Seismicity assessment using earthquake catalogues with uncertain and incomplete data: probabilistic formulation

A novel generalized probabilistic formulation is proposed to assess seismicity using earthquake catalogues with uncertain and incomplete data. The seismicity, described by the complete exceedance rate of magnitudes, is estimated starting from a consistent incomplete exceedance rate which is rationally linked to the catalogue data. Complete and incomplete exceedance rates are represented by similar functional forms and they are related by a completeness function, which expresses the probability that an event is included in a data set. Completeness is considered uncertain and it is defined by a suitable, continuous, analytical, magnitude dependent function. The importance of this work lies on its applicability because it can be useful in seismic zones where information about seismic activity is scarce or simply when the catalogue is incomplete in a range of magnitudes that can have a significant influence on the seismic hazard analysis and on the resulting seismic risk assessment. Moreover, it can also be applied in the common case when the catalogue is considered complete above a given magnitude threshold. Numerical examples are presented to illustrate the influence of catalogue incompleteness on the complete exceedance rate estimations. In companion papers, attention is focused on the estimation of completeness probabilities of available catalogues and on parameter estimation of the exceedance rate functions.