Accounting for source location errors in the bayesian analysis of seismicity and seismic hazard

A method is presented for incorporating the uncertainties associated with hypocentral locations in the formulation of probabilistic models of the time and space distributions of the activity of potential seismic sources, as well as of the resulting seismic hazard functions at sites in their vicinity. For this purpose, a bayesian framework of analysis is adopted, where the probabilistic models considered are assumed to have known forms and uncertain parameters, the distribution of the latter being the result of an a priori assessment and its updating through the incorporation of the direct statistical information, including the uncertainty associated with the relations between the actual hypocentral locations and the reported data. This uncertainty is incorporated in the evaluation of the likelihood function of the parameters to be estimated for a given sample of recorded locations. For the purpose of illustration, the method proposed is applied to the modelling of the seismic sources near a site close to the southern coast of Mexico. The results of two alternate algorithms for the incorporation of location uncertainties are compared with those arising from neglecting those uncertainties. One of them makes use of Monte Carlo simulation, while the other is based on a closed-form analytical integration following the introduction of some simplifying assumptions. For the particular case studied, accounting for location uncertainties gives place to significant changes in the probabilistic models of the seismic sources. Deviations of the same order of magnitude can be ascribed to differences in the mathematical and/or numerical tools used in the uncertainty analysis. The resulting variability of the seismic hazard at the site of interest is less pronounced than that affecting the estimates of activity of individual seismic sources.