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

Abstract

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 analyzed; 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 bMEP are more evident than the corresponding ones of bLS and bML; indeed, in some cases the trend of bMEP variation is opposite those of bLS and bML. 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 analyzed 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 bMEP 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.