Frequently Asked Questions (FAQ) About Return Periods
Your map is for ground motions having a 2% probability of exceedance in 50 years.
Are those values the same as those for 10% in 250?
Yes, basically. This conclusion will be illustrated by using an approximate rule-of-thumb for calculating Return Period (RP).
A typical seismic hazard map may have the title, "Ground motions having 90 percent probability of not being exceeded in 50 years." The 90 percent is a "non-exceedance probability"; the 50 years is an "exposure time." An equivalent alternative title for the same map would be, "Ground motions having 10 percent probability of being exceeded in 50 years." A typical shorthand to describe these ground motions is to say that they are 475-year return-period ground motions. This means the same as saying that these ground motions have an annual probability of occurrence of 1/475 per year. "Return period" is thus just the inverse of the annual probability of occurrence (of getting an exceedance of that ground motion).
To get an approximate value of the return period, RP, given the exposure time, T, and exceedance probability, r = 1 - non-exceedance probability, NEP, (expressed as a decimal, rather than a percent), calculate
RP = T / r* Where r* = r(1 + 0.5r).
r* is an approximation to the value -loge ( NEP ).
In the above case, where r = 0.10, r* = 0.105 which is approximately = -loge ( 0.90 ) = 0.10536 Thus, approximately, when r = 0.10, RP = T / 0.105
Consider the following table.
Rule of Thumb |
Exact |
|||||
| NEP | T | r | r* | Calculation | RP | RP |
| 0.90 | 50 | 0.10 | 0.105 | 50/0.105 | 476.2 | 474.6 |
| 0.90 | 100 | 0.10 | 0.105 | 100/0.105 | 952.4 | 949.1 |
| 0.90 | 250 | 0.10 | 0.105 | 250/0.105 | 2381.0 | 2372.8 |
In this table, the exceedance probability is constant for different exposure times. Compare the results of the above table with those shown below, all for the same exposure time, with differing exceedance probabilities.
Rule of Thumb |
Exact |
|||||
| NEP | T | r | r* | Calculation | RP | RP |
| 0.90 | 50 | 0.10 | 0.105 | 50/0.105 | 476.2 | 474.6 |
| 0.95 | 50 | 0.05 | 0.05125 | 50/0.05125 | 975.6 | 974.8 |
| 0.98 | 50 | 0.02 | 0.0202 | 50/0.0202 | 2475.2 | 2475.9 |
Comparison of the last entry in each table allows us to see that ground motion values having a 2% probability of exceedance in 50 years should be approximately the same as those having 10% probability of being exceeded in 250 years: The annual exceedance probabilities differ by about 4%. Corresponding ground motions should differ by 2% or less in the EUS and 1 percent or less in the WUS, based upon typical relations between ground motion and return period.
