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Composite ground-motion models and logic trees: Methodology, sensitivities, and uncertainties
(2005)
Logic trees have become a popular tool in seismic hazard studies. Commonly, the models corresponding to the end branches of the complete logic tree in a probabalistic seismic hazard analysis (PSHA) are treated separately until the final calculation of the set of hazard curves. This comes at the price that information regarding sensitivities and uncertainties in the ground-motion sections of the logic tree are only obtainable after disaggregation. Furthermore, from this end-branch model perspective even the designers of the logic tree cannot directly tell what ground-motion scenarios most likely would result from their logic trees for a given earthquake at a particular distance, nor how uncertain these scenarios might be or how they would be affected by the choices of the hazard analyst. On the other hand, all this information is already implicitly present in the logic tree. Therefore, with the ground-motion perspective that we propose in the present article, we treat the ground-motion sections of a complete logic tree for seismic hazard as a single composite model representing the complete state-of-knowledge-and-belief of a particular analyst on ground motion in a particular target region. We implement this view by resampling the ground-motion models represented in the ground-motion sections of the logic tree by Monte Carlo simulation (separately for the median values and the sigma values) and then recombining the sets of simulated values in proportion to their logic-tree branch weights. The quantiles of this resampled composite model provide the hazard analyst and the decision maker with a simple, clear, and quantitative representation of the overall physical meaning of the ground-motion section of a logic tree and the accompanying epistemic uncertainty. Quantiles of the composite model also provide an easy way to analyze the sensitivities and uncertainties related to a given logic-tree model. We illustrate this for a composite ground- motion model for central Europe. Further potential fields of applications are seen wherever individual best estimates of ground motion have to be derived from a set of candidate models, for example, for hazard rnaps, sensitivity studies, or for modeling scenario earthquakes
In probabilistic seismic-hazard analysis, epistemic uncertainties are commonly treated within a logic-tree framework in which the branch weights express the degree of belief of an expert in a set of models. For the calculation of the distribution of hazard curves, these branch weights represent subjective probabilities. A major challenge for experts is to provide logically consistent weight estimates (in the sense of Kolmogorovs axioms), to be aware of the multitude of heuristics, and to minimize the biases which affect human judgment under uncertainty. We introduce a platform-independent, interactive program enabling us to quantify, elicit, and transfer expert knowledge into a set of subjective probabilities by applying experimental design theory, following the approach of Curtis and Wood (2004). Instead of determining the set of probabilities for all models in a single step, the computer-driven elicitation process is performed as a sequence of evaluations of relative weights for small subsets of models. From these, the probabilities for the whole model set are determined as a solution of an optimization problem. The result of this process is a set of logically consistent probabilities together with a measure of confidence determined from the amount of conflicting information which is provided by the expert during the relative weighting process. We experiment with different scenarios simulating likely expert behaviors in the context of knowledge elicitation and show the impact this has on the results. The overall aim is to provide a smart elicitation technique, and our findings serve as a guide for practical applications.
Aleatory variability in ground-motion prediction, represented by the standard deviation (sigma) of a ground-motion prediction equation, exerts a very strong influence on the results of probabilistic seismic-hazard analysis (PSHA). This is especially so at the low annual exceedance frequencies considered for nuclear facilities; in these cases, even small reductions in sigma can have a marked effect on the hazard estimates. Proper separation and quantification of aleatory variability and epistemic uncertainty can lead to defensible reductions in sigma. One such approach is the single-station sigma concept, which removes that part of sigma corresponding to repeatable site-specific effects. However, the site-to-site component must then be constrained by site-specific measurements or else modeled as epistemic uncertainty and incorporated into the modeling of site effects. The practical application of the single-station sigma concept, including the characterization of the dynamic properties of the site and the incorporation of site-response effects into the hazard calculations, is illustrated for a PSHA conducted at a rock site under consideration for the potential construction of a nuclear power plant.
The PEGASOS project was a major international seismic hazard study, one of the largest ever conducted anywhere in the world, to assess seismic hazard at four nuclear power plant sites in Switzerland. Before the report of this project has become publicly available, a paper attacking both methodology and results has appeared. Since the general scientific readership may have difficulty in assessing this attack in the absence of the report being attacked, we supply a response in the present paper. The bulk of the attack, besides some misconceived arguments about the role of uncertainties in seismic hazard analysis, is carried by some exercises that purport to be validation exercises. In practice, they are no such thing; they are merely independent sets of hazard calculations based on varying assumptions and procedures, often rather questionable, which come up with various different answers which have no particular significance. (C) 2005 Elsevier B.V. All rights reserved