基于贝叶斯方法的首都圈地区完整性震级评估

Bayesian estimation of completeness magnitude in the Capital Circle Region

  • 摘要: 地震目录的完整性评估是地震活动性分析的基础性工作,常用的基于地震目录的评估方法未能考虑台站信息,对于少震地区无法给出评估结果,并且受到主观选取的计算参数的影响。本文采用基于贝叶斯统计的完整性震级(BMC)评估方法,对2010年至2023年期间中国地震台网记录的首都圈地区的地震目录进行分析,通过迭代优化获得计算最小完整性震级MC的最优扫描半径和先验的MC模型,根据数据误差的高斯分布特征推导出MC的先验和似然的概率分布,最后得到MC的后验估计。BMC将地震台站分布的先验信息与局部观测值相结合,权重由各自的不确定性决定,给出了少震区域的MC估计值,并且降低了结果的不确定性。评估结果显示,2010年至今首都圈地区地震监测能力较强,但MC的空间分布不均匀,监测能力最强的地区其MC可达到0左右,较弱地区仅能达到2.7左右。采用最大曲率法评估了研究区域1966年至2023年整体的完整性震级的变化,结果显示首都圈的地震监测能力逐渐提升,2010年后提升较显著。此外,本文还对比了最大曲率法(MAXC)、拟合优度法(GFT)和中位数分段斜率方法(MBASS)在研究区域的结果,认为方法的选择和计算参数对评估结果有不同程度的影响。

     

    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 Capital 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 catalog 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 (23546 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); ② Integrating 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 heterogeneous monitoring capabilities, with MC reaching 2.7 in regions with relatively weak monitoring capabilities. 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 [ 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 model, has limitations due to its preset starting magnitude. Our findings show a significant improvement 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 analysis. This study demonstrates BMC’s efficacy for robust MC estimation, crucial for accurate seismic hazard characterization and mitigation strategies.

     

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