Civil Engineering Reference
In-Depth Information
18.7
Sample simulation of the primary IM (PGA) for a magnitude 7
event in zone 2: (a) circular decay of the 'average' value (10
μ
log
+
η
);
(b) fi eld of intra-event residuals (the plotted quantity is 10
ε
, i.e.
the factor that multiplies the intensity in plot (a)), note the clusters of
close values caused by spatial correlation; (c) total shake fi eld;
(d) plot of primary IM versus epicentral distance.
are the sources. The shake-fi eld refers to an event on source 2, with the
epicentre identifi ed by a thick dot. Plot (a) shows the average intensity only,
i.e. the intensity obtained by neglecting the intra-event terms
, and illus-
trates the circular nature of the log-mean of the GMPE. Plot (b) shows the
map of intra-event residuals, and small circles highlight the tendency of
ε
ε
values to form cluster of size related to the correlation length. Plot (c)
shows the resulting total shake-fi eld. Plot (d) with the IMs values as a func-
tion of epicentral distance, shows the exponential decay of the GMPE mean,
as well as the important intra-event deviations produced by the
terms.
Once a value of the primary IM is obtained at each site through intepola-
tion from the main shake-fi eld, the assumption of joint lognormality of
s
ir
allows sampling
s
ir
2
from the conditional lognormal distribution (subscripts
i
and
r
have been dropped for clarity) (Bazzurro and Cornell, 2002):
ε
1
(
)
=
f
s
s
⋅
[18.7]
21
∏
()
−
n
2
2
π
det
R
s
σ
ln
s
ln
s
ln
s
2
j
ln
s
ln
s
22 1
2
j
1
1
2
⎡
⎢
⎤
⎥
(
)
(
)
T
exp
−
ln
s
−
m
C
ln
s
−
m
2
ln
s
ln
s
ln
s
ln
s
ln
s
2
ln
s
ln
s
2
1
2
2
1
2
1
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