Civil Engineering Reference
In-Depth Information
Simple statistical data analysis is followed to develop seismic hazard curves
and uniform hazard spectra. Through multiple repetitions of this process,
additional uncertainties regarding different source models, uncertain
parameters of the Gutenberg-Richter relationships, and choice of GMPEs
can be easily incorporated. In numerical integration, by contrast, inclusion
of various uncertainties and probabilistic models can be problematic,
because the number of combinations in a logic tree expands exponentially
and discretisation of non-Gaussian probability distributions can be
troublesome.
1.2.2 Simulation procedure
To demonstrate how the above-mentioned simulation-based PSHA works,
let us consider a simple case for western Canada. The location of interest
is Vancouver and the site condition of interest is fi rm soil (NEHRP site class
C and reference ground condition for national seismic hazard maps in
Canada). The seismic source zone CASR, shown in Fig. 1.2b, is considered
(see Fig. 1.3a for the Gutenberg-Richter relationship of CASR). The ground
motion parameter of interest is SA at 0.2 s.
The fi rst step is to generate the occurrence times of events in CASR. This
can be done by calculating the annual occurrence rate
M
for CASR based
on the Gutenberg-Richter relationship with magnitude bounds:
λ
(
)
−−
(
)
exp
−
β
M
exp
β
M
min
max
λ
=
N
,
[1.2]
M
0
(
)
1
−−
exp
β
M
max
where
M
min
is the minimum magnitude (and is taken to be 4.75); and
N
0
and
β
are the Gutenberg-Richter parameters and are equal to 571.5 and 1.695
for CASR, respectively (
M
w
=
M
L
case; see Fig. 1.3a). The calculated value
of
M
min
) within
CASR (over entire area) in every 5.52 years. Taking the calculated occur-
rence rate as a Poissonian rate, an inter-arrival time to the next event can
be simulated as:
λ
M
is 0.1813. This means that there is one event (of
M
>
(
)
t
=−
ln
1
−
u
λ
,
[1.3]
M
where
u
is a sample from the standard uniform distribution (i.e. a random
number between 0 and 1). For example, considering
u
0.3128, the inter-
arrival time is obtained as 2.07 years. By considering that the occurrence
time of the previous event in CASR is 46.41 years (13th event in Fig. 1.4),
the occurrence time of the next event in CASR is 48.48 years (16th event
in Fig. 1.4). This process can be repeated to generate the occurrence time
for the subsequent events in CASR (and afterwards sequentially).
The next step is to generate a random location of an epicentre within
CASR. Assuming uniform likelihood of events within a source zone, a
=
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