Completeness assessment of earthquake catalogues under uncertain knowledge

A probabilistic model is proposed to quantify the completeness levels of earthquake catalogues used for the estimation of the activity of seismic sources. This variable, related to the probability that an event of a given magnitude is recorded in the earthquake catalogue, reflects both aleatory and epistemic uncertainties about the catalogue information. Two alternative approaches are presented for the estimation of the completeness levels: one is related to a catalogue suspected to be incomplete throughout the magnitude range of interest because the monitoring network is not capable of detecting the occurrence of all seismic events and the other is related to an earthquake catalogue considered to be almost complete above a given threshold magnitude. The completeness probabilities for given magnitudes are described by explicit completeness functions whose parameters are treated as random variables described by their posterior joint probability density function based on a Bayesian estimation. Two case studies are presented: The first one extends throughout the Gulf of Mexico with a seismic catalogue suspected or known to be incomplete and the second one corresponds to a seismic source covering a segment along the southwest coast of Mexico, with an earthquake catalogue known to be almost complete.