Earthquake risk: Including Uncertainties in the Ground Motion Calculations

Abstract

Earthquake risk models used by the insurance industry for estimating the damage caused by an event typically use the mean of the ground motion intensity to predict the damage to a particular building. On the other hand, the ground motion intensity can be modelled as a ran- dom variable. Literature related to ground-motion predictive equation derivation includes, as a rule, the estimate of the standard deviation associated with the distribution of the intensity. The Study Group was asked to find a way to include the uncertainty associated with the predic- tion of the ground motion intensity contained in the standard deviation into the damage calculation, in a way in which the computational effort is not increased significantly
The Study Group proposed a way forward based on Bayes’ theorem for the marginal distribution of damage and found an analytical expression for the damage distribution function. However, the expression is an in- tegral that needs to be evaluated numerically and the Gaussian-Hermite quadrature was proposed to carry out the calculations. The approach seems plausible to be included in the existing models and the additional computational load is estimated as to be marginal relating to the current computational demands.