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A 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 (MLE) and the maximum entropy principle (MEP) 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 these concepts to two case studies, in particular to the recent seismic sequence in Abruzzi (central Italy; mainshock Mw 6.3, 6 April 2009 in L'Aquila) and to an older 1997 sequence (Umbria-Marche, central Italy; mainshock Mw 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. [ABSTRACT FROM AUTHOR]

Abstract: The fruitful collaboration between Italian Research Institutions, particularly Istituto Nazionale di Fisica Nucleare (INFN) and Istituto Nazionale di Geofisica e Vulcanologia (INGV) together with Marine Engineering Companies, led to the development of NEMO-SN-1, the first European cabled seafloor multiparameter observatory. This observatory, deployed at 2060m w.d. about 12 miles off-shore the Eastern coasts of Sicily (Southern Italy), is in real-time acquisition since January 2005 and addressed to different set of measurements: geophysical and oceanographic. In particular the SN-1 seismological data are integrated in the INGV land-based national seismic network, and they arrive in real-time to the Operative Centre in Rome. In the European Commission (EC) European Seafloor Observatory NETwork (ESONET) project, in connection to the Global Monitoring for Environment and Security (GMES) action plan, the NEMO-SN-1 site has been proposed as an European key area, both for its intrinsic importance for geo-hazards and for the availability of infrastructure as a stepwise development in GMES program. Presently, NEMO-SN-1 is the only ESONET site operative. The paper gives a description of SN-1 observatory with examples of data. [Copyright &y& Elsevier]