Estimation Techniques for Seismic Recurrence Parameters for Incomplete Catalogues

In probabilistic seismic hazard analysis, assessment of the three recurrence parameters, namely the mean activity rate λ , 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 λ 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 λ , 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 λ , 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