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Composite Ground-Motion Models and Logic Trees: Methodology, Sensitivities, and Uncertainties

¹ Institut für Geowissenschaften
Universität Potsdam
P.O. Box 601553
D-14415, Potsdam, Germany
 (F.S.)

² Department of Civil and Environmental Engineering
Imperial College London
South Kensington Campus
London SW7 2AZ, United Kingdom
 (J.J.B.)

³ NORSAR/ICG
P.O. Box 53
N-2027 Kjeller, Norway
 (H.B.)

⁴ Laboratoire de Géophysique Interne et Tectonophysique
Université Joseph Fourier
BP 53, F-38041, Grenoble, France
 (F.C.)

⁵ 152 Dracena Drive
Piedmont, California 94177
 (N.A.A.)

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 maps, sensitivity studies, or for modeling scenario earthquakes.

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