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Estimation Techniques for Seismic Recurrence Parameters for Incomplete Catalogues

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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

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Source: Pule et al. (2015). Adapted from Fernandez (1974)

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Authors and Affiliations

  1. University of Pretoria Natural Hazard Centre, University of Pretoria, Pretoria, South Africa

    Andrzej Kijko

  2. Portion 45, Zonderwater, Cullinan, 1000, South Africa

    Petrus Johannes Vermeulen

  3. Department of Geology, University of Pretoria Natural Hazard Centre, University of Pretoria, Pretoria, South Africa

    Ansie Smit

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  1. Andrzej Kijko
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  2. Petrus Johannes Vermeulen
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  3. Ansie Smit
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Correspondence to Andrzej Kijko.

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Kijko, A., Vermeulen, P.J. & Smit, A. Estimation Techniques for Seismic Recurrence Parameters for Incomplete Catalogues. Surv Geophys 43, 597–617 (2022). https://doi.org/10.1007/s10712-021-09672-2

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