Uncertainty of earthquake losses due to model uncertainty of input ground motions in the Los Angeles area

In a recent study we used the Monte Carlo simulation method to evaluate the ground-motion uncertainty of the 2002 update of the California probabilistic seismic hazard model. The resulting ground-motion distribution is used in this article to evaluate the contribution of the hazard model to the uncertainty in earthquake loss ratio, the ratio of the expected loss to the total value of a structure. We use the Hazards U.S. (HAZUS) methodology for loss estimation because it is a widely used and publicly available risk model and intended for regional studies by public agencies and for use by governmental decision makers. We found that the loss ratio uncertainty depends not only on the ground-motion uncertainty but also on the mean ground-motion level. The ground-motion uncertainty, as measured by the coefficient of variation (COV), is amplified when converting to the loss ratio uncertainty because loss increases concavely with ground motion. By comparing the ground-motion uncertainty with the corresponding loss ratio uncertainty for the structural damage of light wood-frame buildings in Los Angeles area, we show that the COV of loss ratio is almost twice the COV of ground motion with a return period of 475 years around the San Andreas fault and other major faults in the area. The loss ratio for the 2475-year ground-motion maps is about a factor of three higher than for the 475-year maps. However, the uncertainties in ground motion and loss ratio for the longer return periods are lower than for the shorter return periods because the uncertainty parameters in the hazard logic tree are independent of the return period, but the mean ground motion increases with return period.