Bayesian estimation of completeness magnitude in the Capital Circle Region

Earthquake catalog completeness, crucial for seismicity analyses, is defined by the completeness magnitude （M_C）—the lowest magnitude at which all earthquakes are reliably detected. Accurate M_C estimation is essential for seismic hazard assessments and earthquake studies. Traditional methods often rely solely 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 Capital Region of China’s （37°—42°N, 114°—120°E） earthquake catalog from 2010 to 2023, a period marked by significant network upgrades. Initially, we assessed the overall completeness from 1966 to 2023 using the Maximum Curvature （MAXC） method, revealing improved monitoring capabilities, especially after 2010, with M_C consistently between 0.5 and 1.5. Focusing on 2010—2023 （23,546 events, 153 stations）, we applied the BMC method, a two-step process: 1） optimizing spatial resolution and prior model parameters based on the relationship between M_C and station density （distance to the k-th nearest station）; 2） integrating prior information with observed M_C 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 M_C estimate; the BMC method integrates station distribution priors with local M_C observations, weighted by their uncertainties, enabling M_C estimation in low-seismicity regions and reducing overall uncertainty. The optimized scanning radius （R） varied spatially, smaller in densely instrumented areas like Beijing. The Capital Region's prior model differed significantly from Taiwan's, highlighting the need for region-specific models. Posterior M_C estimates from BMC showed reduced uncertainty compared to observed M_C from MAXC, demonstrating the value of integrating station data. Results revealed spatially heterogeneous monitoring capabilities, with M_C approaching 0 in parts of Beijing but reaching 2.7 elsewhere. We compared BMC with three FMD-based methods （MAXC, Goodness-of-Fit Test （GFT）, and Median-Based Analysis of Segment Slope （MBASS）） at varying radii （5—75 km）. GFT yielded the most conservative estimates （M_C （GFT）＞M_C （MBASS）＞M_C （MAXC））. Larger radii smoothed spatial variations and potentially overestimated M_C in well-monitored areas, emphasizing the importance of careful radius selection. BMC, unlike Probability-based Magnitude of Completeness （PMC）, optimizes R and incorporates station density, vital for sparse seismicity areas. PMC, while not reliant on the G-R model, has limitations due to its preset starting magnitude. Our findings show significantly improved monitoring since 2010, surpassing previous studies. The spatial M_C variability highlights the importance of localized assessments for hazard analysis. This study demonstrates BMC’s efficacy for robust M_C estimation, crucial for accurate seismic hazard characterization and mitigation strategies.