Uncertainty Analysis of Strong-Motion

Abstract. In this article we present the modelling of uncertainty in strong-motion studies for engineering
applications, particularly for the assessment of earthquake hazard. We examine and quantify
the sources of uncertainty in the basic variables involved in ground motion estimation equations,
including those associated with the seismological parameters, which we derive from a considerable
number of strong-motion records. Models derived from regression analysis result in ground motion
equations with uncertain parameters, which are directly related to the selected basic variables thus
providing an uncertainty measure for the derivative variable. These uncertainties are exemplified
and quantified. An alternative approach is presented which is based on theoretical modelling defining
a functional relationship on a set of independent basic variables. Uncertainty in the derivative
variable is then readily obtained when the uncertainties of the basic variables have been defined.
In order to simplify the presentation, only the case of shallow strike-slip earthquakes is presented.
We conclude that the uncertainty is approximately the same as given by the residuals typical for
regression modelling. This implies that uncertainty in ground motion modelling cannot be reduced
below certain limits,which is in accordance with findings reported in the literature. Finally we discuss
the implications of the presented methodology in hazard analyses, which is sensitive to the truncation
of the internal error term, commonly given as an integral part of ground motion estimation equations.
The presented methodology does not suffer from this shortcoming; it does not require truncation of
the error term and yields realistic hazard estimates.