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GCIM distribution, as indicated by the similarity between the median, 16th
and 84th percentiles of
SA
values of the selected ground motion set and
the GCIM distribution. However, in contrast to Fig. 4.4, Fig. 4.5c and d
illustrate that the ground motions selected based on the weight vector given
by Equation (4.17) have unbiased distributions of
CAV
and
Ds
595. Although
not shown, the selected ground motions also have unbiased distributions of
PGA
,
ASI
,
SI
,
DSI
and
Ds
575. Hence, unlike those ground motions selected
in Fig. 4.4 (based on
SA
ordinates only) the ground motions selected in Fig.
4.5 will not lead to biased seismic response analyses in cases where the
CAV
,
Ds
575 and
Ds
595 values of a ground motion are important (Bradley, 2010a,
Figure 7).
Despite the above ground motion selection algorithm giving no consid-
eration to (implicit) causal parameters, it is insightful to examine such
parameters in order to explain the observations in Fig. 4.4 and Fig. 4.5.
Figure 4.6 and Table 4.2 provide details regarding the amplitude scale
factors and the magnitude and source-to-site distance (
M
w
−
R
rup
) distribu-
8.0
1
7.5
7.0
0.8
0.6
6.5
6.0
0.4
Weights for
SA
only
Consid.
SA
,
CAV
and
Ds
5.5
0.2
Weights for
SA
only
Consid.
SA
,
CAV
and
Ds
5.0
0
10
-1
10
0
10
1
10
2
10
1
10
2
Distance,
R
rup
(km)
Amplitude scale factor,
SF
(a)
(b)
4.6
Comparison of: (a) amplitude scale factors; and (b) magnitude-
distance distribution of the ground motions selected based on two
different weight vectors (after Bradley, 2012b).
Table 4.2
Comparison of the scale factors,
SF
, and mean magnitude and
distance of the selected ground motion sets using two different weight vectors
Weight vector
Considering
SA
only
Considering
SA
,
CAV
,
Ds
Median
SF
1.9
1.1
[10th,90th]
SF
per
cent
iles
[0.5,9]
[0.8,2]
Mean magnitud
e,
M
W
6.94
6.99
Mean distance,
R
rup
65.4
44.5
Source: Bradley (2012b).
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