Assessing the Quality of Earthquake Catalogues: Estimating the Magnitude of Completeness and Its Uncertainty

Abstract We introduce a new method to determine the magnitude of completeness M c 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 M c 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 M c 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 M c for the 1992 Landers aftershock sequence and found that it was underestimated on average by 0.2 with former techniques. Mapping M c on a global scale, M c reveals considerable spatial variations for the Harvard Centroid Moment Tensor (CMT) (5.3 � M c � 6.0) and the International Seismological Centre (ISC) catalogue (4.3 � M c � 5.0).