Probabilistic seismic hazard analysis of civil infrastructure - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 6

exceeding a level gm for a given scenario specifi ed by magnitude m and
distance r ; f M , R , ij and Ω m , r , ij are the probability density function of an earth-

quake scenario with m and r and the scenario domain (for integration),
respectively. In Equation [1.1], the fi rst summation is related to alternative
models and assumptions, while the second summation is related to multiple
source zones in space (such that all major earthquake sources are included
in the calculation). It is noteworthy that the use of discrete models in
Equation [1.1] is for convenience only (e.g. logic tree approach); they can
be replaced by the continuous probability distributions for more general
cases.
In module 1 (Fig. 1.1), seismic sources are determined based on historical
and recent regional seismic activities (i.e. earthquake catalogue) and geo-
logical and paleoseismic knowledge. An example of seismic activities and
delineated source zones for western Canada (Adams and Halchuk, 2003)
is presented in Fig. 1.2. It is noted that the Cascadia subduction zone is
represented by a fault source, while other activities are modelled by areal
sources. The magnitude of the Cascadia subduction event can be as large
as M w 9.0, and the fault rupture zone stretches over 1000 km off south-
western British Columbia (B.C.), Washington, Oregon, and northern Cali-
fornia; this event can pose signifi cant threat due to both intense ground
shaking and tsunamis to cities and towns along the coast. For each identifi ed
seismic source, temporal occurrence and potential earthquake size are then
characterised. A popular approach for well-defi ned fault systems is the use
of slip rate and characteristic earthquake by utilising geodetic and geologi-
cal information. For the Cascadia zone, tsunami records in Japan and tur-
bidite histories off-shore of B.C. and Washington provide estimates of the
recurrence period and earthquake size (Satake et al. , 2003; Goldfi nger et al. ,
2008). For well-studied faults, time-dependent earthquake occurrence
models, such as lognormal or inverse-Gaussian renewal model, may be
more suitable than a time-independent Poisson model (Goda and Hong,
2006). By contrast, the temporal and size characteristics for areal source
zones are best modelled by the Gutenberg-Richter relationship, which
describes annual frequency of earthquakes with magnitudes greater than a
specifi ed value. An illustration of the Gutenberg-Richter model is shown
in Fig. 1.3a; in the fi gure, two sets of recurrence statistics and fi tted relation-
ships are shown, corresponding to two possible cases with different moment-
to-local magnitude ( M w

M L ) conversions (see Atkinson and McCartney,
2005, for details). Using Monte Carlo simulation, synthetic scenario earth-
quakes are generated by drawing random samples from the assumed PSHA
model components. In the fi rst step, a synthetic earthquake catalogue is
constructed, which typically includes occurrence time, location, focal depth,
and earthquake size. The fault plane parameters that are needed for each
earthquake to fully evaluate recent GMPEs include fault length L , fault

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