PERMFILE50024

• Permit No: M1988112
• IBM Index Class Name: Permit File
• Doc Date: 11/8/1988
• Section_Exhibit Name: APPENDIX B SEISMOLOGY STUDY
• Media Type: D
• Archive: No

state 1, K2 transitions to state 2,..., K,, transitions to state
id in n time periods as
n
' wi(K1,K2,...,KN~n)= Pij(m) hij(m) wj(K1,K2,...,KN~n-m), (1)
jai m_i
' where Pij(m) is the probability that a process in state i
will enter state j on the next transition (magnitude Mi will
be followed by magnitude M.) and hi (m) is the probability
' that the holding time between states i and j is m (for example,
the probability that the time between an Mi earthquake and an
M. earthquake is 1,000 years). Equation (1) is a recursive
J
formula for the earthquake hazard. In our case we don't have
sufficient information to treat multiple magnitudes (states),
so I shall restrict attention to the probability of a repeat
of a surface rupture of 2 m adjacent of the site (Mi=6.8 to
7.0; ie. j = i). The initial state holding time t0 ranges
between 1,940 and 4,715 years, and the probability density
' hij(m) is summarized (from Table I) on page 9, above. The
operative equation reduces to
w(l~n) _

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L_~
fin` •-
L~ hii(m+t0) wi(l~n-m).
m_i
(2)
Figure 4 provides the probability calculation using equation
(2) in five year increments for the next 100 years. The
curves differ depending upon how long one assumes the
process has been accumulating strain (represented by she initial
holding time t0) since the last major earthquake. The probab-
ility ranges from approximately 0.5% to 12% pf experiencing
a magnitude 6.8 to 7.0 earthquake in the next 100 yeas.
Assuming that the process has been holding for 3,000 Nears,
which is approximately midway between the 1,940 and 4,715
year period of uncertainty for the occurrence of the _ast earth-
quake, the probability that a magnitude 6.8 to 7.0 earthquake
will occur on the San Luis fault segment in the next :.00 years
is approximately 2 percent.
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