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Maximum entropy estimation of b values at Mt. Etna; comparison with conventional least squares and maximum likelihood results and correlation with volcanic activity

Maximum entropy estimation of b values at Mt. Etna; comparison with conventional least squares and maximum likelihood results and correlation with volcanic activity

Annali di Geofisica 42(3): 515-528

The variations of the b coefficient in the frequency-magnitude relationship for earthquakes which occurred at Mt. Etna from 01/01/90 to 31/12/92 are analysed; the completeness threshold for our earthquakes catalogue is M = 2.30. The b values calculated using the Maximum Entropy Principle (MEP) are compared to those obtained by conventional methods of Least Squares (LS) and Maximum Likelihood (ML). All the differences among the b values computed using these methods, and the reasons for these differences, are discussed and examined. In particular, our results show that the b values obtained by MEP are lower than the others calculated using LS and ML; this implies that, on the average, LS and ML underestimate the seismic hazard at Mt. Etna. Moreover, temporal variations of b (sub MEP) are more evident than the corresponding ones of b (sub LS) and b (sub ML) ; indeed, in some cases the trend of b (sub MEP) variation is opposite those of b (sub LS) and b (sub ML) . A significant correlation between temporal variations of the volcanic activity and the b values is evident only if the MEP is used; this means that, if b temporal variations are analysed in order to detect changes in the volcano dynamics and predict the eruptions, the maximum entropy approach should be preferred. Finally, the observed pattern of b (sub MEP) temporal variations with regard to the changes in the volcanic activity is consistent with the hypothesis of a compressive stress field acting on Mt. Etna.

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