Magnitude distribution versus local seismic hazard

In seismic hazard analysis there are quantities that are dominated by the distribution of strong earthquakes. A typical example is the peak ground acceleration with a 500-year return period at a specific site. This quantity, a(500), is particularly important from the engineering point of view. Due to the scanty number of strong earthquakes in seismic catalogs, the available data are generally not sufficient for a statistical validation of a magnitude distribution model. Different models can explain available data with the same level of statistical likelihood, even if they lead, ceteris paribus, to values of a(500) at the site that are significantly different. Which one is more credible and should be favored for seismic hazard analysis at the considered site? In most cases the traditional fitting tests do not give a meaningful answer. In this article we introduce a particular definition of credibility of a magnitude model, based on the distribution of expected errors in the evaluation of a(500) at a specific site. We show that this concept of credibility is a useful tool for selecting the more appropriate of two competing models.