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<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Ellis,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Your concern on the b-value is actually the same as the ergodic
assumption of Anderson and Brune (1999). The b-value is used to determine the
temporal measure, the annual rate of earthquake exceeding a specific magnitude
(M). For a single characteristic earthquake (M7.7) with 500 years
recurrence interval in the New Madrid seismic zone, the rate is fixed at 0.002
(1/500). But PSHA could derive a range of rate, 0.002 to infinite small, for
the ground motions generated by this single M7.7 earthquake. The rate of ground
motion exceeding (annual probability of exceedance) is equal to 0.002
(earthquake rate) <i><span style='font-style:italic'>times</span></i> the exceeding
probability of ground motion (P, ranging from 1.0 to infinite small). The
ground motion uncertainty is a spatial measure. The return period is defined as
the reciprocal of the annual probability of exceedance in PSHA. This example
demonstrates that it is not the b-value being projected to a larger magnitude, but
exceeding probability of ground motion being used to extrapolate the rate for
ground motion. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Unfortunately, the return period of ground motion has been
interpreted as “the mean (average) time between occurrences of a seismic
hazard – for example, a certain ground motion at a site” (McGuire,
2004). Art also had a similar interpretation on the PSHA ground motion </span></font><font
color=navy><span style='color:navy'>“the ground motion with 2% PE in 50
years is exceeded once, on average over 2,500 years, so that it has a 1/2500
annual probability of being exceeded” (Frankel, 2005). </span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'> These
interpretations are clearly wrong. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Similarly, PSHA can derive a design M7 earthquake from two
faults with M6 and M8 earthquakes by mixing temporal and spatial measures or so-called
de-aggregation. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Thank<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Zhenming<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>___________________________________</span></font><o:p></o:p></p>
<p class=MsoNormal><st1:PersonName w:st="on"><font size=2 face=Arial><span
style='font-size:10.0pt;font-family:Arial'>Zhenming Wang</span></font></st1:PersonName><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>, PhD, PE</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Head, Geologic Hazards Section</span></font><o:p></o:p></p>
<p class=MsoNormal><st1:State w:st="on"><st1:place w:st="on"><font size=2
face=Arial><span style='font-size:10.0pt;font-family:Arial'>Kentucky</span></font></st1:place></st1:State><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'> Geological
Survey</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>228 Mining and <st1:place w:st="on"><st1:PlaceName w:st="on">Mineral</st1:PlaceName>
<st1:PlaceName w:st="on">Resources</st1:PlaceName> <st1:PlaceType w:st="on">Building</st1:PlaceType></st1:place></span></font><o:p></o:p></p>
<p class=MsoNormal><st1:place w:st="on"><st1:PlaceType w:st="on"><font size=2
face=Arial><span style='font-size:10.0pt;font-family:Arial'>University</span></font></st1:PlaceType><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'> of <st1:PlaceName
w:st="on">Kentucky</st1:PlaceName></span></font></st1:place><o:p></o:p></p>
<p class=MsoNormal><st1:place w:st="on"><st1:City w:st="on"><font size=2
face=Arial><span style='font-size:10.0pt;font-family:Arial'>Lexington</span></font></st1:City><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>, <st1:State
w:st="on">Kentucky</st1:State> <st1:PostalCode w:st="on">40506</st1:PostalCode></span></font></st1:place><o:p></o:p></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Phone:(859)257-5500x142</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Email: <a href="mailto:zmwang@uky.edu">zmwang@uky.edu</a></span></font><o:p></o:p></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Website: <a href="http://www.uky.edu/KGS/geologichazards">www.uky.edu/KGS/geologichazards</a></span></font><o:p></o:p></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>____________________________________</span></font><o:p></o:p></p>
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12.0pt'><o:p> </o:p></span></font></p>
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