TY - JOUR A1 - Kühn, Nicolas M. A1 - Scherbaum, Frank A1 - Riggelsen, Carsten T1 - Deriving empirical ground-motion models : balancing data constraints and physical assumptions to optimize prediction capability N2 - Empirical ground-motion models used in seismic hazard analysis are commonly derived by regression of observed ground motions against a chosen set of predictor variables. Commonly, the model building process is based on residual analysis and/or expert knowledge and/or opinion, while the quality of the model is assessed by the goodness-of-fit to the data. Such an approach, however, bears no immediate relation to the predictive power of the model and with increasing complexity of the models is increasingly susceptible to the danger of overfitting. Here, a different, primarily data-driven method for the development of ground-motion models is proposed that makes use of the notion of generalization error to counteract the problem of overfitting. Generalization error directly estimates the average prediction error on data not used for the model generation and, thus, is a good criterion to assess the predictive capabilities of a model. The approach taken here makes only few a priori assumptions. At first, peak ground acceleration and response spectrum values are modeled by flexible, nonphysical functions (polynomials) of the predictor variables. The inclusion of a particular predictor and the order of the polynomials are based on minimizing generalization error. The approach is illustrated for the next generation of ground-motion attenuation dataset. The resulting model is rather complex, comprising 48 parameters, but has considerably lower generalization error than functional forms commonly used in ground-motion models. The model parameters have no physical meaning, but a visual interpretation is possible and can reveal relevant characteristics of the data, for example, the Moho bounce in the distance scaling. In a second step, the regression model is approximated by an equivalent stochastic model, making it physically interpretable. The resulting resolvable stochastic model parameters are comparable to published models for western North America. In general, for large datasets generalization error minimization provides a viable method for the development of empirical ground-motion models. Y1 - 2009 UR - http://bssa.geoscienceworld.org/ U6 - https://doi.org/10.1785/0120080136 SN - 0037-1106 ER - TY - THES A1 - Kühn, Nicolas M. T1 - Empirical ground-motion models for probabilistic seismic hazard analysis : a graphical model perspective Y1 - 2010 CY - Potsdam ER - TY - JOUR A1 - Delavaud, Elise A1 - Scherbaum, Frank A1 - Kühn, Nicolas A1 - Allen, Trevor T1 - Testing the global applicability of ground-motion prediction equations for active shallow crustal regions JF - Bulletin of the Seismological Society of America N2 - Large research initiatives such as the Global Earthquake Model (GEM) or the Seismic HAzard haRmonization in Europe (SHARE) projects concentrate a great collaborative effort on defining a global standard for seismic hazard estimations. In this context, there is an increasing need for identifying ground-motion prediction equations (GMPEs) that can be applied at both global and regional scale. With increasing amounts of strong-motion records that are now available worldwide, observational data can provide a valuable resource to tackle this question. Using the global dataset of Allen and Wald (2009), we evaluate the ability of 11 GMPEs to predict ground-motion in different active shallow crustal regions worldwide. Adopting the approach of Scherbaum et al. (2009), we rank these GMPEs according to their likelihood of having generated the data. In particular, we estimate how strongly data support or reject the models with respect to the state of noninformativeness defined by a uniform weighting. Such rankings derived from this particular global dataset enable us to explore the potential of GMPEs to predict ground motions in their host region and also in other regions depending on the magnitude and distance considered. In the ranking process, we particularly focus on the influence of the distribution of the testing dataset compared with the GMPE's native dataset. One of the results of this study is that some nonindigenous models present a high degree of consistency with the data from a target region. Two models in particular demonstrated a strong power of geographically wide applicability in different geographic regions with respect to the testing dataset: the models of Akkar and Bommer (2010) and Chiou et al. (2010). Y1 - 2012 U6 - https://doi.org/10.1785/0120110113 SN - 0037-1106 VL - 102 IS - 2 SP - 707 EP - 721 PB - Seismological Society of America CY - El Cerrito ER - TY - JOUR A1 - Hermkes, Marcel A1 - Kühn, Nicolas M. A1 - Riggelsen, Carsten T1 - Simultaneous quantification of epistemic and aleatory uncertainty in GMPEs using Gaussian process regression JF - Bulletin of earthquake engineering : official publication of the European Association for Earthquake Engineering N2 - This paper presents a Bayesian non-parametric method based on Gaussian Process (GP) regression to derive ground-motion models for peak-ground parameters and response spectral ordinates. Due to its non-parametric nature there is no need to specify any fixed functional form as in parametric regression models. A GP defines a distribution over functions, which implicitly expresses the uncertainty over the underlying data generating process. An advantage of GP regression is that it is possible to capture the whole uncertainty involved in ground-motion modeling, both in terms of aleatory variability as well as epistemic uncertainty associated with the underlying functional form and data coverage. The distribution over functions is updated in a Bayesian way by computing the posterior distribution of the GP after observing ground-motion data, which in turn can be used to make predictions. The proposed GP regression models is evaluated on a subset of the RESORCE data base for the SIGMA project. The experiments show that GP models have a better generalization error than a simple parametric regression model. A visual assessment of different scenarios demonstrates that the inferred GP models are physically plausible. KW - Gaussian Process regression KW - Epistemic uncertainty KW - Aleatory variability KW - Empirical ground-motion models KW - Bayesian non-parametrics KW - GMPE KW - Generalization error Y1 - 2014 U6 - https://doi.org/10.1007/s10518-013-9507-7 SN - 1570-761X SN - 1573-1456 VL - 12 IS - 1 SP - 449 EP - 466 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Bora, Sanjay Singh A1 - Scherbaum, Frank A1 - Kühn, Nicolas A1 - Stafford, Peter T1 - Fourier spectral- and duration models for the generation of response spectra adjustable to different source-, propagation-, and site conditions JF - Bulletin of earthquake engineering : official publication of the European Association for Earthquake Engineering N2 - One of the major challenges related with the current practice in seismic hazard studies is the adjustment of empirical ground motion prediction equations (GMPEs) to different seismological environments. We believe that the key to accommodating differences in regional seismological attributes of a ground motion model lies in the Fourier spectrum. In the present study, we attempt to explore a new approach for the development of response spectral GMPEs, which is fully consistent with linear system theory when it comes to adjustment issues. This approach consists of developing empirical prediction equations for Fourier spectra and for a particular duration estimate of ground motion which is tuned to optimize the fit between response spectra obtained through the random vibration theory framework and the classical way. The presented analysis for the development of GMPEs is performed on the recently compiled reference database for seismic ground motion in Europe (RESORCE-2012). Although, the main motivation for the presented approach is the adjustability and the use of the corresponding model to generate data driven host-to-target conversions, even as a standalone response spectral model it compares reasonably well with the GMPEs of Ambraseys et al. (Bull Earthq Eng 3:1-53, 2005), Akkar and Bommer (Seismol Res Lett 81(2):195-206, 2010) and Akkar and Cagnan (Bull Seismol Soc Am 100(6):2978-2995, 2010). KW - Ground motion prediction equation KW - Fourier amplitude spectrum KW - Duration KW - Random vibration theory KW - Response Spectrum Y1 - 2014 U6 - https://doi.org/10.1007/s10518-013-9482-z SN - 1570-761X SN - 1573-1456 VL - 12 IS - 1 SP - 467 EP - 493 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Hiemer, Stefan A1 - Scherbaum, Frank A1 - Rößler, Dirk A1 - Kühn, Nicolas T1 - Determination of tau(0) and Rock Site kappa from Records of the 2008/2009 Earthquake Swarm in Western Bohemia JF - Seismological research letters Y1 - 2011 U6 - https://doi.org/10.1785/gssrl.82.3.387 SN - 0895-0695 VL - 82 IS - 3 SP - 387 EP - 393 PB - Seismological Society of America CY - El Cerrito ER - TY - JOUR A1 - Kühn, Nicolas M. A1 - Riggelsen, Carsten A1 - Scherbaum, Frank T1 - Modeling the joint probability of earthquake, site, and ground-motion parameters using bayesian networks JF - Bulletin of the Seismological Society of America N2 - Bayesian networks are a powerful and increasingly popular tool for reasoning under uncertainty, offering intuitive insight into (probabilistic) data-generating processes. They have been successfully applied to many different fields, including bioinformatics. In this paper, Bayesian networks are used to model the joint-probability distribution of selected earthquake, site, and ground-motion parameters. This provides a probabilistic representation of the independencies and dependencies between these variables. In particular, contrary to classical regression, Bayesian networks do not distinguish between target and predictors, treating each variable as random variable. The capability of Bayesian networks to model the ground-motion domain in probabilistic seismic hazard analysis is shown for a generic situation. A Bayesian network is learned based on a subset of the Next Generation Attenuation (NGA) dataset, using 3342 records from 154 earthquakes. Because no prior assumptions about dependencies between particular parameters are made, the learned network displays the most probable model given the data. The learned network shows that the ground-motion parameter (horizontal peak ground acceleration, PGA) is directly connected only to the moment magnitude, Joyner-Boore distance, fault mechanism, source-to-site azimuth, and depth to a shear-wave horizon of 2: 5 km/s (Z2.5). In particular, the effect of V-S30 is mediated by Z2.5. Comparisons of the PGA distributions based on the Bayesian networks with the NGA model of Boore and Atkinson (2008) show a reasonable agreement in ranges of good data coverage. Y1 - 2011 U6 - https://doi.org/10.1785/0120100080 SN - 0037-1106 VL - 101 IS - 1 SP - 235 EP - 249 PB - Seismological Society of America CY - El Cerrito ER - TY - JOUR A1 - Bora, Sanjay Singh A1 - Scherbaum, Frank A1 - Kühn, Nicolas A1 - Stafford, Peter A1 - Edwards, Benjamin T1 - Development of a Response Spectral Ground-Motion Prediction Equation (GMPE) for Seismic-Hazard Analysis from Empirical Fourier Spectral and Duration Models JF - Bulletin of the Seismological Society of America N2 - Empirical ground-motion prediction equations (GMPEs) require adjustment to make them appropriate for site-specific scenarios. However, the process of making such adjustments remains a challenge. This article presents a holistic framework for the development of a response spectral GMPE that is easily adjustable to different seismological conditions and does not suffer from the practical problems associated with adjustments in the response spectral domain. The approach for developing a response spectral GMPE is unique, because it combines the predictions of empirical models for the two model components that characterize the spectral and temporal behavior of the ground motion. Essentially, as described in its initial form by Bora et al. (2014), the approach consists of an empirical model for the Fourier amplitude spectrum (FAS) and a model for the ground-motion duration. These two components are combined within the random vibration theory framework to obtain predictions of response spectral ordinates. In addition, FAS corresponding to individual acceleration records are extrapolated beyond the useable frequencies using the stochastic FAS model, obtained by inversion as described in Edwards and Fah (2013a). To that end, a (oscillator) frequency-dependent duration model, consistent with the empirical FAS model, is also derived. This makes it possible to generate a response spectral model that is easily adjustable to different sets of seismological parameters, such as the stress parameter Delta sigma, quality factor Q, and kappa kappa(0). The dataset used in Bora et al. (2014), a subset of the RESORCE-2012 database, is considered for the present analysis. Based upon the range of the predictor variables in the selected dataset, the present response spectral GMPE should be considered applicable over the magnitude range of 4 <= M-w <= 7.6 at distances <= 200 km. Y1 - 2015 U6 - https://doi.org/10.1785/0120140297 SN - 0037-1106 SN - 1943-3573 VL - 105 IS - 4 SP - 2192 EP - 2218 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Scherbaum, Frank A1 - Kühn, Nicolas M. T1 - Logic tree branch weights and probabilities summing up to one is not enough JF - Earthquake spectra : the professional journal of the Earthquake Engineering Research Institute N2 - Logic trees have become the most popular tool for the quantification of epistemic uncertainties in probabilistic seismic hazard assessment (PSHA). In a logic-tree framework, epistemic uncertainty is expressed in a set of branch weights, by which an expert or an expert group assigns degree-of-belief values to the applicability of the corresponding branch models. Despite the popularity of logic-trees, however, one finds surprisingly few clear commitments to what logic-tree branch weights are assumed to be (even by hazard analysts designing logic trees). In the present paper we argue that it is important for hazard analysts to accept the probabilistic framework from the beginning for assigning logic-tree branch weights. In other words, to accept that logic-tree branch weights are probabilities in the axiomatic sense, independent of one's preference for the philosophical interpretation of probabilities. We demonstrate that interpreting logic-tree branch weights merely as a numerical measure of "model quality," which are then subsequently normalized to sum up to unity, will with increasing number of models inevitably lead to an apparent insensitivity of hazard curves on the logic-tree branch weights, which may even be mistaken for robustness of the results. Finally, we argue that assigning logic-tree branch weights in a sequential fashion may improve their logical consistency. Y1 - 2011 U6 - https://doi.org/10.1193/1.3652744 SN - 8755-2930 VL - 27 IS - 4 SP - 1237 EP - 1251 PB - Earthquake Engineering Research Institute CY - Oakland ER - TY - JOUR A1 - Bussas, Matthias A1 - Sawade, Christoph A1 - Kuhn, Nicolas A1 - Scheffer, Tobias A1 - Landwehr, Niels T1 - Varying-coefficient models for geospatial transfer learning JF - Machine learning N2 - We study prediction problems in which the conditional distribution of the output given the input varies as a function of task variables which, in our applications, represent space and time. In varying-coefficient models, the coefficients of this conditional are allowed to change smoothly in space and time; the strength of the correlations between neighboring points is determined by the data. This is achieved by placing a Gaussian process (GP) prior on the coefficients. Bayesian inference in varying-coefficient models is generally intractable. We show that with an isotropic GP prior, inference in varying-coefficient models resolves to standard inference for a GP that can be solved efficiently. MAP inference in this model resolves to multitask learning using task and instance kernels. We clarify the relationship between varying-coefficient models and the hierarchical Bayesian multitask model and show that inference for hierarchical Bayesian multitask models can be carried out efficiently using graph-Laplacian kernels. We explore the model empirically for the problems of predicting rent and real-estate prices, and predicting the ground motion during seismic events. We find that varying-coefficient models with GP priors excel at predicting rents and real-estate prices. The ground-motion model predicts seismic hazards in the State of California more accurately than the previous state of the art. KW - Transfer learning KW - Varying-coefficient models KW - Housing-price prediction KW - Seismic-hazard models Y1 - 2017 U6 - https://doi.org/10.1007/s10994-017-5639-3 SN - 0885-6125 SN - 1573-0565 VL - 106 SP - 1419 EP - 1440 PB - Springer CY - Dordrecht ER -