Civil Engineering Reference
In-Depth Information
amount of data available to the developer. In the present section the main
options for ground-motion model development are briefl y summarised.
2.3.1 Generic types of GMPE
There are three broad classes of ground-motion model: empirically-based
models; spectral models; and seismological models. Each of these models
can be used to make predictions of the median expected motions from a
given scenario. However, there are very large differences in terms of how
the aleatory variability and epistemic uncertainty are handled in each case.
In each of the following subsections the approach to development of each
type of model is outlined.
Empirical models
Empirical models are developed by fi rst compiling large databases of accel-
erograms as well as metadata that relates to each of these recordings. This
metadata comprises information about the magnitude of the causative
earthquake, the distance from the source to the site and various other
quantities that are used as independent variables within the regression
analysis that is subsequently performed. This regression analysis is most
commonly conducted using the mathematical representation shown in
Equation (2.3). In this equation the total difference that is computed
between the observed logarithmic spectral acceleration, ln
Sa
ij
, and the
model prediction,
), is partitioned into two components that refl ect
the earthquake-specifi c difference between the average motions for the
population (for a given scenario) and the motions for that particular event,
δ
E
,
i
, and the difference between the observed motion and the event-specifi c
average motion,
μ
(
Z
ij
|
θ
{
M
w
,
i
,
R
RUP,
ij
,
V
s
30,
ij
, . . .}
contains all of the metadata relevant to each observation and will typically
include the magnitude of the event, a measure of source-to-site distance,
and information about the site conditions, among potentially other things.
The vector
δ
A
,
ij
. In Equation (2.3), the matrix
Z
ij
=
contains all of the regression coeffi cients and are published in
tabular form with a particular row or column of this table relating to a given
response period.
θ
(
)
++
ln
Sa
ij
=
μθδδ
Z
[2.3]
ij
E i
,
A ij
,
The model that is published consists of two components, as previously
mentioned. These components are the information about the median pre-
diction and the information about the variance components. In the frame-
work outlined in Equation (2.3), the variance components are effectively
(although not exactly) the variances of the
δ
E
,
i
and
δ
A
,
ij
terms. These terms
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