Uncertainty of B-value estimation in connection with magnitude distribution properties of small data sets

We evaluate the efficiency of the maximum likelihood estimator introduced by Aki (1965), using synthetic datasets exhibiting diverse but well defined properties. The deviation of the b-value estimation from its real value is quantified by Monte Carlo simulations as a function of catalogue features and data properties such as the sample size, the magnitude uncertainties distribution, the round-off interval of reported magnitude values and the magnitude range. Within the objective of this study, algorithms have been compiled for the determination of such observational-theoretical deviations and to facilitate the construction of nomograms corresponding to diverse cases of input parameters. In this way, a more accurate estimation of the uncertainty level for the b-value and MC determination can be achieved, contributing to a more robust seismic hazard assessment, especially at low activity areas and induced seismicity sites. Our results indicate that b-value analysis, especially for small datasets should be carried out together with Magnitude range analysis. Nomograms should be constructed and adjusted to each particular case study in order to achieve a more accurate estimation of the b-value and the corresponding uncertainty.