The return period is the average time between occurrences of an event of a given or greater magnitude, expressed as the inverse of its annual probability of exceedance. In earthquake engineering, it is used to characterize seismic hazard levels and to define design earthquakes.
The return period (also called recurrence interval or mean recurrence time) is the average time between occurrences of an event of a specified magnitude or greater. It is formally defined as the inverse of the annual probability of exceedance: if an event has an annual probability of exceedance of p, its return period is T = 1/p. For example, a ground motion with an annual exceedance probability of 2% (a "50-year" event) has a return period of 50 years. The term "return period" is used throughout earthquake engineering, hydrology, and other fields to characterize the frequency of rare events.
The return period is often misunderstood and requires careful interpretation. It does not mean that the event occurs exactly once every T years, nor that the site is "safe" for T years after an event. It is a statistical average over a long time period. For a process with independent events, the probability that at least one event exceeding the specified level occurs in a given T-year period is 1 - e^(-1) β 63%, not 100%. Equivalently, the probability that no such event occurs in T years is approximately 37%. The probability of at least one event in a longer time window can be computed from the Poisson assumption or from more complex time-dependent models. In earthquake engineering, where large events may be quasi-periodic on individual faults, the simple Poisson model may not be appropriate; time-dependent models that account for the earthquake cycle are increasingly used.
The return period is used throughout earthquake engineering practice. Design codes define design earthquakes in terms of return periods: the design basis earthquake (DBE) typically corresponds to a 475-year return period (10% probability of exceedance in 50 years), and the maximum considered earthquake (MCE) typically corresponds to a 2,475-year return period (2% probability of exceedance in 50 years). These return periods are not universal β some codes use different values, and some critical facilities (nuclear power plants, hospitals) are designed for much longer return periods (10,000 years or more). The return period is also used in seismic risk assessment to express the expected annual loss β the product of the probability of an event and the loss it causes, summed over all possible events. In insurance and catastrophe modeling, return periods of 100, 250, 500, and 1,000 years are commonly used to characterize portfolio risk. The key challenge in using return periods is that they are probabilistic concepts applied to rare events β the historical record may not be long enough to reliably estimate the frequency of the most damaging events. Modern practice increasingly uses logic trees and Bayesian methods to quantify the uncertainty in return period estimates, and increasingly uses time-dependent models that account for the earthquake cycle. In Iran, return periods of 475 years (for ordinary buildings) and 2,475 years (for critical facilities) are used following the general international practice, with specific values defined in Standard 2800 and in project-specific studies for major infrastructure.