We introduce a new method to determine the magnitude of completeness Mc and its uncertainty. Our method models the entire magnitude range (emr method) consisting of the self-similar complete part of the frequency-magnitude distribution and the incomplete portion, thus providing a comprehensive seismicity model. We compare the emr method with three existing techniques, finding that emr shows a superior performance when applied to synthetic test cases or real data from regional and global earthquake catalogues. This method, however, is also the most computationally intensive. Accurate knowledge of Mc is essential for many seismicity-based studies, and particularly for mapping out seismicity parameters such as the b-value of the Gutenberg-Richter relationship. By explicitly computing the uncertainties in Mc using a bootstrap approach, we show that uncertainties in b-values are larger than traditionally assumed, especially when considering small sample sizes.
As examples, we investigated temporal variations of Mc for the 1992 Landers aftershock sequence and found that it was underestimated on average by 0.2 with former techniques. Mapping Mc on a global scale, Mc reveals considerable spatial variations for the Harvard Centroid Moment Tensor (CMT) (5.3 ≤ Mc ≤ 6.0) and the International Seismological Centre (isc) catalogue (4.3 ≤ Mc ≤ 5.0).