A robust method to estimate the b-value of the magnitude–frequency distribution of earthquakes

The methods to estimate the b-value of the magnitude–frequency distribution are analyzed based on a certain period of earthquakes in the central egion of China. According to the problems in the traditional methods, least square regression method and maximum likelihood estimation method, a robust fitting method to estimate the b- value is proposed. The least square regression method is suggested not to be used in the future for it sunstability and great deviation from the linerity to the extrem events. The use of maximum likelihood estimation method needs a high accurate assessment of the magnitude of completeness. Compared with the two traditional methods, the proposed method cannot only provide a stable and reliable b-value, but also has a good sensitivity to the occurrence of earthquakes with large magnitudes.The variation of b- value as an earthquake precursor is applied successfully in our study, and the proposed robust fitting method is shown to be more efficient than the maximuml ikelihood estimation method.