The effect of magnitude uncertainty on earthquake activity rates

At present, any seismic hazard analyst seeking advice from the literature on how to handle uncertainty in magnitude values when calculating activity rates for seismic source zones may be alarmed to find two different viewpoints that apparently contradict one another, and that papers advocating one approach fail to mention the other, and vice versa. Superficially, it appears to be demonstrable that the uncertainty in earthquake magnitude either causes an overestimation of the true activity rate, or causes an underestimation. In this short note, it will be demonstrated that the resolution to the dichotomy depends not only on whether magnitude data have been converted, but also on how—a point not previously made. Various authors have proposed a correction factor to remedy the effect of uncertainty on activity rate, but if this is applied wrongly, the problem may be exacerbated. In practice, actual cases may be complex and difficult to resolve.