A Bayesian Merging of Earthquake Magnitudes Determined by Multiple Seismic Networks

Abstract

We introduce a Bayesian algorithm designed to integrate earthquake magnitudes of the same type reported by various seismic networks, aiming to create unified and standardized catalogs suitable for widespread use. The fundamental concept underpinning this algorithm is the utilization of the inherent consistency within each individual network’s magnitude determination process. Assuming that the magnitudes for an earthquake measured by all networks conform to a Gaussian distribution, with a linear function of the unknown true magnitude serving as its mean, we derive the posterior probability distribution of the true magnitude under four different assumptions for the prior distribution: the uninformative uniform distribution, the unbounded Gutenberg–Richter (GR) magnitude–frequency law, the GR magnitude–frequency relationship restricted by the detection rate, and the truncated GR law as priors. We assess the robustness of the method by a test on several synthetic catalogs and then use it to merge the catalogs compiled by five seismic networks in Italy. The results demonstrate that our proposed magnitude-merging algorithm effectively combines the catalogs, resulting in robust and unified data sets that are suitable for seismic hazard assessment and seismicity analysis.