Convergence of the frequency-size distribution of global earthquakes

The Gutenberg-Richter (GR) frequency-magnitude relation is a fundamental empirical law of seismology, but its form remains uncertain for rare extreme events. Here, we show that the temporal evolution of model likelihoods and parameters for the frequency-magnitude distribution of the global Harvard Centroid Moment Tensor catalog is inconsistent with an unbounded GR relation, despite if being the preferred model at the current time. During the recent spate of 12 great earthquakes in the last 8years, record-breaking events result in profound steps in favor of the unbounded GR relation. However, between such events the preferred model gradually converges to the tapered GR relation, and the form of the convergence cannot be explained by random sampling of an unbounded GR distribution. The convergence properties are consistent with a global catalog composed of superposed randomly-sampled regional catalogs, each with different upper bounds, many of which have not yet sampled their largest event.