How to <i>b</i>-Significant When Analyzing <i>b</i>-Value Variations

Abstract Variations of the b-value of the Gutenberg–Richter law are highly relevant in the context of earthquake forecasting because they directly translate into varying probabilities of future large earthquakes. However, when analyzing a specific earthquake catalog, it is difficult to know whether the observed b-value variation is due to random fluctuation or actual physical changes. We address this problem by developing a simple autocorrelation-based method that can quantify the significance of b-value variation objectively (b-significant). Our synthetic tests reveal that the method performs well at detecting b-value variations of various shapes, and we characterize its resolution by identifying the smallest detectable b-value change for a given catalog size. The method also allows finding the ideal number of magnitudes per b-value estimate (or, equivalently, a length- or timescale), for which the pattern of b-values is maximized. For synthetic data, we found that this length scale could be related to the optimal number of magnitudes per estimate in terms of information gain when forecasting magnitudes of future earthquakes. Finally, we revisit the temporal and spatial b-value patterns in the Parkfield section of the San Andreas fault and evaluate their significance using our new approach. We find significant spatial variations along strike and with depth. However, the temporal variation is not significant, despite the visual appearance that change is occurring. We argue that before interpreting any b-value change, it should first b-significant.