Improving the resolvability of MMAX truncation via deeper order statistics

Summary The maximum possible earthquake magnitude (MMAX) is a consequential parameter that is difficult to quantify. In this paper, order statistics concepts are adapted to infer MMAX from an earthquake catalogue. Examining jumps in the ordered sequence of largest events significantly improves inferences of MMAX truncation; I continue this improvement by considering deeper metrics (i.e., jumps in the second, third, fourth, … largest events). I begin by providing a theoretical foundation for these deeper metrics, while highlighting special cases. Synthetic tests are performed to quantify the improvements gained. While the largest information gains arise from the largest event sequence, appreciable gains are found to depths of ten. This approach is also validated on real-data cases, such as Groningen and FORGE, demonstrating their utility. Overall, this approach will contribute to better understanding earthquake hazards and discerning the physical processes that allow earthquakes to grow large.