Estimation of the Maximum Earthquake Magnitude, m max - Potential Pitfalls

This study complements a prior study by Kijko (2004) that provides a statistical estimator of the area-characteristic maximum earthquake magnitude, \(\:{m}_{max}\). This estimator is highly regarded and widely used. However, as this study explains, such estimators are often misapplied owing to the misinterpretation of the time period of the occurrence of \(\:{m}_{max}^{obs}\), which is the largest observed earthquake. Accordingly, here, we examine the sources of such misunderstandings, which can lead to misuse of the procedure and, therefore, significantly affect the estimates of \(\:{\widehat{m}}_{\text{m}\text{a}\text{x}}\) and the overall seismic hazard indicators. As we show in an illustrative example, an assessment of \(\:{m}_{max}\) for the area surrounding Cape Town in South Africa, there is a substantial difference between correct and incorrect estimates of the maximum possible earthquake magnitude resulting from the use of the incorrect time interval. Furthermore, we discuss some insights about the variability of the estimated \(\:{m}_{max}\), noting that the misapplication considered here can lead to overestimation, whereas a lack of data can lead to underestimation. In addition, we provide recommendations for discerning when over- or underestimation could occur. We conclude that the best practice is to incorporate prior information and apply a Bayesian formalism when such information is available.