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# Re: Probabilistic Definition of Seismic Hazards

• To: seaoc(--nospam--at)seaoc.org
• Subject: Re: Probabilistic Definition of Seismic Hazards
• From: "Bill Sherman" <SHERMANWC(--nospam--at)cdm.com>
• Date: Tue, 31 Dec 1996 09:54:42 +0500

```Per comments by Frank E. McClure:

>Seismic hazards are usually defined ... at a specified mean annual frequency
of >EXCEEDANCE, (not mean annual probability of OCCURRENCE) (e. g. 0.002 per
year,  >(1/500) ,or its effective equivalent (e.g. annual probability of
exceedance, mean >return period, probability of exceedance in n years, e.g.,
10% in 50 years).  In >other words, seismic hazards are usually defined ... at
a specified MEAN ANNUAL
>FREQUENCY OF EXCEEDANCE, which is the reciprocal of the MEAN RETURN PERIOD
>for a criterion earthquake with a specific probability of exceedance in n
>years.  It is important to remember that we are discussing MEAN RETURN PERIOD
( the >average return period) not the RETURN PERIOD.

>We start down a very slippery slope if we starting telling our clients or the
>public that the probability of occurrence can be given in terms of a certain
>number of years for earthquakes of a certain magnitude or ground motion
>strength.  Earthquake ground motion strength parameters are usually, for
>building code purposes or earthquake risk assessments, expressed in terms of
>"MEAN (average) ANNUAL FREQUENCY OF EXCEEDANCE ( not OCCURRENCE).

Please clarify what the difference is between annual frequency of occurrence
and annual frequency of exceedance - aren't these different ways of expressing
the same thing?  I do prefer the method of expressing events in terms of
probability of exceedance during a given period, since it gives a better sense
of the risk involved, but I am not clear on what the mathematical difference
is.

If an event has an annual frequency of occurrence of 0.002, then it has a 500
year expected return period.  Then in 50 years, doesn't it have a 10%
probability of being exceeded (0.002x50 = 0.10)?  and statistically, wouldn't
it have a 100% probability of occurring in 500 years?

The problem with using return periods to describe probabilistic events is that
it seems to give a false sense of security.  For example, consider design for
flotation resistance against a 100-year flood.  Such a flood would have a 0.01
annual probability of occurrence. For a 50 year design period, is seems to me
it would have a "50% probability of being exceeded" (0.01/year x 50 years).
If you are concerned with flotation of a structure, designing for a 100-year
flood for a 50-year design life sounds conservative.  But having a 50% risk of
exceedance during the design life sounds very risky.

```