Civil Engineering Reference
In-Depth Information
rejection method can be used by simply generating
x
and
y
locations of an
epicentre (strictly, spherical coordinates, latitude and longitude, should be
converted to plane coordinates, when random samples for a location is
generated), and by accepting (or rejecting) a candidate location, depending
on whether it is inside (or outside) the source zone. For instance, by sam-
pling an epicentre location for the 16th event (which is highlighted in Fig.
1.4), [latitude, longitude]
122.44] is obtained. At the same time,
the focal depth can be generated. For example, by considering the focal
depth as a normal variate (Scherbaum
et al.
, 2004), a depth for the 16th
event is obtained as 16.7 km. The epicentral and hypocentral distances are
calculated as
r
epi
=
[49.17,
−
58.11 km, respectively.
Subsequently, the earthquake magnitude can be simulated by using the
Gutenberg-Richter relationship as:
=
55.64 km and
r
hypo
=
{
(
)
−−
(
)
×
[
(
)
−−
(
)
]
}
m
=−
ln exp
−
β
M
1
u
exp
−
β
M
exp
β
M
β
.
[1.4]
min
min
max
By generating a uniform random sample
u
, the moment magnitude of the
16th event in Fig. 1.4 is obtained as 7.04.
The above steps are the standard procedure. It is noted that the generated
source location corresponds to the location of the epicentre (thus epicentral
distance and hypocentral distance can be calculated). By contrast, in modern
GMPEs, distance measures based on extended fault plane models are often
required (e.g. shortest horizontal distance to projected rupture plane,
Joyner-Boore distance
r
jb
, and shortest rupture plane distance
r
rup
; see Fig.
1.3b). A direct method to compute an extended-source distance measure is
to generate fault plane parameters, such as fault length
L
, fault width
W
,
strike
using their probabilistic information (Scherbaum
et al.
,
2004), and then to calculate the distance exactly.
Alternatively, one can adopt a probabilistic conversion equation from a
point-source distance measure to an extended-source distance measure
(Goda
et al.
, 2010). For example, by taking the direct method, a simulated
fault plane for the 16th event (Fig. 1.4) can be characterised by
L
ϕ
, and dip
δ
=
46.1 km,
W
70.2. Based on this information, the shortest
distances to surface projection of fault plane is obtained as
r
jb
=
13.9 km,
ϕ
=
333.0, and
δ
=
44.9 km.
Finally, a value of SA at 0.2 s for a given earthquake scenario [
M
w
,
r
jb
,
V
S30
] can be calculated by randomly selecting a ground motion model based
on assigned weights (this case, a ground motion model HG07 was chosen;
see Atkinson and Goda (2011) for details) and by sampling random vari-
ability of the selected equation (this case,
=
1.60).
V
S30
is the average shear
wave velocity in the top 30 m from ground surface and one of the most
popular surrogate measures for representing a local soil condition. The
predicted SA at 0.2 s is computed as 0.5032
g
.
The above process needs to be repeated many times so that suffi cient
samples are generated to determine fractile values at probability levels of
ε
=
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