Magnitude probabilities for extreme earthquakes around the globe with Rank-Ordering

Earthquake likelihoods have occupied humankind ever since, and the estimation of potential magnitudes is crucial for a multitude of aspects of safety. In this work, we present a probabilistic analysis of extreme magnitudes in 16 regions across the globe characterized by different seismicity to invert the traditional question of «what probability is associated with certain magnitudes». We combine the Gutenberg-Richter Law and Rank-Ordering-Statistics in a methodological approach to estimate what magnitude ranges can be almost certainly (i.e., with 95%) expected, and what magnitudes become reasonably unlikely beyond those ranges. This approach allows for estimating probabilities for maximal magnitudes per region and comparing thereto the maximal magnitudes (mr) that appeared in reality. The method explores the maximal magnitudes that could occur or be exceeded with a probability of 95%, if the respective mr are equal to or greater than these 95%-predictions, and how probable it is, that also these mr could be reproduced or exceeded. We suspect a lack of great magnitudes in the Alps and a surplus across the Atlantic Ocean from these statistical considerations.