Civil Engineering Reference
In-Depth Information
intensity at the surface given an event (generated in step 1) is predicted in
two steps (2 and 3):
1. Events are generated in terms of magnitude and localisation (event
generation model);
2.
Spatial correlation is fi rst dealt with:
An IM is chosen to predict a 'shake fi eld'
s
gr
1
(lat, long) on a
regular
grid
that covers the entire study region. This IM, called 'primary',
incorporates the spatial correlation (spatial correlation model), and
is predicted on rock/stiff-soil conditions by using a ground motion
prediction equation (GMPE) (class
GMPE
in Fig. 18.2). It represents
the fi eld of 'bedrock' motion.
The primary IM is interpolated at each site from the four closest grid
points (see Fig. 18.9); the use of a regular grid, with grid size related
to the fi eld correlation length only, has two advantages. The fi rst is
that the number of points is independent of the number of
vulnerable
sites, and depends only on the extent of the study region. The second
is that quasi-singular correlation matrices and the associated numeri-
cal problems in the simulation, produced by the fact that sites tend
to be naturally lumped in clusters, are avoided.
3.
Within-site cross-IM correlation is then introduced.
The remaining components of
s
ir
at each site (still 'on rock'), called
'secondary' IMs, are sampled from the conditional distribution (sec-
ondary IM conditional model)
f
(
s
ir
2
|
s
ir
1
). These secondary IMs are still
ground shaking quantities (e.g. spectral ordinates conditional on
peak ground acceleration (PGA)).
Vector
s
ir
is multiplied component-wise times the vector
A
i
of the
amplifi cation functions to obtain surface intensities (amplifi cation
model, implemented in the
Amplifi cation
class). Both simple deter-
ministic code-based amplifi cation, as well as probabilistic amplifi ca-
tion are implemented. In the former case a single constant
amplifi cation factor is used for all frequencies. In the latter the ratio
of surface to bedrock intensity for a number of frequencies is
described by a vector
A
i
of correlated random variables.
Finally, where needed, geotechnical hazards are also predicted to
complete the vector of the secondary IMs (class
geotechHazards
,
with sub-classes, not indicated in Fig. 18.2,
landslide
,
liquefaction
and
coseismicRupture
).
The event generation model consists of a set of seismic sources (class
Source
, Fig. 18.2), described either in terms of a polygonal area or a fault
plane, with:
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