Earthquake Probability of Exceedance (Pe):
Pe: Probability that a certain earthquake level is exceeded in a set time (n years).
Pa: Annual probability of exceedance.
Tr: Return period = 1 / Pa.
Example: Pa = 0.1 → Tr = 10 years.
Pe over n years =
Pe=1−(1−Pa)n=1−(1−1Tr)nPe = 1 - (1 - Pa)^n = 1 - \left(1 - \frac{1}{Tr}\right)^nPe=1−(1−Pa)n=1−(1−Tr1)n
Important Notes:
A 10% chance of exceedance = 90% chance the event won’t exceed.
Old codes used a 10% chance in 50 years → Tr ≈ 475 years.
Modern codes use 2% in 50 years → Tr ≈ 2,500 years.