Can we test for the maximum possible earthquake magnitude?
Holschneider M, Zoeller G, Clements R, Schorlemmer D
We explore the concept of maximum possible earthquake magnitude, M, in a region represented by an earthquake catalog from the viewpoint of statistical testing. For this aim, we assume that earthquake magnitudes are independent events that follow a doubly truncated Gutenberg‐Richter distribution and focus on the upper truncation M. In earlier work, it has been shown that the value of M cannot be well constrained from earthquake catalogs alone. However, for two hypothesized values M and M′, alternative statistical tests may address the question: Which value is more consistent with the data? In other words, is it possible to reject a magnitude within reasonable errors, i.e., the error of the first and the error of the second kind? The results for realistic settings indicate that either the error of the first kind or the error of the second kind is intolerably large. We conclude that it is essentially impossible to infer M in terms of alternative testing with sufficient confidence from an earthquake catalog alone, even in regions like Japan with excellent data availability. These findings are also valid for frequency‐magnitude distributions with different tail behavior, e.g., exponential tapering. Finally, we emphasize that different data may only be useful to provide additional constraints for M, if they do not correlate with the earthquake catalog, i.e., if they have not been recorded in the same observational period. In particular, long‐term geological assessments might be suitable to reduce the errors, while GPS measurements provide overall the same information as the catalogs.