A vectorial modelling of observed macroseismic intensity aimed at the analytical determination of the epicentre is proposed here. The methodology is based on the determination of a plane system of vectors which characterises the macroseismic intensity distribution. The epicentre of each seismic event considered is determined as the centre of this vector system by an analytical expression which is independent from all possible directions of seismic energy propagation. The analysis of the intensity distribution is carried out by a new model called a macroseismic plane, different from the one known as macroseismic field, formed by a set of small areas built around the observed intensity points; hence its name.With the proposed methodology, some earthquakes in southern Italy and eastern Sicily are analysed calculating their epicentres, also for distributions of observed intensity which are particularly complex.

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A study of the intensity distribution of the earthquake of December 5th 1456, which affected a large area of central and southern Italy was carried out, verifying, through a recently proposed methodology, the two hypotheses assumed by different authors for one single seismic event and three distinct and close ones. This methodology is based on a vectorial modelling of the macroseismic intensity distribution which aims at determining the epicentre and the principal (minimum and maximum) attenuation directions.The study was structured, considering each of the two assumed hypotheses, in a set of tests obtained for the macroseismic field and the intensity map, by analysing different configurations of the observed intensity distribution.The results obtained are in agreement with the hypothesis of the time coexistence of three distinct seismic events, for which the calculated epicentres and the principal attenuation directions are compatible with the observed intensity distribution and with the tectonic trend of the Apennine region, respectively.

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