Bayesian estimation of the spatially varying completeness magnitude of earthquake catalogs

Assessing the completeness magnitude M_c of earthquake catalogs is an essential prerequisite for any seismicity analysis. We employ a simple model to compute M_c in space based on the proximity to seismic stations in a network.We showthat a relationship of the form M_c^pred(d) = ad^b + c, 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 a new M_c mapping approach, the Bayesian magnitude of completeness (BMC)method, based on a two-step procedure: (1) a spatial resolution optimization to minimize spatial heterogeneities and uncertainties in M_c estimates and (2) a Bayesian approach that merges prior information about M_c based on the proximity to seismic stations with locally observed values weighted by their respective uncertainties. Contrary to the current M_c mapping procedures, the radius that defines which earthquakes to include in the local magnitude distribution is chosen according to an objective criterion, and there are no gaps in the spatial estimation of M_c. 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.