribution of Global Shallow Earthquakes

Abstract:

The Gutenberg-Richter (GR) law is not only of fundamental importance in statistical seismology but also a cornerstone of non-linear geophysics and complex-systems science. It states that, in terms of seismic moment M or released energy, the distribution of earthquake sizes is a power law. This has important physical implications, as it suggests an origin from a critical branching process or a self-organized-critical system. However, it presents also some conceptual difficulties, due to the fact that the mean value of M provided by the distribution turns out to be infinite. These elementary considerations imply that the GR law cannot be naively extended to arbitrarily large values of M, and one needs to introduce additional parameters to describe the tail of the distribution, coming presumably from finite-size effects.Main and co-workers have examined the problem of the global earthquake-size distribution including recent data (shallow events only). Using a Bayesian information criterion (BIC), they compare the plain GR law with the so-called tapered GR distribution, and conclude that, although the tapered GR gives a significantly better fit before the 2004 Sumatra-Andaman event, the occurrence of this changes the balance of the BIC statistics, making the GR law more suitable; that is, the power law is more parsimonious, or simply, is enough for describing shallow global seismicity when the recent mega-earthquakes are included in the data.

We revisit the problem using distinct statistical tools and considering different parameterizations for the tail. A discussion of results will be presented.