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<p class=MsoNormal><font size=3 color=blue face="Times New Roman"><span
style='font-size:12.0pt;color:blue'>Dear Julio,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 color=blue face="Times New Roman"><span
style='font-size:12.0pt;color:blue'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Your explanation (for a sole characteristic M7 earthquake with
recurrence interval = 250 years that lead to PGA ~ 0.4 g on average in a
site) is a deterministic one and inconsistent with what is known.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>“If we have a fault with sole characteristic M7 earthquake with
recurrence interval = 250 years that lead to PGA ~ 0.4 g on average in a
site, then <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>PGA ~ 0.4 g has a mean return period ~ 500 years.” A PGA ~
0.4 g with a mean return period ~ 500 years means that this PGA will occur
in 500 years (return period – the mean [average] time between occurrences
of a seismic hazard). This contradicts to the basic probability principle. The
probability that one or two PGA of ~0.4g could be observed at the site is about
63% if the M7 earthquake occurs twice in 500 years (assuming Poison
distribution). An event with an occurrence probability of 63% MAY not occur. Everybody
can test this by flipping a coin. The probability that you get one or two heads
is about 63% if you flip the coin twice. You may get two tails from time to
time. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>“In 2000 years we expect 8 M7 earthquakes and in 4 of them PGA
>= 0.4 g.” The only thing known here is the probability of 98.2% that
one or more PGA of ~0.4g could be observed at the site if the M7 earthquake occurs
8 times in 2,000 years (assuming Poison distribution). What is the probability
that four PGA of ~0.4g could be observed at the site? 100%? <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>There are very limited observations for characteristic earthquakes and
the ground motions generated by the characteristic earthquakes at a site. For
example, there are only 3 to 4 characteristic earthquakes (~M7.5) were
documented in the past couple thousands years in the New Madrid Seismic Zone,
and there is no ground motion record. A recurrence interval of about 500 years
was inferred for the characteristic earthquake (~M7.5). The aim of seismic
hazard analysis is to predict the probability that a level of ground motion
could be expected at a site, for example in <st1:City w:st="on">Memphis</st1:City>
or <st1:City w:st="on"><st1:place w:st="on">Paducah</st1:place></st1:City>, if
the characteristic earthquake (~M7.5) occurs. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Greg Hempen<font color=blue><span style='color:blue'> has made a very good
statement: “with so much to learn about earthquakes, we all should take
care to be consistent and not misstate what is understood.” <o:p></o:p></span></font></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Thanks.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Zhenming<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<div>
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face="Times New Roman"><span style='font-size:12.0pt'>
<hr size=2 width="100%" align=center tabindex=-1>
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<p class=MsoNormal><b><font size=2 face=Tahoma><span style='font-size:10.0pt;
font-family:Tahoma;font-weight:bold'>From:</span></font></b><font size=2
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'> Julio J.
Hernández [mailto:julher@cantv.net] <br>
<b><span style='font-weight:bold'>Sent:</span></b> Wednesday, May 21, 2008 2:24
AM<br>
<b><span style='font-weight:bold'>To:</span></b> Central and Eastern U.S.
Earthquake Hazards Listserve<br>
<b><span style='font-weight:bold'>Cc:</span></b> <st1:PersonName w:st="on">Wang,
Zhenming</st1:PersonName><br>
<b><span style='font-weight:bold'>Subject:</span></b> Re:
[CEUS-earthquake-hazards] Comment on <st1:country-region w:st="on"><st1:place
w:st="on">China</st1:place></st1:country-region> quake and hazards map</span></font><o:p></o:p></p>
</div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
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