Characteristic Earthquake Magnitude: Mathematical Versus Empirical Models

Abstract eng:
In the literature concerning the characteristic hypothesis, one basic question is widely discussed: is it possible to justify (by statistical tests) favouring the characteristic magnitude model for the interpretation of available catalogues? No generally accepted answer has been given now a days. In a previous paper (Grandori et al., 2008) we analyzed a different question, perhaps more useful from the engineering point of view: is it possible to judge (on the basis of statistical tests) which one of two competing magnitude models is more reliable (all other things being equal) for the evaluation of a specific hazard quantity at a given site? In that paper we described a method which can give an answer to this question, and we studied the controversy surrounding the comparison between “characteristic-type” magnitude models and the classic doubly truncated exponential model. We found that in many cases a characteristic magnitude model is more reliable than the exponential model. In the present paper we recall the main features of the method and we apply it to the comparison between a mathematical model FM and an empirical (non parametric) distribution F*. The aim is to find an empirical F* which is more reliable than FM, thanks to the substantial reduction of possible errors due to the use of a wrong model FM. We do not give a general method for the construction of such F*, nor we maintain that it exists in all cases. We simply show how, in a study case, we found the way to construct a very satisfactory F*.

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