The waiting-time paradox and the recurrence of earthquakes

Kelian Dascher-Cousineau, & Michael E. Oskin

Submitted September 7, 2025, SCEC Contribution #14939, 2025 SCEC Annual Meeting Poster #TBD

Much of the San Andreas Fault is conjectured to be “overdue”. More time has passed since the last earthquake than the average interevent time of the corresponding fault section. The concurrence of seemingly overdue segments is highly unlikely under standard recurrence models. This statistical outlier casts doubt on the validity of recurrence models prompting contrasting propositions that include overcounting in paleoseismic data or the search for new physical phenomena to explain the long quiescence interval. We test a third option: we should expect it to be a boring time to study earthquakes. We base this inference on the waiting-time paradox, well known in various fields of physics, viscerally familiar to the daily commuter, yet scarcely recognized among statistical seismologists. The paradox posits that a random observer (us) is proportionally more likely to be in a long interval than a short one. The effects can be surprising, increasing quadratically with the coefficient of variation. For instance, a random observer expects to sample an interval twice as long as the average interval in a memoryless Poisson process. Here we investigate the severity of this bias on both simulated and real paleoseismic data for the faults in California, various subduction zones, and the Alpine Fault in New Zealand. In regions with highly regular intervals, wait times conform to intuition: on average we should expect to be half way through the earthquake cycle. On the other hand, many faults, including the San Andreas, feature long tailed recurrence intervals which elevate expected lapse- and wait-times to approximately 60% to 80% of the average interevent time, making the presently observed quiescent interval more likely than previously suggested.

Citation
Dascher-Cousineau, K., & Oskin, M. E. (2025, 09). The waiting-time paradox and the recurrence of earthquakes. Poster Presentation at 2025 SCEC Annual Meeting.

Related Projects & Working Groups
Earthquake Forecasting and Predictability (EFP)