Probability and Uncertainty in Seismic Hazard Analysis

Abstract

In the current practice of probabilistic seismic hazard analysis (PSHA) using logic trees, it is common to use the mean hazard curve to determine ground motions for engineering design. We present the case against the use of the mean hazard curve and explain why this practice should be discontinued and, where necessary, removed from regulations. The identification and quantification of uncertainties is integral to modern seismic hazard analysis. In probabilistic seismic hazard studies, the variability of the earthquake magnitude, earthquake location, and ground motion level (expressed as the number of logarithmic standard deviations above the logarithmic mean) are considered explicitly in the computation of the hazard. In major seismic hazard projects, the scientific uncertainty in the models of the distributions of earthquake magnitude, location, and ground motion are also considered using logic trees (Kulkarni et al. 1984, Coppersmith and Youngs 1986, Reiter 1990, Bommer et al. 2005). The inherent variability considered directly in the hazard computation is called the aleatory variability, and the scientific uncertainty in the models of the earthquake occurrence and ground motion is called the epistemic uncertainty. The terms randomness and uncertainty have also been used for aleatory variability and epistemic uncertainty, respectively; however, the former terms are now commonly used interchangeably. As a result, they are often mixed up when used in hazard analysis. The terms ‘‘aleatory variability’’ and ‘‘epistemic uncertainty’’ are used to provide an unambiguous terminology. This is not simply semantics: distinguishing between the two types of uncertainty is fundamental to the way that they are dealt with in the hazard calculations and how uncertainty is handled in decision making on the basis of the hazard analysis. In application, the key difference is that aleatory variability leads to the shape of the hazard curve and the epistemic uncertainty leads to alternative hazard curves. There is no dilemma regarding the inclusion of the aleatory variability in the hazard calculations, particularly the variability associated with ground-motion prediction equations: a ‘‘hazard curve’’ calculated using only median values from the equations and neglecting the standard deviation has little meaning and cannot be considered a genuine hazard curve. The hazard analyst does, however, have control over the branches of the logic tree and the weights assigned to these, and hence over the degree to which epistemic uncer