Emergence of non-extensive seismic magnitude-frequency distribution from a Bayesian framework

Non-extensive statistical mechanics has been used in recent years as a framework in order to build some seismic frequency-magnitude models. Following a Bayesian procedure through a process of marginalization, it is shown that some of these models can arise from the result shown here, which reinforces the relevance of the non-extensive distributions to explain the data (earthquake’s magnitude) observed during the seismic manifestation. In addition, it makes possible to extend the non-extensive family of distributions, which could explain cases that, eventually, could not be covered by the currently known distributions within this framework. The model obtained was applied to six data samples, corresponding to the frequency-magnitude distributions observed before and after the three strongest earthquakes registered in Chile during the late millennium. In all cases, fit parameters show a strong trend to a particular non-extensive model widely known in literature.