Time window to constrain the corner value of the global seismic-moment distribution

Álvaro Corral,Isabel Serra,Dante R Chialvo

doi:10.1371/journal.pone.0220237

Abstract

It is well accepted that, at the global scale, the Gutenberg-Richter (GR) law describing the distribution of earthquake magnitude or seismic moment has to be modified at the tail to properly account for the most extreme events. It is debated, though, how much additional time of earthquake recording will be necessary to properly constrain this tail. Using the global CMT catalog, we study how three modifications of the GR law that incorporate a corner-value parameter are compatible with the size of the largest observed earthquake in a given time window. Current data lead to a rather large range of parameter values (e.g., corner magnitude from 8.6 to 10.2 for the so-called tapered GR distribution). Updating this estimation in the future will strongly depend on the maximum magnitude observed, but, under reasonable assumptions, the range will be substantially reduced by the end of this century, contrary to claims in previous literature.

Highlights

Statistics of earthquake occurrence, in particular of the most extreme events, must be a fundamental source to assess seismic hazard [1]
Summarizing the main results of the article, we have reconsidered to what extent the available earthquake record can constrain the parameter that characterizes the tail of the global seismicmoment distribution: a corner seismic moment (Mc, or its corresponding moment magnitude mc), for three different distributions
We have corrected some of the drawbacks of previous literature, regarding the number of events necessary for such a purpose

Summary

Introduction

Statistics of earthquake occurrence, in particular of the most extreme events, must be a fundamental source to assess seismic hazard [1]. The cornerstone model for describing the earthquake-size distribution is the Gutenberg-Richter (GR) law [2, 3]. The original version of the GR law states that earthquake magnitudes follow an exponential distribution, and since this is a perfectly “well-behaved” distribution, with all statistical moments (such as the mean and the standard deviation) being finite, the problem of earthquake sizes would seem a rather trivial one. A physical interpretation of the meaning of the GR law needs a proper understanding of magnitude. Magnitude presents several difficulties as a measure of earthquake size [4], and a true physical quantity is given instead by seismic moment [5, 6].

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Discussion

Conclusion