Impact of magnitude uncertainties on seismic catalogue properties

Catalogue-based studies are of central importance in seismological research, to investigate the temporal, spatial and size distribution of earthquakes in specified study areas. Methods for estimating the fundamental catalogue parameters like the Gutenberg-Richter (G-R) b-value and the completeness magnitude (M-c) are well established and routinely applied. However, the magnitudes reported in seismicity catalogues contain measurement uncertainties which may significantly distort the estimation of the derived parameters. In this study, we use numerical simulations of synthetic data sets to assess the reliability of different methods for determining b-value and M-c, assuming the G-R law validity. After contaminating the synthetic catalogues with Gaussian noise (with selected standard deviations), the analysis is performed for numerous data sets of different sample size (N). The noise introduced to the data generally leads to a systematic overestimation of magnitudes close to and above M-c. This fact causes an increase of the average number of events above M-c, which in turn leads to an apparent decrease of the b-value. This may result to a significant overestimation of seismicity rate even well above the actual completeness level. The b-value can in general be reliably estimated even for relatively small data sets (N < 1000) when only magnitudes higher than the actual completeness level are used. Nevertheless, a correction of the total number of events belonging in each magnitude class (i.e. 0.1 unit) should be considered, to deal with the magnitude uncertainty effect. Because magnitude uncertainties (here with the form of Gaussian noise) are inevitable in all instrumental catalogues, this finding is fundamental for seismicity rate and seismic hazard assessment analyses. Also important is that for some data analyses significant bias cannot necessarily be avoided by choosing a high M-c value for analysis. In such cases, there may be a risk of severe miscalculation of seismicity rate regardless the selected magnitude threshold, unless possible bias is properly assessed.