Uncertainty on Estimated Magnitudes: A New Approach based   on a  Point Poisson Process of Dimension 2

Abstract The magnitudes recorded in seismic catalogues are subject to uncertainties that can have a significant impact when estimating the parameters of seismic recurrence models. In this paper, we propose an innovative approach based on a Poisson point process of dimension 2 that models both the magnitude hazard and the associated uncertainty. We define estimators of the parameters of the Gutenberg Richter (a, b) model that maximize the likelihood of the data with respect to the model. We apply the approach to the Alps region in France and compares it to other approaches proposed in the literature.