Abstract

The Gutenberg–Richter relation for earthquake magnitudes is the most famous empirical law in seismology. It states that the frequency of earthquake magnitudes follows an exponential distribution; this has been found to be a robust feature of seismicity above the completeness magnitude, and it is independent of whether global, regional, or local seismicity is analyzed. However, the exponent b of the distribution varies significantly in space and time, which is important for process understanding and seismic hazard assessment; this is particularly true because of the fact that the Gutenberg–Richter b‐value acts as a proxy for the stress state and quantifies the ratio of large‐to‐small earthquakes. In our work, we focus on the automatic detection of statistically significant temporal changes of the b‐value in seismicity data. In our approach, we use Bayes factors for model selection and estimate multiple change‐points of the frequency–magnitude distribution in time. The method is first applied to synthetic data, showing its capability to detect change‐points as function of the size of the sample and the b‐value contrast. Finally, we apply this approach to examples of observational data sets for which b‐value changes have previously been stated. Our analysis of foreshock and aftershock sequences related to mainshocks, as well as earthquake swarms, shows that only a portion of the b‐value changes is statistically significant.

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