Uncertainties in ground motion prediction in probabilistic seismic hazard analysis (PSHA) of civil infrastructure - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 39

current estimates of standard deviation that have been obtained using this
approach. In the vast majority of cases the distributions of the basic vari-
ables, such as the stress parameter, or site kappa, are not known. To obtain
an estimate of the aleatory variability of ground-motions the σ X i terms in

Equation (2.7), or, more precisely, the entire distribution of the basic vari-
ables, should refl ect the aleatory variability in these parameters. In addition,
the aleatory covariance among the parameters should also be known and
used within this framework. However, given that this approach is imple-
mented in data-poor regions, this information is not known a priori . The
result is that there is signifi cant epistemic uncertainty associated with what
the parametric aleatory variability should be. Presently, the approach of
model developers is to assume what the total uncertainty is in each model
parameter and to then further assume what the breakdown is between
epistemic and aleatory contributions. It is this subjective assignment of vari-
ance components that currently undermines the confi dence in estimates of
the standard deviations associated with these stochastic-based models.
One fi nal point that is worth raising in terms of the estimates of uncer-
tainty for stochastic models is related to the discussion in Section 2.2.1
concerning the fact that a requirement of a ground-motion model is that is
defi nes the distribution of ground-motion amplitudes for a given earth-
quake scenario. It is clear from the discussion in the present section that
the stochastic-based models are heavily biased toward providing estimates
of just one of the two parameters required to defi ne the distribution of
ground-motion amplitudes, that being the mean logarithmic motion. For
hazard and risk applications, where both parameters of the ground-motion
distribution are very infl uential, the drawbacks associated with the defi ni-
tion of the variance are considerable.

Seismological models

While empirical and spectral models are by far the most commonly used
models in hazard and risk applications, seismological simulations have also
been used in the past, particularly when scenario events are considered, or
when one looks to recreate the effects of a historic event. Seismological
models can be broadly grouped into kinematic models and dynamic models.
The former relates to those models that prescribe a slip distribution over a
rupture surface and then relate these source slip amplitudes to the displace-
ment amplitudes that would be experienced at some other point in space.
On the other hand, dynamic models prescribe initial and boundary condi-
tions for a rupture that is allowed to grow in accordance with some physical
laws. These dynamic models can either follow deterministic rules or
can incorporate stochastic features as well in order to replicate source
complexity. Once the source excitation is defi ned, either kinematically or