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Re: Probabilistic Definition of Seismic Hazards

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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.