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Estimation Techniques for Seismic Recurrence Parameters for Incomplete Catalogues
Surveys in Geophysics ( IF 4.6 ) Pub Date : 2021-11-20 , DOI: 10.1007/s10712-021-09672-2
Andrzej Kijko 1 , Petrus Johannes Vermeulen 2 , Ansie Smit 3
Affiliation  

Abstract

In probabilistic seismic hazard analysis, assessment of the three recurrence parameters, namely the mean activity rate \(\lambda\), Gutenberg–Richter \(b\)-value, and maximum possible seismic event magnitude \(m_{\max }\), is paramount. Over the years, several assessment procedures have been developed, each with its advantages and disadvantages. Typically, estimation techniques for the mean activity rate \(\lambda\) and the Gutenberg–Richter \(b\)-value are discussed and evaluated separately from those designed for the maximum possible event magnitude \(m_{\max }\). Yet, the three parameters are typically defined in terms of joint distributions for \(\lambda\), \(b\), and \(m_{\max }\). In this study, we focused on systematically constructing joint distributions for the three recurrence parameters for considering complete and incomplete seismic event catalogues. The Bayesian formalism is introduced to constrain the parameter estimates with independent a priori information. Further, we discuss an iterative technique to solve the systems of equations sequentially. The procedures are compared and illustrated using Monte Carlo simulation and a seismic event catalogue for Cape Town, South Africa.

Article Highlights

  • Probabilistic seismic hazard analysis in case of incomplete catalogues

  • Assessment of the hazard recurrence parameters, activity rate \(\lambda\), frequency-magnitude Gutenberg–Richter \(b\)-value and area characteristic, maximum possible seismic event magnitude \(m_{\max}\)

  • Application of Bayesian formalism to constrain hazard parameters estimation



中文翻译:

不完全目录的地震重现参数估计技术

摘要

在概率地震危险性分析中,评估三个重复参数,即平均活动率\(\lambda\)、Gutenberg–Richter \(b\)值和最大可能地震事件震级\(m_{\max }\ ),是最重要的。多年来,已经开发了几种评估程序,每种程序都有其优点和缺点。通常,平均活动率\(\lambda\)和 Gutenberg–Richter \(b\)值的估计技术与为最大可能事件幅度\(m_{\max }\)设计的技术分开讨论和评估. 然而,这三个参数通常是根据\(\lambda\), \(b\)\(m_{\max }\)。在这项研究中,我们专注于系统地构建三个递归参数的联合分布,以考虑完整和不完整的地震事件目录。引入贝叶斯形式主义来约束具有独立先验信息的参数估计。此外,我们讨论了一种按顺序求解方程组的迭代技术。使用蒙特卡罗模拟和南非开普敦的地震事件目录对这些程序进行了比较和说明。

文章亮点

  • 目录不完整情况下的概率地震危险性分析

  • 灾害复发参数评估,活动率\(\lambda\),频率-幅度Gutenberg–Richter \(b\) -值和面积特征,最大可能地震事件幅度\(m_{\max}\)

  • 贝叶斯形式主义在约束危险参数估计中的应用

更新日期:2021-11-20
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