TY - JOUR A1 - Landwehr, Niels A1 - Kuehn, Nicolas M. A1 - Scheffer, Tobias A1 - Abrahamson, Norman A. T1 - A Nonergodic Ground-Motion Model for California with Spatially Varying Coefficients JF - Bulletin of the Seismological Society of America N2 - Traditional probabilistic seismic-hazard analysis as well as the estimation of ground-motion models (GMMs) is based on the ergodic assumption, which means that the distribution of ground motions over time at a given site is the same as their spatial distribution over all sites for the same magnitude, distance, and site condition. With a large increase in the number of recorded ground-motion data, there are now repeated observations at given sites and from multiple earthquakes in small regions, so that assumption can be relaxed. We use a novel approach to develop a nonergodic GMM, which is cast as a varying-coefficient model (VCM). In this model, the coefficients are allowed to vary by geographical location, which makes it possible to incorporate effects of spatially varying source, path, and site conditions. Hence, a separate set of coefficients is estimated for each source and site coordinate in the data set. The coefficients are constrained to be similar for spatially nearby locations. This is achieved by placing a Gaussian process prior on the coefficients. The amount of correlation is determined by the data. The spatial correlation structure of the model allows one to extrapolate the varying coefficients to a new location and trace the corresponding uncertainties. The approach is illustrated with the Next Generation Attenuation-West2 data set, using only Californian records. The VCM outperforms a traditionally estimated GMM in terms of generalization error and leads to a reduction in the aleatory standard deviation by similar to 40%, which has important implications for seismic-hazard calculations. The scaling of the model with respect to its predictor variables such as magnitude and distance is physically plausible. The epistemic uncertainty associated with the predicted ground motions is small in places where events or stations are close and large where data are sparse. Y1 - 2016 U6 - https://doi.org/10.1785/0120160118 SN - 0037-1106 SN - 1943-3573 VL - 106 SP - 2574 EP - 2583 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Scherbaum, Frank A1 - Bommer, Julian J. A1 - Bungum, Hilmar A1 - Cotton, Fabrice A1 - Abrahamson, Norman A. T1 - Composite ground-motion models and logic trees: Methodology, sensitivities, and uncertainties N2 - 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 Y1 - 2005 SN - 0037-1106 ER - TY - JOUR A1 - Musson, R. M. W. A1 - Toro, G. R. A1 - Coppersmith, Kevin J. A1 - Bommer, Julian J. A1 - Deichmann, N. A1 - Bungum, Hilmar A1 - Cotton, Fabrice A1 - Scherbaum, Frank A1 - Slejko, Dario A1 - Abrahamson, Norman A. T1 - Evaluating hazard results for Switzerland and how not to do it : a discussion of "Problems in the application of the SSHAC probability method for assessing earthquake hazards at Swiss nuclear power plants" by J-U Klugel N2 - 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 Y1 - 2005 ER - TY - JOUR A1 - Bommer, Julian J. A1 - Scherbaum, Frank A1 - Bungum, Hilmar A1 - Cotton, Fabrice A1 - Sabetta, F. A1 - Abrahamson, Norman A. T1 - On the use of logic trees for ground-motion prediction equations in seismic-hazard analysis N2 - Logic trees are widely used in probabilistic seismic hazard analysis as a tool to capture the epistemic uncertainty associated with the seismogenic sources and the ground-motion prediction models used in estimating the hazard. Combining two or more ground-motion relations within a logic tree will generally require several conversions to be made, because there are several definitions available for both the predicted ground-motion parameters and the explanatory parameters within the predictive ground-motion relations. Procedures for making conversions for each of these factors are presented, using a suite of predictive equations in current use for illustration. The sensitivity of the resulting ground-motion models to these conversions is shown to be pronounced for some of the parameters, especially the measure of source-to-site distance, highlighting the need to take into account any incompatibilities among the selected equations. Procedures are also presented for assigning weights to the branches in the ground-motion section of the logic tree in a transparent fashion, considering both intrinsic merits of the individual equations and their degree of applicability to the particular application Y1 - 2005 SN - 0037-1106 ER - TY - JOUR A1 - Bommer, Julian J. A1 - Abrahamson, Norman A. A1 - Strasser, F. O. A1 - Pecker, Alain A1 - Bard, Pierre-Yves A1 - Bungum, Hilmar A1 - Cotton, Fabrice A1 - Fäh, Donat A1 - Sabetta, F. A1 - Scherbaum, Frank A1 - Studer, Jost T1 - The challenge of defining upper bounds on earthquake ground motions Y1 - 2004 SN - 0895-0695 ER - TY - JOUR A1 - Al Atik, Linda A1 - Abrahamson, Norman A. A1 - Bommer, Julian J. A1 - Scherbaum, Frank A1 - Cotton, Fabrice A1 - Kuehn, Nicolas T1 - The variability of ground-motion prediction models and its components Y1 - 2010 UR - http://srl.geoscienceworld.org/ U6 - https://doi.org/10.1785/gssrl.81.5.794 SN - 0895-0695 ER -