Earthquake catalogues and modelling strategies. A new testing procedure for the comparison between competing models

In this paper we consider the procedures that, on the basis of an earthquake catalogue, yield the magnitude distribution function F _M (F _M generators). In particular, our attention is focused on the F _M generators that are currently used in the frame of the probabilistic seismic hazard analysis at a site. From an engineering point of view, the behaviour of F _M in the range of strong earthquakes is of crucial importance. On the other hand, in general, the statistical validation of F _M in that range is not feasible because of an insufficient number of strong earthquakes in available catalogues.Our investigation is limited to the problem of the comparison between competing F _M generators. We show that a simple empirical F _M generator (called the CFP generator) can be more reliable than generators based on mathematical models. The numerical experiments that support this statement regards two test-sites and two mathematical models of magnitude distribution, namely the truncated-exponential and the characteristic-type models.The main conclusion is the suggestion of a test (called the CFP-test) that can be summarized as follows. Let X be a site for which, with current criteria, a specific F _M ^X generator based on a mathematical model has been selected. At this point, following the comparison approach described in the paper, the F _M ^X generator is compared with the empirical CFP generator. It can happen (actually it happens in many of our numerical experiments) that this test indicates the CFP generator as more reliable than the selected F _M ^X generator.