TY - JOUR A1 - Esfahani, Reza Dokht Dolatabadi A1 - Vogel, Kristin A1 - Cotton, Fabrice A1 - Ohrnberger, Matthias A1 - Scherbaum, Frank A1 - Kriegerowski, Marius T1 - Exploring the dimensionality of ground-motion data by applying autoencoder techniques JF - Bulletin of the Seismological Society of America : BSSA N2 - In this article, we address the question of how observed ground-motion data can most effectively be modeled for engineering seismological purposes. Toward this goal, we use a data-driven method, based on a deep-learning autoencoder with a variable number of nodes in the bottleneck layer, to determine how many parameters are needed to reconstruct synthetic and observed ground-motion data in terms of their median values and scatter. The reconstruction error as a function of the number of nodes in the bottleneck is used as an indicator of the underlying dimensionality of ground-motion data, that is, the minimum number of predictor variables needed in a ground-motion model. Two synthetic and one observed datasets are studied to prove the performance of the proposed method. We find that mapping ground-motion data to a 2D manifold primarily captures magnitude and distance information and is suited for an approximate data reconstruction. The data reconstruction improves with an increasing number of bottleneck nodes of up to three and four, but it saturates if more nodes are added to the bottleneck. Y1 - 2021 U6 - https://doi.org/10.1785/0120200285 SN - 0037-1106 SN - 1943-3573 VL - 111 IS - 3 SP - 1563 EP - 1576 PB - Seismological Society of America CY - El Cerito, Calif. 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 - TY - JOUR A1 - Bommer, Julian J. A1 - Douglas, John A1 - Scherbaum, Frank A1 - Cotton, Fabrice A1 - Bungum, Hilmar A1 - Faeh, Donat T1 - On the selection of ground-motion prediction equations for seismic hazard analysis Y1 - 2010 UR - http://srl.geoscienceworld.org/ U6 - https://doi.org/10.1785/gssrl.81.5.783 SN - 0895-0695 ER - TY - JOUR A1 - Molkenthin, Christian A1 - Scherbaum, Frank A1 - Griewank, Andreas A1 - Kühn, Nicolas A1 - Stafford, Peter J. A1 - Leovey, Hernan T1 - Sensitivity of Probabilistic Seismic Hazard Obtained by Algorithmic Differentiation: A Feasibility Study JF - Bulletin of the Seismological Society of America N2 - Probabilistic seismic-hazard analysis (PSHA) is the current tool of the trade used to estimate the future seismic demands at a site of interest. A modern PSHA represents a complex framework that combines different models with numerous inputs. It is important to understand and assess the impact of these inputs on the model output in a quantitative way. Sensitivity analysis is a valuable tool for quantifying changes of a model output as inputs are perturbed, identifying critical input parameters, and obtaining insight about the model behavior. Differential sensitivity analysis relies on calculating first-order partial derivatives of the model output with respect to its inputs; however, obtaining the derivatives of complex models can be challenging. In this study, we show how differential sensitivity analysis of a complex framework such as PSHA can be carried out using algorithmic/automatic differentiation (AD). AD has already been successfully applied for sensitivity analyses in various domains such as oceanography and aerodynamics. First, we demonstrate the feasibility of the AD methodology by comparing AD-derived sensitivities with analytically derived sensitivities for a basic case of PSHA using a simple ground-motion prediction equation. Second, we derive sensitivities via AD for a more complex PSHA study using a stochastic simulation approach for the prediction of ground motions. The presented approach is general enough to accommodate more advanced PSHA studies of greater complexity. Y1 - 2015 U6 - https://doi.org/10.1785/0120140294 SN - 0037-1106 SN - 1943-3573 VL - 105 IS - 3 SP - 1810 EP - 1822 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Molkenthin, Christian A1 - Scherbaum, Frank A1 - Griewank, Andreas A1 - Kuehn, Nicolas A1 - Stafford, Peter T1 - A Study of the sensitivity of response spectral amplitudes on seismological parameters using algorithmic differentiation JF - Bulletin of the Seismological Society of America N2 - Response spectra are of fundamental importance in earthquake engineering and represent a standard measure in seismic design for the assessment of structural performance. However, unlike Fourier spectral amplitudes, the relationship of response spectral amplitudes to seismological source, path, and site characteristics is not immediately obvious and might even be considered counterintuitive for high oscillator frequencies. The understanding of this relationship is nevertheless important for seismic-hazard analysis. The purpose of the present study is to comprehensively characterize the variation of response spectral amplitudes due to perturbations of the causative seismological parameters. This is done by calculating the absolute parameter sensitivities (sensitivity coefficients) defined as the partial derivatives of the model output with respect to its input parameters. To derive sensitivities, we apply algorithmic differentiation (AD). This powerful approach is extensively used for sensitivity analysis of complex models in meteorology or aerodynamics. To the best of our knowledge, AD has not been explored yet in the seismic-hazard context. Within the present study, AD was successfully implemented for a proven and extensively applied simulation program for response spectra (Stochastic Method SIMulation [SMSIM]) using the TAPENADE AD tool. We assess the effects and importance of input parameter perturbations on the shape of response spectra for different regional stochastic models in a quantitative way. Additionally, we perform sensitivity analysis regarding adjustment issues of groundmotion prediction equations. Y1 - 2014 U6 - https://doi.org/10.1785/0120140022 SN - 0037-1106 SN - 1943-3573 VL - 104 IS - 5 SP - 2240 EP - 2252 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Scherbaum, Frank A1 - Cotton, Fabrice A1 - Staedtke, Helmut T1 - The estimation of minimum-misfit stochastic models from empirical ground-motion prediction equations N2 - In areas of moderate to low seismic activity there is commonly a lack of recorded strong ground motion. As a consequence, the prediction of ground motion expected for hypothetical future earthquakes is often performed by employing empirical models from other regions. In this context, Campbell's hybrid empirical approach (Campbell, 2003, 2004) provides a methodological framework to adapt ground-motion prediction equations to arbitrary target regions by using response spectral host-to-target-region-conversion filters. For this purpose, the empirical ground-motion prediction equation has to be quantified in terms of a stochastic model. The problem we address here is how to do this in a systematic way and how to assess the corresponding uncertainties. For the determination of the model parameters we use a genetic algorithm search. The stochastic model spectra were calculated by using a speed-optimized version of SMSIM (Boore, 2000). For most of the empirical ground-motion models, we obtain sets of stochastic models that match the empirical models within the full magnitude and distance ranges of their generating data sets fairly well. The overall quality of fit and the resulting model parameter sets strongly depend on the particular choice of the distance metric used for the stochastic model. We suggest the use of the hypocentral distance metric for the stochastic Simulation of strong ground motion because it provides the lowest-misfit stochastic models for most empirical equations. This is in agreement with the results of two recent studies of hypocenter locations in finite-source models which indicate that hypocenters are often located close to regions of large slip (Mai et al., 2005; Manighetti et al., 2005). Because essentially all empirical ground-motion prediction equations contain data from different geographical regions, the model parameters corresponding to the lowest-misfit stochastic models cannot necessarily be expected to represent single, physically realizable host regions but to model the generating data sets in an average way. In addition, the differences between the lowest-misfit stochastic models and the empirical ground-motion prediction equation are strongly distance, magnitude, and frequency dependent, which, according to the laws of uncertainty propagation, will increase the variance of the corresponding hybrid empirical model predictions (Scherbaum et al., 2005). As a consequence, the selection of empirical ground-motion models for host-to-target-region conversions requires considerable judgment of the ground-motion analyst Y1 - 2006 U6 - https://doi.org/10.1785/0120050015 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 - 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 - Scherbaum, Frank A1 - Cotton, Fabrice A1 - Smit, P. T1 - On the use of response spectral-reference data for the selection and ranking of ground-motion models for seismic-hazard analysis in regions of moderate seismicity : the case of rock motion N2 - The use of ground-motion-prediction equations to estimate ground shaking has become a very popular approach for seismic-hazard assessment, especially in the framework of a logic-tree approach. Owing to the large number of existing published ground-motion models, however, the selection and ranking of appropriate models for a particular target area often pose serious practical problems. Here we show how observed around-motion records can help to guide this process in a systematic and comprehensible way. A key element in this context is a new, likelihood based, goodness-of-fit measure that has the property not only to quantify the model fit but also to measure in some degree how well the underlying statistical model assumptions are met. By design, this measure naturally scales between 0 and 1, with a value of 0.5 for a situation in which the model perfectly matches the sample distribution both in terms of mean and standard deviation. We have used it in combination with other goodness-of-fit measures to derive a simple classification scheme to quantify how well a candidate ground-rnotion-prediction equation models a particular set of observed-response spectra. This scheme is demonstrated to perform well in recognizing a number of popular ground-motion models from their rock-site- recording, subsets. This indicates its potential for aiding the assignment of logic-tree weights in a consistent and reproducible way. We have applied our scheme to the border region of France, Germany, and Switzerland where the M-w 4.8 St. Die earthquake of 22 February 2003 in eastern France recently provided a small set of observed-response spectra. These records are best modeled by the ground-motion-prediction equation of Berge-Thierry et al. (2003), which is based on the analysis of predominantly European data. The fact that the Swiss model of Bay et al. (2003) is not able to model the observed records in an acceptable way may indicate general problems arising from the use of weak-motion data for strong-motion prediction Y1 - 2004 SN - 0037-1106 ER -