Uncertainties in ground motion prediction in probabilistic seismic hazard analysis (PSHA) of civil infrastructure - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 50

reduction is offset by an increase in the epistemic uncertainty associated
with accurately defi ning the characteristics of the target region.

2.5.2 Semi-empirical approaches

The NGA project was relatively unique in that it combined traditional
empirically based regression techniques with constraints from numerical
simulations in order to capture aspects of ground-motion scaling that could
not be extracted from the data alone. The features that have been con-
strained thus far include the nonlinear site response and the large magni-
tude scaling (which are in some ways coupled). While this may be considered
an advancement in many ways the current approaches to combining these
theoretical constraints with empirical approaches is not correct. The problem
is that when one imposes a theoretical constraint upon the way in which a
particular term of a model should scale one does not currently also allocate
a component of uncertainty to this part of the model. The consequence is
that a component of uncertainty that is associated with this component is
forced to be allocated to another part of the model. In the case that theo-
retical constraints are imposed in regions where there is zero data, this will
not infl uence the derived models coeffi cients. However, when there is some
data then neglecting the relevant component of uncertainty infl uences the
overall model fi t. To clarify the situation here, let us consider a particular
example. Imagine that numerical analyses are used to obtain a theoretical
model for nonlinear site response, and that this model component can be
represented by g site ( V s 30 , . . .). One way to incorporate this scaling into a
regression analysis would be to work with the following mathematical
framework:

( ) =

′ (

) ++ ′

y = ln Sa − g V ,... μθ Z δ δ [2.17]

ij ij site s 30 , ij ij E i , A ij ,

Note that in Equation (2.17) the ultimate model for median predictions
is given by

g site ( V s 30, ij , . . .). Furthermore, the intra-event
residual here also has a slightly different interpretation because in an
empirical dataset the intra-event residual is actually composed of a path-
specifi c component, a site-specifi c component, and a residual error term. If
we were to account for the theoretical constraint appropriately, we would
also account for the site-specifi c component of the intra-event residual
and this would also be subtracted from the dependent variable. However,
as we cannot know this term a priori we are forced to allocate this compo-
nent of the residual into what should just be the path and residual error
components.
This problem has not yet been recognised and addressed by ground-
motion developers, but will become increasingly relevant as further

μ ( Z ij | θ ) ≡ μ ′ ( Z ij | θ ) +