Bayesian estimation of completeness magnitude in the Capital Circle Region

Zhang Fan; Han Xiaoming; Bao Jinzhe; Yang Xiaozhong

doi:10.11939/jass.20230140

Abstract：Earthquake catalog completeness,crucial for seismicity analyses,is defined by the completeness magnitude(Mc):The lowest magnitude at which all earthquakes are reliably detected.Accurate MC estimation is essential for seismic hazard assessments and earthquake studies.Traditional methods often solely rely on the frequency-magnitude distribution(FMD)and Gutenberg-Richter(G-R)law,neglecting station coverage,making them unsuitable for regions with low seismicity and susceptible to the subjective selection of calculation parameters.This study utilizes the Bayesian magnitude of completeness(BMC)method to analyze the Capi-tal Circle Region of China's(37°N—42°N,114°E—120°E)earthquake catalog from 2010 to 2023,a period marked by significant network upgrades.Initially,we assessed the overall cata-log completeness from 1966 to 2023 using the maximum curvature(MAXC)method,and the results revealed improved monitoring capabilities,especially after 2010,with MC consistently between 0.5 and 1.5.Focusing on 2010-2023(23 546 events,153 stations),we employed the BMC method with a two-step process:① Optimizing spatial resolution and prior model parameters based on the relationship between MC and station density(distance to the k-th nearest station);②Integrating prior information with observed MC values using Bayesian inference.Iterative optimization yielded the optimal scanning radius and prior MC model,from which assuming Gaussian-distributed errors,prior and likelihood distributions were derived,leading to a posterior MC estimate;the BMC method integrates station distribution priors with local MC observations,weighted by their uncertainties,enabling MC estimation in low-seismicity regions and reducing overall uncertainty.The optimized scanning radius R varied spatially,smaller in densely instrumented areas like Beijing.The prior model of Capital Circle Region differed significantly from that of Taiwan,highlighting the need for region-specific models.Posterior MC estimates from BMC showed reduced uncertainty compared to observed MC from MAXC,demonstrating the value of integrating station data.Results revealed spatially hetero-geneous monitoring capabilities,with MC reaching 2.7 in regions with relatively weak monitor-ing capabilities.We compared BMC with three FMD-based methods[MAXC,goodness-of-fittest(GFT),and median-based analysis of segment slope(MBASS)]at varying radii(5-75 km).GFT yielded the most conservative estimates[MC(GFT)＞MC(MBASS)＞MC(MAXC)].Larger radii smoothed spatial variations and potentially overestimated MC in well-monitored areas,emphasizing the importance of careful radius selection.BMC,unlike probability-based magnitude of completeness(PMC),optimizes R and incorporates station,but does not account for variations among individual stations.PMC,while not reliant on the G-R mode l,has limitations due to its preset starting magnitude.Our findings show a significant improve-ment in the seismic network's monitoring capabilities after 2010 compared to previous levels.The spatial MC variability highlights the importance of localized assessments for hazard analy-sis.This study demonstrates BMC's efficacy for robust MC estimation,crucial for accurate seis-mic hazard characterization and mitigation strategies.