Bayesian Estimation of the Spatially Varying Completeness Magnitude of Earthquake Catalogs

Assessing the completeness magnitude Mc of earthquake catalogs is an essential prerequisite for any seismicity analysis. We employ a simple model to com- puteMc inspacebasedontheproximitytoseismicstationsinanetwork.Weshowthata relationship of the form M predd ad bc, with d the distance to the kth nearest seismic station, fits the observations well, k depending on the minimum number of stations being required to trigger an event declaration in a catalog. We then propose anewMc mappingapproach,theBayesianmagnitude ofcompleteness (BMC)method, based on a two-step procedure: (1) a spatial resolution optimization to minimize spatial heterogeneities and uncertainties in Mc estimates and (2) a Bayesian approach that merges prior information about Mc based on the proximity to seismic stations with locally observed values weighted by their respective uncertainties. Contrary to the cur- rentMc mappingprocedures,theradiusthatdefineswhichearthquakestoincludeinthe local magnitude distribution is chosen according to an objective criterion, and there are no gaps in the spatial estimation of Mc. The method solely requires the coordinates of seismic stations. Here, we investigate the Taiwan Central Weather Bureau (CWB) seismic network and earthquake catalog over the period 1994-2010.