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Statistical Grounds for Favoring the Characteristic Magnitude Model: A Case Study

Department of Structural Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32 20133, Milano, Italy

In the frame of probabilistic seismic hazard analysis, the characteristic magnitude model is often favored on the basis of general geological, physical, and mechanical considerations. However, it is generally recognized that the seismic record in most seismic zones is too short for a statistical validation of the characteristic hypothesis: different and simpler models can explain available catalogs as successfully as a characteristic magnitude model, even if they lead (all other things being equal) to important differences in the final results of the seismic hazard analysis. In other words, when two competing magnitude models are proposed, it is difficult to justify (on the basis of statistical tests) favoring one or the other model for the interpretation of the available catalog.

We observe that most of the problems of seismic hazard analysis actually raise the question: which one of the alternative models is more reliable for the estimation of a specific hazard quantity at a given site? In this article, we describe a method that can give a statistically based answer to this question. The answer depends, obviously, on the mathematical structure of the two models, as well as on the nature of the site and on the target quantity. Changing the site or the target quantity leads in general to different outcomes of the comparison between the models. What is interesting to observe is that, with the proposed method, given the site and the target quantity, the comparison is independent of the magnitude values contained in the available catalog.

We describe in detail the comparison between a characteristic magnitude model and the doubly truncated exponential model, alternatively applied to the evaluation of the peak ground acceleration (PGA) with a 500-yr return period at a specific site. We show that, for the two test sites considered in our study, a set of appropriate statistical tests clearly indicate the characteristic model as more reliable than the exponential model.

A simple nonparametric procedure (free from modeling errors) is also presented and compared with the mathematical models.