A Bayesian Merging of Earthquake Magnitudes Determined by Multiple Seismic Networks

We introduce a Bayesian algorithm designed to integrate earthquake magnitudes ofthe same type reported by various seismic networks, aiming to create unified and stand-ardized catalogs suitable for widespread use. The fundamental concept underpinningthis algorithm is the utilization of the inherent consistency within each individual net-work's magnitude determination process. Assuming that the magnitudes for an earth-quake measured by all networks conform to a Gaussian distribution, with a linearfunction of the unknown true magnitude serving as its mean, we derive the posteriorprobability distribution of the true magnitude under four different assumptions for theprior distribution: the uninformative uniform distribution, the unbounded Gutenberg-Richter (GR) magnitude-frequency law, the GR magnitude-frequency relationshiprestricted by the detection rate, and the truncated GR law as priors. We assess therobustness of the method by a test on several synthetic catalogs and then use it tomerge the catalogs compiled by five seismic networks in Italy. The results demonstratethat our proposed magnitude-merging algorithm effectively combines the catalogs,resulting in robust and unified data sets that are suitable for seismic hazard assessmentand seismicity analysis.