Estimating seismic-source rate parameters associated with incomplete catalogues and superimposed Poisson-renewal generating processes

A probabilistic model is presented to quantify parameters that define the exceedance rates of earthquake magnitudes. Incompleteness of seismic catalogues and superposition of Poisson-renewal earthquake generation processes are both taken into account within a Bayesian framework. The formulation can be transformed into the parameter estimation of single Poisson or renewal process. The incomplete exceedance rate parameters are estimated from incomplete data, so that the estimated values are equal to those of the complete rate. Two cases are studied: the first one corresponds to a seismic source in the Gulf of Mexico and the other to a seismic source in the southern Pacific coast of Mexico.