Please use this identifier to cite or link to this item: http://hdl.handle.net/2122/6680
AuthorsDe Santis, A.* 
Cianchini, G.* 
Favali, P.* 
Beranzoli, L.* 
Boschi, E.* 
TitleThe Gutenberg-Richter law and Entropy of earthquakes: two case studies in Central Italy
Issue Date2010
Series/Report no./ (2010)
URIhttp://hdl.handle.net/2122/6680
KeywordsEarthquakes
Gutenber-Richter Law
b-value
Entropy
Subject Classification04. Solid Earth::04.06. Seismology::04.06.02. Earthquake interactions and probability 
05. General::05.05. Mathematical geophysics::05.05.99. General or miscellaneous 
AbstractA cumulative frequency-magnitude relation, the Gutenberg-Richter law, dominates the statistics of the occurrence of earthquakes. Although it is an empirical law, some authors have tried to give some physical meaning to its a and b parameters. Here we recall some theoretical expressions for the probability of occurrence of an earthquake with magnitude M in terms of a and b values. A direct consequence of the Maximum Likelihood Estimation and the Maximum Entropy Principle is that a and b values can be expressed as a function of the mean magnitude of a seismic sequence over a certain area. We then introduce the definition of the Shannon entropy of earthquakes and show how it is related to the b-value. In this way, we also give a physical interpretation to the b-value: the negative logarithm of b is the entropy of the magnitude frequency of earthquake occurrence. An application of the above concepts to two case studies, i.e. to the recent seismic sequence in Abruzzi (Central Italy; main shock M = 6.3, 6 April, 2009 in L’Aquila) and to an older 1997 sequence (Umbria-Marche, Central Italy; main shock M = 6.0, 26 September 1997 in Colfiorito), confirms their potential to help in understanding the physics of earthquakes. In particular, from the comparison of the two cases, a simple scheme of different regimes in succession is proposed in order to describe the dynamics of both sequences.
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